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<title>DP Chemistry: Uncertainty & errors </title>
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<meta name="description" content="1. Accuracy and precisionWhen marking titration results it is not unusual to come across something like this:Titration of 25.00 cm3 of x mol dm-3 hydrochloric acid with a standardized solution of 1.00 mol dm-3 sodium hydroxide solution.Average volume of 1.00 mol dm-3 NaOH(aq) required to titrate 25.00 cm3 of x mol dm-3 HCl(aq) = 25.00 cm3The student then proceeds to calculate the unknown concentration of the hydrochloric...">
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<meta itemprop="description" content="1. Accuracy and precisionWhen marking titration results it is not unusual to come across something like this:Titration of 25.00 cm3 of x mol dm-3 hydrochloric acid with a standardized solution of 1.00 mol dm-3 sodium hydroxide solution.Average volume of 1.00 mol dm-3 NaOH(aq) required to titrate 25.00 cm3 of x mol dm-3 HCl(aq) = 25.00 cm3The student then proceeds to calculate the unknown concentration of the hydrochloric...">
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href="../19287/proteins-enzymes--1.html">Proteins & enzymes </a></li><li><a href="../19291/lipids-1.html">Lipids</a></li><li><a href="../19299/carbohydrates--1.html">Carbohydrates </a></li><li><a href="../19305/vitamins--1.html">Vitamins </a></li><li><a href="../19313/biochemistry-the-environment--1.html">Biochemistry & the environment </a></li><li><a href="../19336/proteins-enzymes-ahl--1.html">Proteins & enzymes (AHL) </a></li><li><a href="../19347/nucleic-acids--1.html">Nucleic acids </a></li><li><a href="../19361/biological-pigments--1.html">Biological pigments </a></li><li><a href="../19366/stereochemistry-in-biomolecules-1.html">Stereochemistry in biomolecules</a></li></ul></li><li><a href="../19390/option-c--1.html" class="father">Option C </a><ul class="level-2"><li><a href="../19391/energy-sources-1.html">Energy sources</a></li><li><a href="../19407/fossil-fuels-1.html">Fossil fuels</a></li><li><a href="../19411/nuclear-fusion-nuclear-fission-reactions-1.html">Nuclear fusion & nuclear fission reactions</a></li><li><a href="../19429/solar-energy-1.html">Solar energy</a></li><li><a href="../19437/environmental-impact-global-warming-1.html">Environmental impact - global warming</a></li><li><a href="../19453/electrochemistry-rechargeable-batteries-fuel-cells-1.html">Electrochemistry, rechargeable batteries & fuel cells</a></li><li><a href="../19458/nuclear-fusion-fission-hl--1.html">Nuclear fusion & fission (HL) </a></li><li><a href="../19470/photovoltaic-cells-and-dsscs-1.html">Photovoltaic cells and DSSCs</a></li></ul></li><li><a href="../19078/option-d-1.html" class="father">Option D</a><ul class="level-2"><li><a href="../19079/pharmaceutical-products-drug-action--1.html">Pharmaceutical products & drug action </a></li><li><a href="../19158/aspirin-penicillin--1.html">Aspirin & penicillin </a></li><li><a href="../19174/opiates-1.html">Opiates</a></li><li><a href="../19184/ph-regulation-of-the-stomach-1.html">pH regulation of the stomach</a></li><li><a href="../19194/antiviral-medications--1.html">Antiviral medications </a></li><li><a href="../19211/environmental-impact-of-some-medications-1.html">Environmental impact of some medications</a></li><li><a href="../19254/taxol-a-chiral-auxiliary-case-study-1.html">Taxol - a chiral auxiliary case study</a></li><li><a href="../19258/nuclear-medicine--1.html">Nuclear medicine </a></li><li><a href="../19273/drug-detection-analysis--1.html">Drug detection & analysis </a></li></ul></li></ul></li><li><a href="../16592/practical-scheme-of-work-ia--1.html">Practical scheme of work & IA </a><ul class="level-1"><li><a href="../16682/internal-assessment-1.html" class="father">Internal Assessment</a><ul class="level-2"><li><a href="../18892/scaffolding-the-investigation-1.html">'Scaffolding' the investigation</a></li><li><a href="../18896/timing-organisation--1.html">Timing & organisation </a></li><li><a href="../18905/choosing-the-research-question-1.html">Choosing the research question</a></li><li><a href="../18946/personal-engagement-1.html">Personal engagement</a></li><li><a href="../18950/exploration-1.html">Exploration</a></li><li><a href="../18957/analysis-1.html">Analysis</a></li><li><a href="../18965/evaluation-1.html">Evaluation</a></li><li><a href="../18966/communication-1.html">Communication</a></li><li><a href="../19882/internal-standardization-of-the-ia-1.html">Internal standardization of the IA</a></li><li><a href="../19901/submitting-the-samples-for-moderation-2.html">Submitting the samples for moderation</a></li><li><a href="../33754/ten-suggestions-for-ias-using-secondary-data-1.html">Ten suggestions for IAs using secondary data</a></li><li><a href="../37544/gaining-full-marks-for-a-databased-ia--1.html">Gaining full marks for a databased IA </a></li><li><a href="../19506/ia-example-marking-exercise--1.html">IA example & marking exercise </a></li><li><a href="../23929/genuine-examples-of-moderated-ia-reports-1.html">Genuine examples of moderated IA reports</a></li><li><a href="../25234/examples-of-teacher-marked-ia-reports--1.html">Examples of teacher-marked IA reports </a></li><li><a href="../37542/history-of-internal-assessment-1.html">History of Internal Assessment</a></li></ul></li><li><a href="../16598/mandatory-laboratory-components-1.html" class="father">Mandatory laboratory components</a><ul class="level-2"><li><a href="../16613/formula-of-magnesium-oxide--1.html">Formula of magnesium oxide </a></li><li><a href="../16612/determining-the-mr-of-an-unknown-gas-1.html">Determining the <i>M</i><sub>r</sub> of an unknown gas</a></li><li><a href="../16615/acid-base-titrations--1.html">Acid-base titrations </a></li><li><a href="../16616/a-green-acid-base-practical-1.html">A green acid-base practical</a></li><li><a href="../16617/analysis-of-aspirin-tablets-1.html">Analysis of aspirin tablets</a></li><li><a href="../16618/caco3-in-egg-shells-1.html">CaCO<sub>3</sub> in egg shells</a></li><li><a href="../16644/enthalpy-changes-1.html">Enthalpy changes</a></li><li><a href="../16631/reaction-rates-1.html">Reaction rates</a></li><li><a href="../16635/rate-dependent-factors-1.html">Rate-dependent factors</a></li><li><a href="../16636/determining-ea-for-a-reaction-1.html">Determining <i>E</i><sub>a</sub> for a reaction</a></li><li><a href="../16637/iodination-of-propanone-1.html">Iodination of propanone</a></li><li><a href="../18144/titrations-with-a-ph-meter-1.html">Titrations with a pH meter</a></li><li><a href="../18355/redox-titration-with-kmno4--1.html">Redox titration with KMnO<sub>4</sub> </a></li><li><a href="../16640/voltaic-cells-1.html">Voltaic cells</a></li><li><a href="../16659/3-d-molecular-modelling--1.html">3-D molecular modelling </a></li></ul></li><li><a href="../17168/other-good-practicals-1.html" class="father">Other good practicals</a><ul class="level-2"><li><a href="../17196/common-chemical-reactions-1.html">Common chemical reactions</a></li><li><a href="../227/elements-oxides-of-the-third-period--1.html">Elements & oxides of the third period </a></li><li><a href="../17239/the-halogens-1.html">The halogens</a></li><li><a href="../17162/boiling-points-of-mixtures-1.html">Boiling points of mixtures</a></li><li><a href="../17170/polarity-of-molecules-1.html">Polarity of molecules</a></li><li><a href="../18083/le-chateliers-principle--1.html">Le Chatelier's principle </a></li><li><a href="../19582/determining-kc-for-an-esterification-reaction-1.html">Determining <i>K</i><sub>c</sub> for an esterification reaction</a></li><li><a href="../18164/redox-reactions-of-vanadium--1.html">Redox reactions of vanadium </a></li><li><a href="../18351/chlorine-in-swimming-pools--1.html">Chlorine in swimming pools </a></li><li><a href="../18178/analysis-of-cuii-ions-in-solution--1.html">Analysis of Cu(II) ions in solution </a></li><li><a href="../18179/percentage-of-copper-in-brass-1.html">Percentage of copper in brass</a></li><li><a href="../18356/electrolytic-cells--1.html">Electrolytic cells </a></li><li><a href="../18598/reactions-of-organic-compounds-1.html">Reactions of organic compounds</a></li><li><a href="../18752/hydrolysis-of-halogenoalkanes-1.html">Hydrolysis of halogenoalkanes</a></li><li><a href="../18784/preparation-of-13-dinitrobenzene--1.html">Preparation of 1,3-dinitrobenzene </a></li><li><a href="../19022/determination-of-an-organic-structure-1.html">Determination of an organic structure</a></li><li><a href="../19887/preparation-of-nylon-66-1.html">Preparation of nylon 6,6</a></li><li><a href="../19343/determination-of-vitamin-c-content--1.html">Determination of vitamin C content </a></li><li><a href="../19342/hydrolysis-of-starch--1.html">Hydrolysis of starch </a></li><li><a href="../19159/preparation-purification-of-aspirin--1.html">Preparation & purification of aspirin </a></li></ul></li><li><a href="../18851/ict-in-practical-work-1.html" class="father">ICT in practical work</a><ul 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Chemistry?</a></li><li><a href="../3505/a-modern-paradigm-1.html">A modern paradigm</a></li></ul></li></ul></li><li><a href="../17783/fast-track-to-tests-questions-1.html">Fast track to tests & questions</a><ul class="level-1"><li><a href="../17784/sl-multiple-choice-tests-on-individual-topics-1.html">SL Multiple choice tests on individual topics</a></li><li><a href="../24351/sl-multiple-choice-quizzes-on-sub-topics-1.html">SL Multiple choice 'quizzes' on sub-topics</a></li><li><a href="../31519/sl-practice-paper-1-exams-1.html">SL Practice Paper 1 exams</a></li><li><a href="../17786/sl-questions-on-each-sub-topic-1.html">SL Questions on each sub-topic</a></li><li><a href="../20431/sl-paper-3-section-a-questions-1.html">SL Paper 3 Section A questions</a></li><li><a href="../17792/sl-questions-on-the-options-1.html">SL Questions on the options</a></li><li><a href="../24897/sl-quizzes-on-option-sub-topics--1.html">SL Quizzes on option sub-topics </a></li><li><a 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class="expander fa fa-caret-right "></i><a href="../24660/mc-test-the-equilibrium-law-1.html" title="MC test: The equilibrium law">MC test: The equilibrium law</a></li><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../40961/equilibrium-law-questions-1.html" title="Equilibrium law questions">Equilibrium law questions</a></li></ul></ul><li class=" parent" style="padding-left: 14px"><i class="expander fa fa-caret-right "></i><a href="../18120/topics-8-18--1.html" title="Topics 8 & 18 ">Topics 8 & 18 </a></li><ul class="level-2 "><li class=" parent" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../18124/theories-of-acids-bases--1.html" title="Theories of acids & bases ">Theories of acids & bases </a></li><ul class="level-3 "><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../24662/mc-test-theories-of-acids-bases-1.html" title="MC test: Theories of acids & bases">MC test: Theories of acids & bases</a></li><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../40963/theories-of-acids-bases-questions-1.html" title="Theories of acids & bases questions">Theories of acids & bases questions</a></li></ul><li class=" parent" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../18126/properties-of-acids-bases-1.html" title="Properties of acids & bases">Properties of acids & bases</a></li><ul class="level-3 "><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../24663/mc-test-properties-of-acids-bases--1.html" title="MC test: Properties of acids & bases ">MC test: Properties of acids & bases </a></li><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../40964/properties-of-acids-bases-questions-1.html" title="Properties of acids & bases questions">Properties of acids & bases questions</a></li></ul><li class=" parent" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../18140/ph-scale-1.html" title="pH scale">pH scale</a></li><ul class="level-3 "><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../24668/mc-test-the-ph-scale-1.html" title="MC test: The pH scale">MC test: The pH scale</a></li><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../40971/ph-scale-questions-1.html" title="pH scale questions">pH scale questions</a></li></ul><li class=" parent" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../18152/strong-weak-acids-bases-1.html" title="Strong & weak acids & bases">Strong & weak acids & bases</a></li><ul class="level-3 "><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../24670/mc-test-strong-weak-acids-bases-1.html" title="MC test: Strong & weak acids & bases">MC test: Strong & weak acids & bases</a></li><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../40972/strong-weak-acid-bases-questions-1.html" title="Strong & weak acid & bases questions">Strong & weak acid & bases questions</a></li></ul><li class=" parent" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../18156/acid-deposition-1.html" title="Acid deposition">Acid deposition</a></li><ul class="level-3 "><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../24674/mc-test-acid-deposition-1.html" title="MC test: Acid deposition">MC test: Acid deposition</a></li><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../40983/acid-deposition-questions-1.html" title="Acid deposition questions">Acid deposition questions</a></li></ul><li class=" parent" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../18160/lewis-acids-bases-1.html" title="Lewis acids & bases">Lewis acids & bases</a></li><ul class="level-3 "><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../24710/mc-test-lewis-acids-bases-1.html" title="MC test: Lewis acids & bases">MC test: Lewis acids & bases</a></li><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../40986/lewis-acids-bases-questions-1.html" title="Lewis acids & bases questions">Lewis acids & bases questions</a></li></ul><li class=" parent" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../18250/acid-base-calculations-1.html" title="Acid base calculations">Acid base calculations</a></li><ul class="level-3 "><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../24714/mc-test-calculations-involving-acids-bases--1.html" title="MC test: Calculations involving acids & bases ">MC test: Calculations involving acids & bases </a></li><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../40988/acid-base-calculations-questions--1.html" title="Acid-base calculations questions ">Acid-base calculations questions </a></li></ul><li class=" parent" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../26161/ph-titration-curves-1.html" title="pH titration curves">pH titration curves</a></li><ul class="level-3 "><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../26158/mc-test-ph-curves-1.html" title="MC test: pH curves">MC test: pH curves</a></li><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../41000/ph-curves-questions--1.html" title="pH curves questions ">pH curves questions </a></li></ul></ul><li class=" parent" style="padding-left: 14px"><i class="expander fa fa-caret-right "></i><a href="../18350/topics-9-19-1.html" title="Topics 9 & 19">Topics 9 & 19</a></li><ul class="level-2 "><li class=" parent" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../18365/oxidation-reduction-1.html" title="Oxidation & reduction">Oxidation & reduction</a></li><ul class="level-3 "><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../24725/mc-test-oxidation-reduction-1.html" title="MC test: Oxidation & reduction">MC test: Oxidation & reduction</a></li><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../41033/oxidation-reduction-questions-1--1.html" title="Oxidation & reduction questions (1) ">Oxidation & reduction questions (1) </a></li><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../41034/oxidation-reduction-questions-2-1.html" title="Oxidation & reduction questions (2)">Oxidation & reduction questions (2)</a></li><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../41035/oxidation-reduction-questions-3-1.html" title="Oxidation & reduction questions (3)">Oxidation & reduction questions (3)</a></li></ul><li class=" parent" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../18383/electrochemical-cells-1.html" title="Electrochemical cells">Electrochemical cells</a></li><ul class="level-3 "><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../24740/mc-test-electrochemical-cells-1.html" title="MC test: Electrochemical cells">MC test: Electrochemical cells</a></li><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../41072/electrochemical-cells-questions--1.html" title="Electrochemical cells questions ">Electrochemical cells questions </a></li></ul><li class=" parent" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../18401/electrochemical-cells-ahl--1.html" title="Electrochemical cells (AHL) ">Electrochemical cells (AHL) </a></li><ul class="level-3 "><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../24742/mc-test-electrochemical-cells-ahl-1.html" title="MC test: Electrochemical cells (AHL)">MC test: Electrochemical cells (AHL)</a></li><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../41098/electrochemical-cells-1-ahl-questions-1.html" title="Electrochemical cells (1) (AHL) questions">Electrochemical cells (1) (AHL) questions</a></li><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../41099/electrochemical-cells-2-ahl-questions-1.html" title="Electrochemical cells (2) (AHL) questions">Electrochemical cells (2) (AHL) questions</a></li></ul></ul><li class=" parent" style="padding-left: 14px"><i class="expander fa fa-caret-right "></i><a href="../18475/topics-10-20--1.html" title="Topics 10 & 20 ">Topics 10 & 20 </a></li><ul class="level-2 "><li class=" parent" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../18497/fundamentals-of-organic-chemistry--1.html" title="Fundamentals of organic chemistry ">Fundamentals of organic chemistry </a></li><ul class="level-3 "><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../24749/mc-test-fundamentals-of-organic-chemistry-1.html" title="MC test: Fundamentals of organic chemistry">MC test: Fundamentals of organic chemistry</a></li><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../41111/fundamentals-of-organic-chemistry-1-questions-1.html" title="Fundamentals of organic chemistry (1) questions">Fundamentals of organic chemistry (1) questions</a></li><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../41112/fundamentals-of-organic-chemistry-2-questions-1.html" title="Fundamentals of organic chemistry (2) questions">Fundamentals of organic chemistry (2) questions</a></li></ul><li class=" parent" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../18597/alkanes-alkenes-addition-polymers-1.html" title="Alkanes, alkenes & addition polymers">Alkanes, alkenes & addition polymers</a></li><ul class="level-3 "><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../24750/mc-test-alkanes-alkenes-addition-polymers-1.html" title="MC test: Alkanes, alkenes & addition polymers">MC test: Alkanes, alkenes & addition polymers</a></li><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../41121/alkanes-questions-1.html" title="Alkanes questions">Alkanes questions</a></li><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../41124/alkenes-questions-1.html" title="Alkenes questions">Alkenes questions</a></li></ul><li class=" parent" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../18741/alcohols--1.html" title="Alcohols ">Alcohols </a></li><ul class="level-3 "><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../24772/mc-test-alcohols-1.html" title="MC test: Alcohols">MC test: Alcohols</a></li><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../41125/alcohols-questions-1.html" title="Alcohols questions">Alcohols questions</a></li></ul><li class=" parent" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../18742/halogenoalkanes-benzene--1.html" title="Halogenoalkanes & benzene ">Halogenoalkanes & benzene </a></li><ul class="level-3 "><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../24797/mc-test-halogenoalkanes-benzene-1.html" title="MC test: Halogenoalkanes & benzene">MC test: Halogenoalkanes & benzene</a></li><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../41130/halogenoalkanes-benzene-questions-1.html" title="Halogenoalkanes & benzene questions">Halogenoalkanes & benzene questions</a></li></ul><li class=" parent" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../18762/nucleophilic-substitution--1.html" title="Nucleophilic substitution ">Nucleophilic substitution </a></li><ul class="level-3 "><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../24757/mc-test-nucleophilic-substitution-1.html" title="MC test: Nucleophilic substitution">MC test: Nucleophilic substitution</a></li><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../41138/nucleophilic-substitution-questions-1.html" title="Nucleophilic substitution questions">Nucleophilic substitution questions</a></li></ul><li class=" parent" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../18766/electrophilic-addition--1.html" title="Electrophilic addition ">Electrophilic addition </a></li><ul class="level-3 "><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../24805/mc-test-electrophilic-addition-electrophilic-substitution-reacti-2.html" title="MC test: Electrophilic addition & electrophilic substitution reactions">MC test: Electrophilic addition & electrophilic substitution reactions</a></li><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../41148/electrophilic-addition-questions-1.html" title="Electrophilic addition questions">Electrophilic addition questions</a></li></ul><li class=" parent" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../18780/electrophilic-substitution--2.html" title="Electrophilic substitution ">Electrophilic substitution </a></li><ul class="level-3 "><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../41149/electrophilic-substitution-questions-1.html" title="Electrophilic substitution questions">Electrophilic substitution questions</a></li></ul><li class=" parent" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../18793/reduction-reactions--1.html" title="Reduction reactions ">Reduction reactions </a></li><ul class="level-3 "><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../24811/mc-test-reduction-reactions-1.html" title="MC test: Reduction reactions">MC test: Reduction reactions</a></li><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../41150/reduction-reactions-questions-1.html" title="Reduction reactions questions">Reduction reactions questions</a></li></ul><li class=" parent" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../18797/synthetic-routes--1.html" title="Synthetic routes ">Synthetic routes </a></li><ul class="level-3 "><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../24822/mc-test-synthetic-routes-1.html" title="MC test: Synthetic routes">MC test: Synthetic routes</a></li><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../41152/synthetic-routes-questions--1.html" title="Synthetic routes questions ">Synthetic routes questions </a></li></ul><li class=" parent" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../18844/stereoisomerism--1.html" title="Stereoisomerism ">Stereoisomerism </a></li><ul class="level-3 "><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../24817/mc-test-stereoisomerism-1.html" title="MC test: Stereoisomerism">MC test: Stereoisomerism</a></li><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../41166/stereoisomerism-questions-1.html" title="Stereoisomerism questions">Stereoisomerism questions</a></li></ul></ul><li class="ancestor parent" style="padding-left: 14px"><i class="expander fa fa-caret-right fa-rotate-90"></i><a href="../17285/topics-11-21--1.html" title="Topics 11 & 21 ">Topics 11 & 21 </a></li><ul class="level-2 expanded"><li class="current parent" style="padding-left: 28px"><i class="expander fa fa-caret-right fa-rotate-90"></i><a href="uncertainty-errors--1.html" title="Uncertainty & errors ">Uncertainty & errors </a></li><ul class="level-3 expanded"><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../24818/mc-test-uncertainties-errors-1.html" title="MC test: Uncertainties & errors">MC test: Uncertainties & errors</a></li><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../38869/uncertainty-error-questions--1.html" title="Uncertainty & error questions ">Uncertainty & error questions </a></li></ul><li class=" parent" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../15014/graphical-techniques-1.html" title="Graphical techniques">Graphical techniques</a></li><ul class="level-3 "><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../24819/mc-test-graphical-techniques-1.html" title="MC test: Graphical techniques">MC test: Graphical techniques</a></li><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../39387/graphical-techniques-questions--1.html" title="Graphical techniques questions ">Graphical techniques questions </a></li></ul><li class=" parent" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../18968/spectroscopic-identification-of-organic-compounds-1.html" title="Spectroscopic identification of organic compounds">Spectroscopic identification of organic compounds</a></li><ul class="level-3 "><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../24820/mc-test-spectroscopic-identification-of-organic-compounds--1.html" title="MC test: Spectroscopic identification of organic compounds ">MC test: Spectroscopic identification of organic compounds </a></li><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../39388/index-of-hydrogen-deficiency-questions-1.html" title="Index of hydrogen deficiency questions">Index of hydrogen deficiency questions</a></li><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../39351/identification-from-spectra-question-1-1.html" title="Identification from spectra - Question 1">Identification from spectra - Question 1</a></li><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../39353/identification-from-spectra-question-2-1.html" title="Identification from spectra - Question 2">Identification from spectra - Question 2</a></li><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../39354/identification-from-spectra-question-3-1.html" title="Identification from spectra - Question 3">Identification from spectra - Question 3</a></li><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../39355/identification-from-spectra-question-4-1.html" title="Identification from spectra - Question 4">Identification from spectra - Question 4</a></li><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../39356/identification-from-spectra-question-5-1.html" title="Identification from spectra - Question 5">Identification from spectra - Question 5</a></li><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../39357/identification-from-spectra-question-6-1.html" title="Identification from spectra - Question 6">Identification from spectra - Question 6</a></li><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../39358/identification-from-spectra-question-7-1.html" title="Identification from spectra - Question 7">Identification from spectra - Question 7</a></li><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../39359/identification-from-spectra-question-8-1.html" title="Identification from spectra - Question 8">Identification from spectra - Question 8</a></li><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../39360/identification-from-spectra-question-9-1.html" title="Identification from spectra - Question 9">Identification from spectra - Question 9</a></li><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../39361/identification-from-spectra-question-10-1.html" title="Identification from spectra - Question 10">Identification from spectra - Question 10</a></li></ul><li class=" parent" style="padding-left: 28px"><i class="expander fa fa-caret-right "></i><a href="../19027/spectroscopic-identification-of-organic-compounds-ahl--1.html" title="Spectroscopic identification of organic compounds (AHL) ">Spectroscopic identification of organic compounds (AHL) </a></li><ul class="level-3 "><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../24821/mc-test-spectroscopic-identification-of-organic-compounds-ahl-1.html" title="MC test: Spectroscopic identification of organic compounds (AHL)">MC test: Spectroscopic identification of organic compounds (AHL)</a></li><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../39375/identification-from-spectra-question-11-1.html" title="Identification from spectra - Question 11">Identification from spectra - Question 11</a></li><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../39376/identification-from-spectra-question-12-1.html" title="Identification from spectra - Question 12">Identification from spectra - Question 12</a></li><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../39377/identification-from-spectra-question-13-1.html" title="Identification from spectra - Question 13">Identification from spectra - Question 13</a></li><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../39378/identification-from-spectra-question-14-1.html" title="Identification from spectra - Question 14">Identification from spectra - Question 14</a></li><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../39379/identification-from-spectra-question-15-1.html" title="Identification from spectra - Question 15">Identification from spectra - Question 15</a></li><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../39380/identification-from-spectra-question-16-1.html" title="Identification from spectra - Question 16">Identification from spectra - Question 16</a></li><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../39381/identification-from-spectra-question-17-1.html" title="Identification from spectra - Question 17">Identification from spectra - Question 17</a></li><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../39382/identification-from-spectra-question-18-1.html" title="Identification from spectra - Question 18">Identification from spectra - Question 18</a></li><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../39383/identification-from-spectra-question-19-1.html" title="Identification from spectra - Question 19">Identification from spectra - Question 19</a></li><li class="" style="padding-left: 42px"><i class="expander fa fa-caret-right "></i><a href="../39385/identification-from-spectra-question-20-1.html" title="Identification from spectra - Question 20">Identification from spectra - Question 20</a></li></ul></ul></ul><li class=" parent" style="padding-left: 0px"><i class="expander fa fa-caret-right "></i><a href="../16441/the-nature-of-science-1.html" title="The Nature of Science">The Nature of Science</a></li><ul class="level-1 "><li class="" style="padding-left: 14px"><i class="expander fa fa-caret-right "></i><a href="../16450/key-terms-concepts-1.html" title="Key terms & concepts">Key terms & concepts</a></li><li class="" style="padding-left: 14px"><i class="expander fa fa-caret-right "></i><a href="../34566/nos-critical-thinking-1.html" title="NOS & Critical Thinking">NOS & Critical Thinking</a></li><li class="" style="padding-left: 14px"><i class="expander fa fa-caret-right "></i><a href="../32100/how-the-elements-were-named-1.html" title="How the elements were named">How the elements were named</a></li><li class="" 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Accuracy and precisionWhen marking titration results it is not unusual to come across something like this:Titration of 25.00 cm3 of x mol dm-3 hydrochloric acid with a standardized solution of 1.00 mol dm-3 sodium hydroxide...%0Ahttps%3A%2F%2Fwww.thinkib.net%2Fchemistry%2Fpage%2F17276%2Funcertainty-errors-"><i class="fa fa-envelope"></i><span>Email</span></a></li></ul></li><li><a class="" href="chemistry/teaching-materials"><i class="fa fa-puzzle-piece colored"></i><span>Teaching materials</span></a></li></ul><div class="page-actions no-print navbar inline hidden-desktop"><div class="navbar-inner"><ul class="nav"><li><a class="presentation" href="#" onclick="return false;"><i class="fa fa-desktop"></i></a></li><li><a class="print-section-blog" href="#" onclick="return false;"><i class="fa fa-print"></i></a></li><li><a class="page-bookmarker" data-ticket="IB Docs (2) Team" data-pid="17276" href="#" onclick="return false;"><i class="fa fa-star"></i></a></li><li><a class="personal-notes" href="#" onclick="return false;"><i class="fa fa-file-text"></i></a></li><li><a class="" data-toggle="modal" href="#modal-feedback" onclick="return false;"><i class="fa fa-envelope-o"></i></a></li><li class="dropdown"><a class="dropdown-toggle" data-toggle="dropdown" data-target="#" href="#"><i class="fa fa-share-alt"></i></a><ul class="dropdown-menu" role="menu"><li><a class="" target="_blank" title="Share on Twitter" href="https://twitter.com/share?text=%22Uncertainty+%26+errors+%22+-+via+%40InThinker+%23chemistry%0A&url=https%3A%2F%2Fwww.thinkib.net%2Fchemistry%2Fpage%2F17276%2Funcertainty-errors-"><i class="fa fa-twitter-square"></i><span>Twitter</span></a></li><li><a class="" target="_blank" title="Share on Facebook" href="https://www.facebook.com/sharer.php?u=https%3A%2F%2Fwww.thinkib.net%2Fchemistry%2Fpage%2F17276%2Funcertainty-errors-&t=Uncertainty+&+errors+"><i class="fa fa-facebook-square"></i><span>Facebook</span></a></li><li><a class="" href="http://www.linkedin.com/shareArticle?mini=true&url=https%3A%2F%2Fwww.thinkib.net%2Fchemistry%2Fpage%2F17276%2Funcertainty-errors-"><i class="fa fa-linkedin-square"></i><span>LinkedIn</span></a></li><li><a class="" href="https://plus.google.com/share?url=https%3A%2F%2Fwww.thinkib.net%2Fchemistry%2Fpage%2F17276%2Funcertainty-errors-"><i class="fa fa-google-plus-square"></i><span>Google +</span></a></li><li><a class="" href="mailto:?subject=Uncertainty & errors &body=1. Accuracy and precisionWhen marking titration results it is not unusual to come across something like this:Titration of 25.00 cm3 of x mol dm-3 hydrochloric acid with a standardized solution of 1.00 mol dm-3 sodium hydroxide...%0Ahttps%3A%2F%2Fwww.thinkib.net%2Fchemistry%2Fpage%2F17276%2Funcertainty-errors-"><i class="fa fa-envelope"></i><span>Email</span></a></li></ul></li><li><a class="" href="chemistry/teaching-materials"><i class="fa fa-puzzle-piece colored"></i></a></li></ul></div></div><h1 class="section-title">Uncertainty & errors </h1><ul class="breadcrumb"><li><a title="Home" href="https://www.thinkib.net/chemistry"><i class="fa fa-home"></i></a><span class="divider"><i class="fa fa-chevron-right"></i></span></li><li><a title="Go to: Core & AHL" href="../16347/core-ahl-1.html">Core & AHL</a><span class="divider"><i class="fa fa-chevron-right"></i></span></li><li><a title="Go to: Teaching each topic & sub-topic" href="../16329/teaching-each-topic-sub-topic-1.html">Teaching each topic & sub-topic</a><span class="divider"><i class="fa fa-chevron-right"></i></span></li><li><a title="Go to: Topics 11 & 21 " href="../17285/topics-11-21--1.html">Topics 11 & 21 </a><span class="divider"><i class="fa fa-chevron-right"></i></span></li><li><span>Uncertainty & errors </span></li></ul><div id="std-sidebox-task-added-msg"></div><div id="modal-feedback" class="modal hide fade text-left" tabindex="-1" role="dialog" aria-labelledby="log-in form" aria-hidden="true">
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</div><section id="main-content"><div id="toc-1672972950" class="toc"><a href="#" class="toc-switcher" title="Show table of contents"><small><i class="fa fa-reorder"></i> Table of contents <span class="pull-right"><i class="fa fa-chevron-down"></i></span></small></a></div><h1><img class="ico" src="../../../img/icons/standard-1.png"> <img class="ico" src="../../../img/icons/higher-1.png"> 11.1 Uncertainty & errors in measurement & results (2 hours)</h1><div class="pinkBg"><div><h2>Pause for thought</h2><p><strong>1. Accuracy and precision</strong></p><p>When marking titration results it is not unusual to come across something like this:</p><p>Titration of 25.00 cm<sup>3</sup> of <em>x</em> mol dm<sup>-3</sup> hydrochloric acid with a standardized solution of 1.00 mol dm<sup>-3</sup> sodium hydroxide solution.</p><p align="center"><img alt="" class="noborder" height="87" src="../../../ib/chemistry/images/Core and AHL/Topic 11 uncertainty/Titration table.png" width="640"><br>Average volume of 1.00 mol dm<sup>-3</sup> NaOH(aq) required to titrate 25.00 cm<sup>3</sup> of <em>x</em> mol dm<sup>-3</sup> HCl(aq) = 25.00 cm<sup>3</sup></p><p>The student then proceeds to calculate the unknown concentration of the hydrochloric acid as 1.00 mol dm<sup>-3</sup> and work out the associated uncertainty by summing up the percentage uncertainties of the apparatus used to give an answer something like 1.00 ± 0.02 mol dm<sup>-3</sup>. They then think that they have listed all their uncertainties and applied them as they are supposed to do.<br><br>There is no awareness that the results achieved by the experimenter are poor and not precise. Titration is a reproducible procedure. If the burette and pipette are accurate to ± 0.10 cm<sup>3</sup> and 0.05 cm<sup>3</sup> respectively then the ‘accurate readings’ on the burette should be in agreement within ± 0.15 cm<sup>3</sup>. A difference of more than 0.15 cm<sup>3</sup> in the accurate results suggests that the experimenter was not carrying out the procedure correctly. They should, in fact continue to repeat the titration until they do get agreement to within ± 0.15 cm<sup>3</sup> for their ‘accurate’ results. Too often when evaluating an experiment students blindly follow the instructions on how to calculate uncertainties without applying or understanding the real assumptions made. Even if they do get reproducible accurate titration results they should also question whether the concentration of the ‘standardized’ sodium hydroxide solution made up by the teacher/technician (and therefore beyond their control) was exactly 1.00 mol dm<sup>-3</sup>. An example like this can be used to illustrate the importance of distinguishing between random errors and systematic errors. Repeating the titration several times will help to reduce random errors although none of the values should differ by more than ± 0.15 cm<sup>3</sup>. If the concentration of the sodium hydroxide solution was in fact 1.10 mol dm<sup>-3</sup> then a systematic error of 10% will apply no matter how many titrations are completed or at least until the correct concentration of the standardized solution is used.</p><hr class="hidden"><p><strong>2. Determining the uncertainty associated with a reading</strong></p><p>Consider using a 1 metre ruler with an uncertainty of ± 0.01 metre to measure a 2 metre length. Because the ruler would be needed to be used twice the length would be expressed as 2.00 ± 0.02 metres as the uncertainties are simply added. This is quite logical as the first measured value would lie between 0.99 and 1.01 m. The second value would be the same so when adding them together the value would lie between 1.98 and 2.02 m, i.e. 2.00 ± 0.02 m. Similarly if a thermometer accurate to ± 0.5 <sup>o</sup>C is used to measure a temperature difference then if the two readings were 19.1 <sup>o</sup>C and 26.9 <sup>o</sup>C the temperature difference should be recorded as 7.8 ± 1.0 <sup>o</sup>C as uncertainties are also added when the measured values are subtracted.<br>In fact, although seemingly logical, this is a simplified approach. A more sophisticated treatment uses the relationship:</p><hr class="hidden"><p style="text-align: center;">The cumulative (or total) uncertainty = the square root of the sum of the squares of the absolute uncertainties.</p><hr class="hidden"><p>If this is applied to the metre ruler data above the cumulative uncertainty = √[(0.01)<sup>2</sup> + (0.01)<sup>2</sup>] = 0.014 = 0.01 to one significant figure.</p><hr class="hidden"><p>The IB generally wants to see an awareness of uncertainties rather than insisting on a particular approach and accepts any recognised method of calculation of cumulative uncertainties.</p><hr class="hidden"><p><img alt="" class="left noborder" height="400" src="../../../ib/chemistry/images/Core%20and%20AHL/Topic%2011%20uncertainty/VEE%20GEE%2020114-Series%20Burets-500x500.jpg" title="If the burette says + or - 0.05 cm3 should the uncertainty for thevolume actually used be + or - 0.05 cm3 or 0.10 cm3? or " width="400">It is not quite so obvious when certain instruments are used even though technically two readings are taken. Consider measuring the mass of something using a balance accurate to ± 0.001 g. If the balance is reading zero and say an empty weighing bottle is placed on the balance then the mass of the weighing bottle might be recorded as 20.034 ± 0.001 g. If about ten grams of magnesium are placed in the weighing bottle and the new mass is 30.456 g then it would be usual to record the accurate mass of the magnesium as 10.422 ± 0.002 g. But is this really correct? When the balance was reading zero it is actually accurate to ± 0.001 g i.e. zero is a mass between - 0.001 and + 0.001 g so the mass of the weighing bottle should really be recorded as 20.034 ± 0.002 g and the mass of the magnesium, which is now the result of three separate readings, 10.422 ± 0.003 g. A sensible person will question whether this sort of pedantic attention to detail is really necessary. It isn't, but because of teacher's insecurity with how their IA marks are moderated it has almost become so. In fact instruments that rely on two readings for any measurement e.g. a balance or a burette state on them their uncertainty. A burette for example might say 50 cm<sup>3</sup> accurate to 0.05 cm<sup>3</sup><sup> </sup>(see image on left - although it gives the units as ml rather than cm<sup>3</sup>). What many people take this to mean is that the uncertainty for the actual volume measured can be taken as ± 0.05 cm<sup>3</sup> even though it has been arrived at by taking the difference between the final and initial readings so arguably should actually be quoted as ± 0.10 cm<sup>3</sup>. Luckily the IA moderators are told to accept <strong>either</strong> the actual uncertainty stated on the instrument (or the estimated uncertainty if no value is given) <strong>or</strong> double the uncertainty when moderating student's internal assessment work if the student reports it in their Individual Scientific Investigation.</p><hr class="hidden"></div></div><hr class="hidden"><div class="box"><h2>Nature of Science</h2><p>Replication of quantitative measurements is crucial to ensure reliability—precision, accuracy, systematic, and random errors can only be interpreted properly through replication.</p><hr class="hidden"></div><hr class="hidden"><div class="box"><table align="left" border="0" cellpadding="10" cellspacing="0"><tbody><tr><td style="width: 50%;" valign="top"><div class="yellowBg"><div><h2><strong><strong>Learning outcomes</strong></strong></h2><p>After studying this topic students should be able to:</p><p><strong><strong>Understand:</strong></strong></p><ul><li>Qualitative data are not obtained from measurement but include all non-numerical information obtained from observations.</li><li>Quantitative data are obtained from measurements. They are affected by human limitations such as reaction times and are always associated with random errors/uncertainties, determined by the apparatus used to measure them.</li><li>The impact of the uncertainties on the final result is shown by the propagation of random errors in data processing.</li><li>Systematic errors in measurement are caused by experimental design and procedure and normally lead to a deviation in a particular direction.</li><li>Random errors, but not systematic errors, will be reduced by repeated trials and measurements.</li></ul><p><strong>Apply their knowledge to:</strong></p><ul><li>Distinguish between random errors and systematic errors.</li><li>Record all measurements together with their associated uncertainties as a range (±) to an appropriate precision.</li><li>Discuss ways to reduce uncertainties in an experiment.</li><li>Propagate uncertainties in processed data, including the use of percentage uncertainties.</li><li>Discuss the impact of systematic errors on the results obtained in all experimental work and how they can be reduced.</li><li>Estimate whether particular sources of error are likely to have a major or minor effect on the final result.</li><li>Calculate the percentage error by comparing the experimental result with a theoretical or accepted result whenever possible.</li><li>Distinguish between accuracy and precision when evaluating results.</li></ul></div></div></td><td style="width: 50%;" valign="top"><h4><b><span style="font-weight: normal;"></span></b></h4><div class="yellowBg"><div><h4><b><span style="font-weight: normal;"><strong>Clarification notes</strong></span></b></h4><p>The number of significant figures given in a result is based on the figures given in the data.<br>When adding or subtracting, the final answer should be given to the least number of decimal places. When multiplying or dividing the final answer should be given to the least number of significant figures.<br>The value of the data should be recorded to the same precision as the random error.<br>SI units should be used throughout (unless specifically stated otherwise).</p><hr class="hidden"><h4>International-mindedness</h4><p>The International Standards Organization (ISO) published the Guide to the Expression of Uncertainty in Measurement in 1995. This was a result of seven international organizations, including IUPAC, collaborating together. It has been translated into several different languages and has been widely adopted in most countries.</p></div></div></td></tr></tbody></table></div><hr class="hidden"><div class="box"><table align="left" border="0" cellpadding="10" cellspacing="0"><tbody><tr><td style="width: 50%;" valign="top"><h2><span style=""><span style="font-weight: normal;">Teaching tips</span></span></h2><p><span style=""><span style="font-weight: normal;">Probably the two most important concepts for students </span></span>to understand are distinguishing between accurate and precise and also distinguishing between random and systematic. The dartboard analogy is good for accurate and precise. The darts may all land very close together to illustrate precise but if they are far from the bull's eye they are not very accurate.</p><p>It is probably best to teach this sub-topic when students are actually doing a practical which requires it as they can then put it into context. A good experiment is the<a href="chemistry/practicals-for-sl-and-hl/acid-base-titrations-.htm"> </a> <a href="../16615/acid-base-titrations--1.html" title="New 2014 programme (First exams 2016) » Practical scheme of work » Mandatory laboratory components » Acid-base titrations ">acid-base titrations </a> practical. This is good as it involves the uncertainties associated with a burette, a pipette, a volumetric flask and a balance. To calculate the overall uncertainty the students will need to work out the percentage uncertainty associated with each instrument and then add these together to get the total percentage uncertainty. Finally they will need to restate this as the actual uncertainty associated with the value they have obtained for the molar mass of the hydrated oxalic acid crystals.</p><p>It is worth pointing out other uncertainties and assumptions made even if they cannot quantify these. For example, how pure is the oxalic acid, was all the mass of the oxalic acid weighed out transferred to the volumetric flask and how accurately did the technician make up the standard solution of hydroxide solution?</p><p>Impress upon students that many instruments they use, such as electronic balances, pipettes, volumetric flasks and pipettes do in fact have very low uncertainties. The real uncertainties in their results will more likely be due to impure chemicals, incomplete reactions, heat loss, failure to keep controlled variables controlled or wrongly stated concentrations. Probably the most common instrument they will use for accurate work that has the greatest degree of uncertainty is a thermometer. Often these can only be read to half a degree and the uncertainty is often quoted as ± 0.5<sup> o</sup>C. If the thermometer is being used to measure a 10 <sup>o</sup>C difference in temperature then the uncertainty from the two reading is ± 1.0<sup> </sup><sup>o</sup>C which leads to an uncertainty of ten per cent. It is here that temperature probes connected to a data logger can significantly reduce the amount of uncertainty. It may be worth pointing out that an inaccurate thermometer (i.e. one that is wrongly calibrated) can still give an accurate result when measuring a temperature difference as the systematic error will effectively cancel out.</p><p>For help and guidance on the correct use of significant figures (sometimes called 'significant digits' by the IB) see the page on significant figures in the section on practical work. It is good practice to get students to always use scientific notation when using numbers or quantities as this makes the correct use of significant figures much clearer and easier.</p><hr class="hidden"></td><td style="width: 50%;" valign="top"><h4><span style="font-weight: normal; ">Study guide</span></h4><p style="margin: 0px 0px 1em; padding: 0px; color: rgb(0, 0, 0); font-size: 1em;"><img alt="" src="../../../ib/chemistry/images/2014%20Basic%20information/New%20cover.jpg" style="width: 67px; height: 96px;"></p><p style="margin: 0px 0px 1em; padding: 0px; color: rgb(0, 0, 0); font-size: 1em;"></p><hr class="hidden"><p style="margin: 0px 0px 1em; padding: 0px; color: rgb(0, 0, 0); font-size: 1em;"><span style="font-weight: normal;">Pages 99 & 100</span></p><hr class="hidden"><h2>Questions</h2><p>For ten 'quiz' multiple choice questions with the answers explained see <a href="../24818/mc-test-uncertainties-errors-1.html" title="Core & AHL » Teaching each topic & sub-topic » Topics 11 & 21 » Uncertainty & errors » MC test: Uncertainties & errors">MC test: Uncertainties & errors</a>.</p><p style="margin: 0px 0px 1em; padding: 0px; color: rgb(0, 0, 0); font-size: 1em;">For short-answer questions see <a href="chemistry/page/17277/uncertainty-error-questions-" title="Core & AHL » Teaching each topic & sub-topic » Topics 11 & 21 » Uncertainty & errors » Uncertainty & error questions ">Uncertainty & error questions </a> together with the worked answers on a separate page <a href="chemistry/page/24314/uncertainty-error-answers" title="Core & AHL » Teaching each topic & sub-topic » Topics 11 & 21 » Uncertainty & errors » Uncertainty & error answers">Uncertainty & error answers</a><a href="chemistry/page/24164/empirical-molecular-formula-answers-" title="Core & AHL » Teaching each topic & sub-topic » Topic 1 » The mole & Avogadro's constant » Empirical & molecular formula answers ">. </a></p><hr class="hidden"><h4>Vocabulary list</h4><p><span style=""><span style="font-weight: normal;">quantitative data<br>error<br>random error<br>systematic error</span></span><br><span style=""><span style="font-weight: normal;">uncertainty<br>percentage uncertainty<br>qualitative data</span></span></p><hr class="hidden"><h4><strong><span style="font-family: "Arial Narrow",Arial,Helvetica,sans-serif; font-size: 17px; font-weight: bold;"><span style="font-weight: normal;">IM, TOK, 'Utilization' etc.</span></span></strong></h4><p>See <a href="../17269/topics-11-21--1.html" title="New 2014 programme (First exams 2016) » Core & AHL » Incorporating IM, TOK, Utilization etc. » Topics 11 & 21 ">separate page</a> which covers all of Topic 11.</p><hr class="hidden"><h2>Practical work</h2><p><img class="ico" src="../../../img/icons/lab-1.png"> There are many practicals suitable for assessment that involve uncertainties and significant figures. I usually introduce the concepts with the first <a href="../16615/acid-base-titrations--1.html" title="New 2014 programme (First exams 2016) » Practical scheme of work » Mandatory laboratory components » Acid-base titrations ">Acid-base titrations </a>practical. Another good practical for uncertainties is <a href="../16644/enthalpy-changes-1.html" title="New 2014 programme (First exams 2016) » Practical scheme of work » Mandatory laboratory components » Enthalpy changes">Enthalpy changes</a>.</p></td></tr></tbody></table></div><hr class="hidden"><div class="greenBg"><h2 id="header-13">Teaching slides</h2><p>Teachers may wish to share these slides with students for learning or for reviewing key concepts.</p><div id="myCarousel-14" class="carousel slide" data-id="351"><!-- Carousel items --><div class="carousel-inner"><div class="active item"><a class="fancy" href="../../../tib-galleries/3-351/1111.png" rel="gallery-351" title=""><img alt="" src="files/tib-galleries/3-351/1111.png"></a><div class="carousel-caption"><p>Uncertainty & errors in measurement & results: </p></div></div><div class="item"><a class="fancy" href="../../../tib-galleries/3-351/1112.png" rel="gallery-351" title=""><img alt="" src="files/tib-galleries/3-351/1112.png"></a><div class="carousel-caption"><p>Uncertainty & errors in measurement & results: </p></div></div><div class="item"><a class="fancy" href="../../../tib-galleries/3-351/1113.png" rel="gallery-351" title=""><img alt="" src="files/tib-galleries/3-351/1113.png"></a><div class="carousel-caption"><p>Uncertainty & errors in measurement & results: </p></div></div><div class="item"><a class="fancy" href="../../../tib-galleries/3-351/1114.png" rel="gallery-351" title=""><img alt="" src="files/tib-galleries/3-351/1114.png"></a><div class="carousel-caption"><p>Uncertainty & errors in measurement & results: </p></div></div><div class="item"><a class="fancy" href="/files/tib-galleries/3-351/changed-.png" rel="gallery-351" title=""><img alt="" src="/files/tib-galleries/3-351/changed-.png"></a><div class="carousel-caption"><p>Uncertainty & errors in measurement & results: </p></div></div><div class="item"><a class="fancy" href="../../../tib-galleries/3-351/1116.png" rel="gallery-351" title=""><img alt="" src="files/tib-galleries/3-351/1116.png"></a><div class="carousel-caption"><p>Uncertainty & errors in measurement & results: </p></div></div><div class="item"><a class="fancy" href="../../../tib-galleries/3-351/1117.png" rel="gallery-351" title=""><img alt="" src="files/tib-galleries/3-351/1117.png"></a><div class="carousel-caption"><p>Uncertainty & errors in measurement & results: </p></div></div><div class="item"><a class="fancy" href="../../../tib-galleries/3-351/1118.png" rel="gallery-351" title=""><img alt="" src="files/tib-galleries/3-351/1118.png"></a><div class="carousel-caption"><p>Uncertainty & errors in measurement & results: </p></div></div><div class="item"><a class="fancy" href="../../../tib-galleries/3-351/1119.png" rel="gallery-351" title=""><img alt="" src="files/tib-galleries/3-351/1119.png"></a><div class="carousel-caption"><p>Uncertainty & errors in measurement & results: </p></div></div><div class="item"><a class="fancy" href="/files/tib-galleries/3-351/new-10.png" rel="gallery-351" title=""><img alt="" src="/files/tib-galleries/3-351/new-10.png"></a><div class="carousel-caption"><p>Uncertainty & errors in measurement & results: </p></div></div><div class="item"><a class="fancy" href="../../../tib-galleries/3-351/111-111.png" rel="gallery-351" title=""><img alt="" src="files/tib-galleries/3-351/111-111.png"></a><div class="carousel-caption"><p>Uncertainty & errors in measurement & results: </p></div></div><div class="item"><a class="fancy" href="../../../tib-galleries/3-351/11112.png" rel="gallery-351" title=""><img alt="" src="files/tib-galleries/3-351/11112.png"></a><div class="carousel-caption"><p>Uncertainty & errors in measurement & results: </p></div></div></div><!-- Carousel nav --><a class="carousel-control left" href="#myCarousel-14" data-slide="prev">‹</a><a class="carousel-control right" href="#myCarousel-14" data-slide="next">›</a><div class="tib-indicators"><img class="" title="Click to view" style="margin: 10px 4px; width: 48px; height: 48px;" alt="" src="files/tib-galleries/3-351/1111-thumb128.jpg"><img class="" title="Click to view" style="margin: 5px 4px; width: 48px; height: 48px;" alt="" src="files/tib-galleries/3-351/1112-thumb128.jpg"><img class="" title="Click to view" style="margin: 5px 4px; width: 48px; height: 48px;" alt="" src="files/tib-galleries/3-351/1113-thumb128.jpg"><img class="" title="Click to view" style="margin: 5px 4px; width: 48px; height: 48px;" alt="" src="files/tib-galleries/3-351/1114-thumb128.jpg"><img class="" title="Click to view" style="margin: 5px 4px; width: 48px; height: 48px;" alt="" src="/files/tib-galleries/3-351/changed--thumb128.png"><img class="" title="Click to view" style="margin: 5px 4px; width: 48px; height: 48px;" alt="" src="files/tib-galleries/3-351/1116-thumb128.jpg"><img class="" title="Click to view" style="margin: 5px 4px; width: 48px; height: 48px;" alt="" src="files/tib-galleries/3-351/1117-thumb128.jpg"><img class="" title="Click to view" style="margin: 5px 4px; width: 48px; height: 48px;" alt="" src="files/tib-galleries/3-351/1118-thumb128.jpg"><img class="" title="Click to view" style="margin: 5px 4px; width: 48px; height: 48px;" alt="" src="files/tib-galleries/3-351/1119-thumb128.jpg"><img class="" title="Click to view" style="margin: 5px 4px; width: 48px; height: 48px;" alt="" src="/files/tib-galleries/3-351/new-10-thumb128.png"><img class="" title="Click to view" style="margin: 5px 4px; width: 48px; height: 48px;" alt="" src="files/tib-galleries/3-351/111-111-thumb128.jpg"><img class="" title="Click to view" style="margin: 5px 4px; width: 48px; height: 48px;" alt="" src="files/tib-galleries/3-351/11112-thumb128.jpg"></div></div><p> </p></div><hr class="hidden"><div class="blueBg"><h2><span style="font-weight: bold;">Other resources</span></h2><p><strong>1.</strong> Stephanie Bell at the National Physics Laboratory has produced a really good guide entitled,<a href="http://www.npl.co.uk/publications/guides/a-beginners-guide-to-uncertainty-of-measurement"> "Beginners Guide to Uncertainty of Measurement" <img class="ico" src="../../../img/icons/pdf-1.png">.</a> An electronic version can be downloaded free.</p><p><strong>2. </strong>Precision versus accuracy by The Chemistry Solution. It contains some useful information for answering multiple choice questions on this topic.</p><p style="text-align: center;"><iframe allowfullscreen="" frameborder="0" height="280" src="//www.youtube.com/embed/TzLnO04uO30?rel=0" width="360"></iframe></p><p style="text-align: center;"><a href="http://youtu.be/TzLnO04uO30">Precision v accuracy <img class="ico" src="../../../img/icons/video-1.png"><span class="anchor" id="video-1" name="video-1"> </span></a></p><hr class="hidden"><p><strong>3.</strong> Uncertainty in measurements by lewischemistry.</p><p style="text-align: center;"><iframe allowfullscreen="" frameborder="0" height="280" src="//www.youtube.com/embed/F7YKc4SOZz4?rel=0" width="360"></iframe></p><p style="text-align: center; "><a href="http://youtu.be/F7YKc4SOZz4">Uncertainty in measurements <img class="ico" height="16" src="../../../img/icons/video-1.png" width="16"><span class="anchor" id="video-2" name="video-2"> </span></a></p><p style="text-align: center; "></p><hr class="hidden"><p><strong>4. </strong>Using significant figures by Brightstorm<strong> </strong></p><p style="text-align: center;"><iframe allowfullscreen="" frameborder="0" height="280" src="//www.youtube.com/embed/_jZAe9xeTFA?rel=0" width="360"></iframe></p><p style="text-align: center;"><a href="http://youtu.be/_jZAe9xeTFA">Using significant figures <img class="ico" src="../../../img/icons/video-1.png"><span class="anchor" id="video-3" name="video-3"> </span></a></p><hr class="hidden"><p><strong>5. </strong>Calculating overall uncertainties by Richard Thornley</p><p style="text-align: center;"><iframe allowfullscreen="" frameborder="0" height="280" src="//www.youtube.com/embed/B7dKWE-0FZY?rel=0" width="360"></iframe></p><div style="text-align: center;"><object height="280" width="360"><param name="movie" value="//www.youtube.com/v/B7dKWE-0FZY?version=3&hl=en_GB&rel=0"><param name="allowFullScreen" value="true"><param name="allowscriptaccess" value="always"></object><a href="http://youtu.be/B7dKWE-0FZY">Calculating overall uncertainties </a><a href="http://youtu.be/_jZAe9xeTFA"><img class="ico" src="../../../img/icons/video-1.png"><span class="anchor" id="video-4" name="video-4"> </span></a><hr class="hidden"></div><p style="text-align: center; "></p></div></section></article><section id="media-extras"><div class="page-actions no-print navbar inline hidden-desktop"><div class="navbar-inner"><ul class="nav"><li><a class="presentation" href="#" onclick="return false;"><i class="fa fa-desktop"></i></a></li><li><a class="print-section-blog" href="#" onclick="return false;"><i class="fa fa-print"></i></a></li><li><a class="page-bookmarker" data-ticket="IB Docs (2) Team" data-pid="17276" href="#" onclick="return false;"><i class="fa fa-star"></i></a></li><li><a class="personal-notes" href="#" onclick="return false;"><i class="fa fa-file-text"></i></a></li><li><a class="" data-toggle="modal" href="#modal-feedback" onclick="return false;"><i class="fa fa-envelope-o"></i></a></li><li class="dropdown"><a class="dropdown-toggle" data-toggle="dropdown" data-target="#" href="#"><i class="fa fa-share-alt"></i></a><ul class="dropdown-menu" role="menu"><li><a class="" target="_blank" title="Share on Twitter" href="https://twitter.com/share?text=%22Uncertainty+%26+errors+%22+-+via+%40InThinker+%23chemistry%0A&url=https%3A%2F%2Fwww.thinkib.net%2Fchemistry%2Fpage%2F17276%2Funcertainty-errors-"><i class="fa fa-twitter-square"></i><span>Twitter</span></a></li><li><a class="" target="_blank" title="Share on Facebook" href="https://www.facebook.com/sharer.php?u=https%3A%2F%2Fwww.thinkib.net%2Fchemistry%2Fpage%2F17276%2Funcertainty-errors-&t=Uncertainty+&+errors+"><i class="fa fa-facebook-square"></i><span>Facebook</span></a></li><li><a class="" href="http://www.linkedin.com/shareArticle?mini=true&url=https%3A%2F%2Fwww.thinkib.net%2Fchemistry%2Fpage%2F17276%2Funcertainty-errors-"><i class="fa fa-linkedin-square"></i><span>LinkedIn</span></a></li><li><a class="" href="https://plus.google.com/share?url=https%3A%2F%2Fwww.thinkib.net%2Fchemistry%2Fpage%2F17276%2Funcertainty-errors-"><i class="fa fa-google-plus-square"></i><span>Google +</span></a></li><li><a class="" href="mailto:?subject=Uncertainty & errors &body=1. Accuracy and precisionWhen marking titration results it is not unusual to come across something like this:Titration of 25.00 cm3 of x mol dm-3 hydrochloric acid with a standardized solution of 1.00 mol dm-3 sodium hydroxide...%0Ahttps%3A%2F%2Fwww.thinkib.net%2Fchemistry%2Fpage%2F17276%2Funcertainty-errors-"><i class="fa fa-envelope"></i><span>Email</span></a></li></ul></li><li><a class="" href="chemistry/teaching-materials"><i class="fa fa-puzzle-piece colored"></i></a></li></ul></div></div><div style="border-top: solid 1px #eee;border-bottom: solid 1px #eee;padding: 4px 0 4px 0;line-height: 1em;color: #666;font-size: .8em"><small><em>All materials on this website are for the exclusive use of teachers and students at subscribing schools for the period of their subscription. 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