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This video is about orders of magnitude.

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We will begin with the basics of orders of magnitude, and then see a few examples of

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the order of magnitude of common values.

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Let's look at the basics.

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There are different ways to define order of magnitude, but a simple way to put it is that

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a number rounded to the nearest power of 10 is called an order of magnitude.

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Calculating orders of magnitude can be helpful when comparing values, and when deciding whether

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a calculated result is sensible or not.

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For example, the average height of humans is somewhere around 160 to 170 cm, so when

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we round it to the nearest power of 10, we get 100, or 10 to the power of 2.

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Now imagine that after a calculation, we get that the height of a human is 6300 cm.

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Rounding 6300 to the nearest power of 10, we get 10000, which is 10 to the power of 4.

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Now we know from experience that the order of magnitude of our answer should be 100 or

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10 to the power of 2.

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Since we get an answer with an order of magnitude of 10 to the power of 4, we know right away

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that it must be wrong.

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Of course, here we are not saying that humans in general are 100 cm tall, but we are saying

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that their height is closer to 100 than to 1000 or 10000.

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Let's see a few more examples.

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I will start by rounding the mess of our turtle to the nearest power of 10, which is 1000,

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and this is equal to 10 to the power of 3.

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So the order of magnitude here is 10 to the power of 3.

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For the bumblebee bet, I will convert the 0.03 into scientific notation, which is 3

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times 10 to the power of negative 2.

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Next, I will round the 3 to the nearest power of 10, and since this number in scientific

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notation is always between 1 and 10, I have to round 3 to either 1 or 10.

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It is closer to 1, so we get 1 times 10 to the power of negative 2, and this is equal

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to 10 to the power of negative 2, which is the order of magnitude here.

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We have to do a bit more work with the diameter of a hydrogen atom.

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Its size is 120 p.m. or picometers, and since pico stands for 10 to the power of negative

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12, we can write 120 times 10 to the power of negative 12.

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Let's round 120 to the nearest power of 10, which will be 100, and we get 10 to the power

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of negative 12 here.

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100 is 10 to the power of 2, so we can continue as 10 to the power of 2 times 10 to the power

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of negative 12, and combining the powers, so adding 2 and negative 12, gives us 10 to

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the power of negative 10 meters, which is the order of magnitude here.

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Let's see a short summary of this video.

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We learned that a number rounded to the nearest power of 10 is called an order of magnitude.

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We said that orders of magnitude are used to compare values, which can help decide whether

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the result of a calculation is sensible or not, and through our examples we have seen

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that when finding the order of magnitude of a number, we often have to work with scientific

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notation and metric multipliers.

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This concludes our learning about orders of magnitude.

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In the next video, we will discuss estimation.