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 ten, the second one mental math, and the third one division.
Let’s start converting fractions to decimals with power of ten. 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 ten. 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 zero decimal seven.
Here’s another example, eight-hundredths. Again we’re looking at the power of tenths, 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: zero decimal zero eight. Converting fractions to decimals with power of ten works any time that you have a fraction with the denominator that is a power of ten, whether that be a ten, one hundred, one thousand, ten thousand. As long as it’s a power of ten, you can use this strategy to convert fractions to decimals. But unfortunately, we don’t always get to work with powers of ten 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 twenty to a tenth, hundredth or thousandth? So maybe you think, we can change this twenty to ten 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 denominator, you can come up with a fraction with a base of one hundred. Three-twentieths equals fifteen-hundredths. The final answer then looks like this: zero decimal one five.
But not everything is easily converted with powers of ten or mental math. It would be really difficult for us to try to convert this three-eighths into a power of ten 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 thirty? 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 sixty? Seven times. Seven times eight is fifty-six. Sixty minus fifty-six is four. Bring down a zero. How many times does eight go into forty? Five times. Five times eight is forty. There is no remainder, and we have just discovered that the decimal form of three-eighths is three hundred and seventy-five thousand, zero decimal three seven five.
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 twenty to one hundred 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 twenty. I know that twenty goes into three zero times. And twenty would then go into thirty one time. One times twenty is twenty. Thirty minus twenty is ten. Bring down a zero. How many times does twenty go into one hundred? The answer is five times. Five times twenty is one hundred, and we have a remainder of zero. We found the same answer by using a different strategy, three-twentieths is in fact fifteen-hundredths, zero decimal one five.
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.