Dividing by 0.1 and 0.01

Let's say we're trying to figure out what 2 divided by 1/10 is. So, pause this video and see if you can have a go at that.

All right, now there's a couple of ways that we could approach this. We could just try to think of everything in terms of tenths since we're dividing by one-tenth. Instead of two ones, we could rewrite that two as the same thing as twenty tenths. Twenty tenths divided by, and I could rewrite this as 1/10.

So, if you have 20 of something, and if you want to divide it into groups of one of that something, how many groups are you going to have? Well, you're going to have 20 groups. So this is going to be equal to 20. It's interesting; 2 divided by 1/10 is equal to 20.

Now, what if I were to take—I'm no, no, I'm just going to make up another number. Let's say if I were to take 7 divided by 1/10. What is that going to be equal to? Well, same idea: seven ones is the same thing as seventy tenths. If I divide that by one-tenth, well, seventy of something divided into groups of one of that something is going to be 70 equal groups. So this is going to be equal to 70.

So, 7 divided by 1/10 is equal to 70. 2 divided by 1/10 is equal to 20. You might notice a pattern. Now, there are other ways that we could have approached this. We could have said something like 2 divided by 1/10 is the same thing as 2 over 1/10, and I could write 1/10 like that.

So when you divide by a fraction, that's the same thing as multiplying by the reciprocal. So this is the same thing as 2 times 10. That pattern might be a little bit clearer, which is going to be equal to 20. When you divide by a tenth, it's the same thing as multiplying by 10. The same thing happened over here when we divided by a tenth; it was the same thing as multiplying 7 by 10 to get to 70.

So what do you think is going to happen if we divide by a hundredth? Let's say I have 6, and I am going to—let me make that into a different color. So, let's say I have 6 and I want to divide that by a hundredth. Pause this video and see if you can figure that out.

Well, one way to approach it is we can express everything in terms of hundredths. I really enjoy saying hundredths! So six could be rewritten as each whole is equal to a hundred hundredths. Therefore, six wholes or six ones is going to be equal to six hundred hundredths. So this is going to be equal to 600 hundredths, and then that's going to be divided into equal groups of one hundredth.

So if I have 600 of something and I'm dividing it into equal groups of one of that something, how many equal groups am I going to have? Well, I'm going to have 600 equal groups. Now, another way that we could have approached this is we could have approached it with fractions. We could have said, "Hey, this thing is the same thing as 6 over 100," which I could express like this, which is equal to 6 times the reciprocal of 100. So that's 6 times the reciprocal of 100, which is 100 over 1, or we could just write that as 100, which once again gets us to 600.

So maybe you're seeing a pattern again: when you divide by a hundredth, that's equivalent to multiplying by a hundred. When you divide by a tenth, that's the equivalent as multiplying by ten. So, I'll leave you there and encourage you to think about that.