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This video is about absolute, fractional, and percentage uncertainty.

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We will briefly return to absolute uncertainty,

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the topic that we covered in more depth in the previous video,

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and then we will see a few examples of calculating fractional and percentage uncertainty.

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Due to the measuring tools that we use and the way we carry out measurements,

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we never actually get an exact value when we measure something.

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Instead, we get a range in which our measured value lies.

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We use absolute uncertainty to show this range when we record our data values.

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So when we say that the mass of an apple is 278.6 plus minus 0.1 gram,

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where 0.1 gram is the absolute uncertainty,

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we mean that we don't know exactly the mass of the apple,

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but it lies somewhere between 278.5 and 278.7 grams.

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Similarly, when we measure the temperature of the C and get 6.0 plus minus 0.5 degrees Celsius,

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we mean that the water temperature is somewhere between 5.5 and 6.5 degrees Celsius,

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and probably conclude that we should wear a wet suit when we go for a swim.

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Finally, when the time taken by an object to fall from a table is 0.50 plus minus 0.25 seconds,

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the estimated value of this time is somewhere between 0.25 and 0.75 seconds.

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Next, let's discuss fractional and percentage uncertainty.

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Let's say we record our measured value as x plus data x, where data x is the absolute uncertainty.

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Then, the fractional uncertainty is expressed as the absolute uncertainty divided by the measured quantity,

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in other words, data x over x. To find a percentage uncertainty,

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we just have to convert our fractional uncertainty into a percentage, so multiply by 100%.

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Let's see two examples. In the first example, we have a kitten whose mass is given to be 400

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plus minus 80 grams, and we have to find the fractional and the percentage uncertainty in the

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mess of this kitten. The measured mass is 400 grams, and the absolute uncertainty in the mass,

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data m is 80 grams. Based on what we discussed above, the fractional uncertainty is data m over m.

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This is equal to 80 over 400, and after simplifying, so canceling the zeros and dividing 8 by 40,

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we get 1 over 5. This is the fractional uncertainty in the mess of the kitten.

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To find the percentage uncertainty, we simply have to multiply the fractional uncertainty by 100%.

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So we get 1 over 5 times 100%, and since 1 over 5 is 0.2, this is equal to 20%.

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This is the percentage uncertainty in the mess of the kitten.

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The uncertainty, in example, is given a bit differently. Sometimes, instead of the absolute uncertainty,

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the percentage uncertainty is given together with the measured value.

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So here we are given that the time it takes for a toy car to roll down a slope is 15 seconds

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plus minus 10%. So we are given the percentage uncertainty, and we have to find the fractional

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and the absolute uncertainty. Let's start with the fractional uncertainty in the time,

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which is delta t over t. To find this, we simply have to convert 10% into a fraction or decimal.

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So we get 10%, divided by 100%, which is equal to 0.1 or 1 over 10. This is the fractional uncertainty.

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It is okay to leave the fractional uncertainty in a decimal form.

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Finally, let's find the absolute uncertainty, which is delta t. To do this, we have to multiply the

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measured value, so 15 seconds, by the fractional uncertainty, so 0.1. Another way to think about it

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is that here we have to find 10% of 15 seconds. This is equal to 1.5 seconds, and this is the

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absolute uncertainty here. Let's summarize what we have discussed in this video. We have seen that

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measurement in sciences does not give us an exact value, so we use absolute uncertainty to

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express the range where measured value lies. We also learned that when a quantity is given as x

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plus minus delta x, the absolute uncertainty in this quantity is plus minus delta x. The fractional

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uncertainty is delta x over x, and the percentage uncertainty is delta x over x multiplied by 100%.

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This wraps up our discussion about absolute, fractional, and percentage uncertainty.

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In the next video, we will learn about propagating uncertainties.