Lesson Video: Converting Fractions to Decimals Mathematics • 7th Grade

We show you how to use three strategies to convert fractions to decimals. We use power of ten when the denominator is a power of 10, a bit of mental math to get a denominator with a power of 10, and dividing the numerator by the denominator.


Video Transcript

Let’s look at some strategies for converting fractions to decimals. Here’re the three strategies we’re going to try. The first one is by using power of 10, the second one mental math, and the third one division.

Let’s start converting fractions to decimals with power of 10. Seven-tenths, we can easily convert seven-tenths to a decimal if we remember what the decimal place values are. Here’s a place value chart. Starting after the decimal point, you get tenths, hundredths, and thousandths. The fraction we’re trying to convert has a denominator of 10. This means that our numerator of seven would go in the tenths place. Our fraction doesn’t have anything in the ones place, so we place a zero there, and then put the seven in the tenths place. The decimal form of seven-tenths is 0.7.

Here’s another example, eight hundredths. Again, we’re looking at the power of 10s, thinking about place value, where should the eight go? We place the eight in the hundredths place. This fraction has no whole numbers. Eight hundredths in decimal form looks like this, 0.08. Converting fractions to decimals with power of 10 works any time that you have a fraction with the denominator that is a power of 10, whether that be a 10, 100, 1000, 10000. As long as it’s a power of 10, you can use this strategy to convert fractions to decimals.

But unfortunately, we don’t always get to work with powers of 10 in the denominator. Sometimes, there’re other things. So what should we do when we have a denominator like this one? We’re gonna solve this one with mental math. First, you have to think about the place value system with decimals, ones, decimal, tenths, hundredths, thousandths. So we need to come up with a strategy to take our denominator and put it into one of these systems. How can we change this 20 to a tenth, hundredth, or thousandth? So maybe you think we can change this 20 to 10 by dividing by two. But that doesn’t work easily because three is not divisible by two. So you try again with the hundredths. Then you realize that if you multiply by five for the numerator and the denominator, you can come up with a fraction with a base of 100. Three twentieths equals fifteen hundredths. The final answer then looks like this, 0.15.

But not everything is easily converted with powers of 10 or mental math. It would be really difficult for us to try to convert this three-eighths into a power of 10 using mental math. That’s when we need our third strategy. That’s why we need to know how to convert fractions to decimals with division. So we’ll go back to our example of three-eighths. We wanna convert three-eighths to decimal form. So we set up our problem to do division. We put three inside the box and the eight on the outside. We know that eight goes in the three zero times. And then we bring up our decimal. We then ask the question, how many times does eight go into 30? And that’s three times.

When we subtract, we get six. We bring down another zero and need to ask the question, how many times does eight go into 60? Seven times, seven times eight is 56. 60 minus 56 is four. Bring down a zero. How many times does eight go into 40? Five times, five times eight is 40. There is no remainder. And we have just discovered that the decimal form of three-eighths is 375 thousandths, 0.375.

I want to quickly go back and look at the example we used for our mental math problem. Because maybe it was really hard for you to think about how to convert 20 to 100 in your head. And if that is ever the case, if you’re struggling to use mental math, division will always work. Let’s try it here. We’re going to divide three by 20. I know that 20 goes into three zero times. And 20 would then go into 30 one time. One times 20 is 20. 30 minus 20 is 10. Bring down a zero. How many times does 20 go into 100? The answer is five times. Five times 20 is 100, and we have a remainder of zero. We found the same answer by using a different strategy, three twentieths is in fact fifteen hundredths, 0.15.

Okay, so I know I said we’re going to look at three strategies. But I do have one more strategy we’re going to look at. This one is just a bonus strategy. Sometimes, the simplest and most practical way to convert fractions to decimals is just to use a calculator. A calculator is a helpful tool to help best divide more complex fractions and convert them into decimals. Each of these strategies will help you convert fractions to decimals.

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