This video is about orders of magnitude.
We will begin with the basics of orders of magnitude, and then see a few examples of
the order of magnitude of common values.
Let's look at the basics.
There are different ways to define order of magnitude, but a simple way to put it is that
a number rounded to the nearest power of 10 is called an order of magnitude.
Calculating orders of magnitude can be helpful when comparing values, and when deciding whether
a calculated result is sensible or not.
For example, the average height of humans is somewhere around 160 to 170 cm, so when
we round it to the nearest power of 10, we get 100, or 10 to the power of 2.
Now imagine that after a calculation, we get that the height of a human is 6300 cm.
Rounding 6300 to the nearest power of 10, we get 10000, which is 10 to the power of 4.
Now we know from experience that the order of magnitude of our answer should be 100 or
10 to the power of 2.
Since we get an answer with an order of magnitude of 10 to the power of 4, we know right away
that it must be wrong.
Of course, here we are not saying that humans in general are 100 cm tall, but we are saying
that their height is closer to 100 than to 1000 or 10000.
Let's see a few more examples.
I will start by rounding the mess of our turtle to the nearest power of 10, which is 1000,
and this is equal to 10 to the power of 3.
So the order of magnitude here is 10 to the power of 3.
For the bumblebee bet, I will convert the 0.03 into scientific notation, which is 3
times 10 to the power of negative 2.
Next, I will round the 3 to the nearest power of 10, and since this number in scientific
notation is always between 1 and 10, I have to round 3 to either 1 or 10.
It is closer to 1, so we get 1 times 10 to the power of negative 2, and this is equal
to 10 to the power of negative 2, which is the order of magnitude here.
We have to do a bit more work with the diameter of a hydrogen atom.
Its size is 120 p.m. or picometers, and since pico stands for 10 to the power of negative
12, we can write 120 times 10 to the power of negative 12.
Let's round 120 to the nearest power of 10, which will be 100, and we get 10 to the power
of negative 12 here.
100 is 10 to the power of 2, so we can continue as 10 to the power of 2 times 10 to the power
of negative 12, and combining the powers, so adding 2 and negative 12, gives us 10 to
the power of negative 10 meters, which is the order of magnitude here.
Let's see a short summary of this video.
We learned that a number rounded to the nearest power of 10 is called an order of magnitude.
We said that orders of magnitude are used to compare values, which can help decide whether
the result of a calculation is sensible or not, and through our examples we have seen
that when finding the order of magnitude of a number, we often have to work with scientific
notation and metric multipliers.
This concludes our learning about orders of magnitude.
In the next video, we will discuss estimation.