### Video Transcript

Fill in the blank using symbol less than, greater than, or equals to. 5.3 divided by 10 blank 5.3 times 0.1.

There are a couple of ways that we can answer this question. The first one is to simply calculate the values of 5.3 divided by 10 and of 5.3 times 0.1. Let’s begin by calculating the value of 5.3 divided by 10. We know that to divide by 10, we need to move every single digit in our number one space to the right. This means that the five moves from being in the ones column to the tenths column, and then the three, which is currently in the tenths column, moves to the hundredths column. And so, 5.3 divided by 10 is 0.53.

But how do we calculate the value of 5.3 times 0.1? Well, let’s begin by imagining there are no decimal points in our question. Let’s work out 53 times one. This, of course, is the multiplicative identity property. We know if we multiply any number by one, we just get that original number, so 53 times one is 53. But then, of course, 5.3 is 10 times smaller than 53 and 0.1 is 10 times smaller than one. And so, the answer to 5.3 times 0.1 will be 10 times smaller than 53 and then another 10 times smaller. That’s the same as being 100 times smaller. Or we could simply divide by 10 by moving the digits one space to the right and then divide by 10 again to move them one space to the right once again. Either way, 53 divided by 100 or divided by 10 and then divided by 10 is 0.53. And so, in fact, the correct symbol is an equal sign.

But there was another way we could have worked this out. Let’s write 0.1 as a fraction in its simplest form. 0.1 as a fraction is equal to one-tenth. So, 5.3 times 0.1 is the same as 5.3 times one-tenth. We can multiply this by writing 5.3 as 5.3 over one, and then multiplying the numerator and the denominators. When we do, we get 5.3 over 10. But that, of course, is the same as saying 5.3 divided by 10. And that of course was the calculation that we had on the left-hand side of our problem. Either way, we see that the symbol that we’re going to use is the equal sign.