File "CE, Topic 1.1.2 - Ref from PaperPlainz on Vimeo.vtt"

Path: /PaperPlainz/Topic 1 Concept Explanations/CE, Topic 112 - Ref from PaperPlainz on Vimeovtt
File size: 7.79 KB
MIME-type: text/plain
Charset: utf-8

WEBVTT

00:00.000 --> 00:04.280
This video is about scientific notation and metric multipliers.

00:04.280 --> 00:10.880
We will discuss why scientific notation is used, see how scientific notation looks like,

00:10.880 --> 00:16.640
discuss examples of how to convert to and from scientific notation, briefly talk about

00:16.640 --> 00:23.560
what metric multipliers are, and finish up with some examples about using metric multipliers.

00:23.560 --> 00:28.880
Let's just start by saying that scientific notation means exactly the same thing as standard

00:28.880 --> 00:29.880
form.

00:29.880 --> 00:34.960
The expression standard form is mainly used in a UK and a few other places.

00:34.960 --> 00:37.640
So why do we use scientific notation?

00:37.640 --> 00:43.240
Simply put, scientific notation is used to express very large and very small numbers.

00:43.240 --> 00:48.640
Its name comes from the fact that it is in the sciences where we come across such numbers.

00:48.640 --> 00:53.680
For example, the distance between stars is very large while the diameter of an atom is

00:53.680 --> 00:55.960
really small.

00:55.960 --> 00:58.920
Let's see how scientific notation looks like.

00:58.920 --> 01:04.800
Scientific notation is a number between 1 and 10 multiplied by 10 to an integer or

01:04.800 --> 01:07.080
whole number power.

01:07.080 --> 01:11.320
Let's see two examples of numbers that are written in scientific notation.

01:11.320 --> 01:18.600
You can see that both 7.1 and 1.836 are numbers between 1 and 10, and they are multiplied

01:18.600 --> 01:23.920
by 10 to the power of 4 and 10 to the power of negative 2 respectively.

01:23.920 --> 01:28.000
Note that both 4 and negative 2 are integers.

01:28.000 --> 01:33.280
Just a side note that scientific notation has a few other technical details, but I won't

01:33.280 --> 01:38.560
go into these because they are not really relevant to what we are covering in this video.

01:38.560 --> 01:41.360
Next we'll see how to work with scientific notation.

01:41.360 --> 01:43.720
We'll convert these four numbers.

01:43.720 --> 01:48.880
Let's start by moving the decimal point to get a number between 1 and 10.

01:48.880 --> 01:54.960
This gives us 4.933867.

01:54.960 --> 02:00.480
In scientific notation, we have to multiply this by 10 to a certain power.

02:00.480 --> 02:05.720
To find the power, we have to see by how many places we move the decimal point and in which

02:05.720 --> 02:06.720
direction.

02:06.720 --> 02:11.440
Here, we move the decimal point by 4 places to the left.

02:11.440 --> 02:17.440
Since we moved the decimal place to the left, the power of 10 will be positive 4.

02:17.440 --> 02:22.560
For the next number, we will move the decimal point 7 places to the right.

02:22.560 --> 02:25.840
This gives us 1.306.

02:25.840 --> 02:29.040
Let's figure out the power of 10 in the multiplication.

02:29.040 --> 02:34.240
Since here, we move the decimal point by 7 places to the right, the power of 10 will

02:34.240 --> 02:36.160
be negative 7.

02:36.160 --> 02:40.560
An important point is that when we move the decimal point to the left, we get a positive

02:40.560 --> 02:45.200
power and when we move it to the right, we get a negative power.

02:45.200 --> 02:50.360
Another way to remember this is that when we convert a large number into scientific notation,

02:50.360 --> 02:55.840
the power will be positive and when we convert a small number into scientific notation, the

02:55.840 --> 02:58.360
power will be negative.

02:58.360 --> 03:03.040
Next let's see how to convert from scientific notation to a regular number.

03:03.040 --> 03:09.720
We will start by writing down 7.1 and since we have a positive 4 in the power of 10 and

03:09.720 --> 03:14.960
we are converting from scientific notation to a regular number, we will move the decimal

03:14.960 --> 03:18.120
point 4 places to the right.

03:18.120 --> 03:25.240
To finish up, we will fill in the empty spaces with zeros, so we get 71,000.

03:25.240 --> 03:31.880
For the next number, we will also start by writing down 1.836 and since here the power

03:31.880 --> 03:39.680
of 10 is negative 2, we will move the decimal point 2 places to the left so it ends up here.

03:39.680 --> 03:44.440
Then we'll fill in the empty space with a zero and I will put another zero in front

03:44.440 --> 03:50.280
of the decimal place and get 0.01836.

03:50.280 --> 03:55.080
You can also give your answer as 0.01836.

03:55.080 --> 03:59.240
Let's continue with metric or SI multipliers.

03:59.240 --> 04:04.000
Note that another name for metric multipliers is prefixes.

04:04.000 --> 04:09.640
Metric multipliers are used with units and similarly to scientific notation, they help

04:09.640 --> 04:12.120
abbreviate large and small numbers.

04:12.680 --> 04:16.360
Let's see a few examples of metric multipliers.

04:16.360 --> 04:21.920
Mega denoted with capital M stands for 10 to the power of 6 and everyday use of this

04:21.920 --> 04:29.320
is in megabytes, which basically means 10 to the power of 6 or 1 million bytes.

04:29.320 --> 04:35.040
Kilo abbreviated with the letter K stands for 10 to the power of 3 and can be seen in

04:35.040 --> 04:36.360
kilogram.

04:36.760 --> 04:43.280
Centi abbreviated with lowercase c stands for 10 to the power of negative 2 and is found

04:43.280 --> 04:50.920
in centimeters and milli lowercase m is 10 to the power of negative 3 and can be seen

04:50.920 --> 04:53.240
in millimeters or milliliters.

04:53.240 --> 04:57.600
Finally, let's see how metric multipliers are used.

04:57.600 --> 05:03.240
Before discussing examples, just a quick note that metric multipliers are found on page 5

05:03.240 --> 05:06.920
of the data booklet, so there's no need to memorize them.

05:06.920 --> 05:10.800
Let's see two examples of using metric multipliers.

05:10.800 --> 05:14.440
We'll start by writing down 28000.

05:14.440 --> 05:20.080
Millie stands for 10 to the power of negative 3, so here we get a multiplication by 10 to

05:20.080 --> 05:25.240
the power of negative 3, so we have to move the decimal point from the end of the number

05:25.240 --> 05:27.760
three places to the left.

05:27.760 --> 05:31.040
This gives us 28 meters.

05:31.040 --> 05:38.800
Let's write down 7.53 and since mega stands for 10 to the power of 6, here we get times

05:38.800 --> 05:41.200
10 to the power of 6.

05:41.200 --> 05:48.800
Let's again write down 7.53 and move the decimal point six places to the right.

05:48.800 --> 05:57.720
After filling in the empty spaces with zeros, we end up with 7,530,000 watts.

05:57.720 --> 05:59.760
Let's summarize this video.

05:59.760 --> 06:04.520
We learned that scientific notation is used to abbreviate large and small numbers, so

06:04.520 --> 06:10.560
that scientific notation is a number between 1 and 10 multiplied by 10 to an integer or

06:10.560 --> 06:12.560
whole number power.

06:12.560 --> 06:17.840
Through examples, we discussed that when converting a large number into scientific notation,

06:17.840 --> 06:24.680
the power of 10 is positive and when converting a small number, the power of 10 is negative.

06:24.680 --> 06:29.680
We also learned that metric multipliers are used with units to abbreviate large and small

06:29.680 --> 06:35.280
numbers and we concluded that there is no need to memorize the metric multipliers because

06:35.280 --> 06:39.000
they are found on page 5 of the data booklet.

06:39.000 --> 06:43.960
This completes our discussion of scientific notation and metric multipliers.

06:43.960 --> 06:46.960
In the next video, we will talk about significant figures.