# Video: Dividing Integers by Powers of 10 in Equivalent Expressions Involving Decimals

0.004 ÷ 0.021 = (400 ÷ 21) ÷ ＿.

02:38

### Video Transcript

0.004 divided by 0.021 is equal to 400 divided by 21 divided by blank.

To help us sort this out, I want to take 0.004 divided by 0.021 and write it as a fraction. We wouldn’t normally take decimal numbers and write them as fractions. But in this case, we want to do it to show equivalence. Here, we have 0.004 over 0.021 equal to 400 divided by 21. And that value is divided by something else. When we think about equivalent fractions, we know that if we multiply something by the numerator, we must multiply that same amount by the denominator.

To go from 0.004 to 400, we move our decimal place one, two, three, four, five time. Moving the decimal place five times to the right tells us that we’ve multiplied 0.004 by 100000. In the denominator, our decimal has moved over once, twice, three times, meaning our denominator has only been multiplied by 1000.

In order to keep these values the same, we would need to move the decimal place one, two more times. We would need to multiply the denominator of 21 by 100. If we multiply our denominator by 100, it would look like this. Let’s take our format and put it back in the division format: 400 divided by 21 divided by... Here’s where something a little tricky is going on.

We’ve taken this multiplication symbol and turned it into a division symbol. And that means we’ll need to flip our fraction one over 100. Multiplying something by one over 100 is the same thing as dividing something by 100.

Here, in order to keep both sides balanced, to keep everything equal, we will need to divide 400 divided by 21 by 100.