Converting Between Fractions, Decimals, and Percents
Believe it or not, fractions, decimals, and percents are all related! If you say a number in the form of a decimal, like .35, it can also be said in the form of a fraction and in the form of a percent. Therefore, it is important that you learn how to convert one to the other, and vice versa. This page will help you convert between fractions, decimals, and percents, so that you can express your numbers however you need to.
Converting Fractions to Decimals
First, we’re going to take a look at converting fractions to decimals. In order to do this conversion, we’re going to need to use long division. If you don’t remember how to do long division, you can refresh your memory by reading the page on Long Division. Otherwise, you’re ready to learn how to change fractions into decimals.
Remember that a fraction indicates division. For example, if you have 3/5 (three fifths), this actually means "three divided by five." Of course, if you want your answer in the form of a fraction, you leave it as 3/5. However, if you want to figure out the decimal number, you will perform that division, like this:
Notice that we put our divisor, 5, on the outside of the division sign, and our dividend, 3, on the inside of the division sign. The numerator of the fraction will always be placed on the inside, as the dividend, and the denominator of the fraction will always be placed on the outside, as the divisor. Then, we performed normal long division. Since we know we cannot put 5 into 3, we added a decimal point, and a zero (0) and then we placed a decimal point in our answer, so that we wouldn’t forget that it’s part of the answer. Then, we continued with division and ended up with 0.6 as our answer. This means that 3/5 can also be written as 0.6—they mean the exact same thing. Therefore, 3/5 = 0.6
Let’s try one more. Let’s say you have the fraction 16/20 and you want to change it into a decimal. Set up long division, as normal, like this:
Thus, 16/20 can also be written as a decimal, which is 0.8. Therefore, 16/20 = 0.8
Converting Decimals to Fractions
Just as we can change fractions into decimals, we can also change decimals into fractions! In order to change decimals into fractions, you need to remember place value. The first decimal place after the decimal is the "tenths" place. The second decimal place is the "hundredths" place. The third decimal place is the "thousandths" place, the fourth decimal place is the "ten thousandths" place, and the fifth decimal place is the "hundred thousandths" place, and so on. It’s important to remember, and know, how many decimal places you have before you can convert decimals to fractions.
For example, let’s say we have the decimal number 0.45 and we want to change it into a fraction. The first step is to figure out what decimal place value you’re working with. In our example, there are two decimal place values filled, which means it is filled to the hundredths place value. Now, we can write our decimal as a fraction. The numerator is the decimal number we see, so in this example the numerator would be 45. The denominator is the place value reached in the decimal, so for this example, since the decimal reaches the hundredths place value, we use 100 as our denominator. Thus, our fraction is 45/100.
The last step of this process is to make sure the fraction is reduced (simplified) all the way. Our fraction is not reduced, so we need to reduce it. Here is the work for reducing our fraction:
Thus, our final answer is 9/20. We know that 9/20 cannot be reduced any further, because there are no common factors (besides 1) between 9 and 20. Therefore, we end with 9/20 as our answer.
Let’s try this one more time. Now your decimal is 0.535, and you want to change it into a fraction. Try it on your own, and then we’ll go through the problem so you can check your answer.
First, you need to figure out how many decimal place values are filled. You see that there are 3 place values filled, so you know that the thousandths place value is filled. Next, you take the decimal number you see, and convert it into the numerator. In this case, your numerator is 535. Finally, you take the place value number, in this case, it’s 1,000, and use it as the denominator. Thus, your fraction is 535/1,000.
Did you remember to reduce it? This one can be reduced, like this:
Thus, your final answer is 107/200.
Converting Decimals to Percents
Converting decimals to percents is all about moving decimal places. For example, let’s say that you have the decimal number 0.55, and you want to change it to a percent. In order to do this, you are simply going to move the decimal point 2 places to the right. Thus, once you move the decimal, you will have 55%. Moving the decimal looks like this:
After you move the decimal point two places to the right, you simply add a percent sign (%) to the end of the number.
One thing to note is that when changing decimals to percents, you will always move the decimal two spaces to the right. This will not change, no matter what kind of number you have.
Let’s try this one more time. Our new decimal is 0.79, and we want to change it into a percent. Try it on your own, and then keep reading for the answer.
Did you get 79%? If you did, you’re right! You move the decimal point two spaces to the right, which would put it after the 9. Then, you just add a percent sign to the end of the number, which makes the final answer 79%.
Converting Percents to Decimals
Converting percents to decimals is also largely about moving the decimal places. Basically, we’re going to do the "opposite" of what we did in order to convert decimals to percents. For example, let’s say that you have 81%, and you want to change it into a decimal. In order to do this, you are going to get rid of the percent sign (%) and then you are going to move the decimal point two places to the left. Thus, once you move the decimal, you will have .81. Moving the decimal looks like this:
Thus, your final answer is 0.81.
Let’s try one more. Your new percent is 90%. Follow the above directions and then compare your answer with ours.
Solution: did you get 0.90? If you did, you’re right! First, you get rid of the percent sign. Then, you move the decimal point two places to the left; so, in this case, it’s going from after the zero to before the 9, to make your final answer 0.90!
Converting Percents to Fractions
Converting percents to fractions is very similar to converting decimals to fractions; in fact, you will follow almost the exact same steps. First, you need to get rid of the percent sign. Then, you will take that number and use it as your numerator. Last, you will use 100 as your denominator; there you have it—a fraction!
Let’s say you have 95% and you want to change it to a fraction. First, you would get rid of the percent sign (%) so that you just have 95. You will use 95 as your numerator. Next, you will use 100 as your denominator. So far, your fraction is 95/100. Your last step, as always, is to check and make sure it is reduced all the way. This fraction needs to be reduced, which can be done like this:
Converting Fractions to Percents
There are two ways to convert fractions into percents. The first way is using a proportion. The second way is by changing the fraction into a decimal, and then converting the decimal into a percent. They both work the same way; it does not matter which method you use, you’ll get the same answer. Use whichever method makes more sense to you.
The first method we’ll go through is using a proportion. We’ll set up the proportion, and then use cross multiplication and a variable to solve for the percent.
First, we need to set up the proportion. We’ll start with the fraction 3/5. Next, we set 3/5 equal to x/100. When written out, it looks like this:
Now, you’re going to cross multiply in order to get an equation. Cross multiplying means you are going to multiply the numbers that are diagonally across from each other. For this example, you would be multiplying 3*100, and 5*x (we’re using the * here to mean multiplication, so that it doesn’t get confused with the variable x). Once we multiply those numbers together, we are going to set the products equal to each other, like this:
Now, we would begin solving the equation for x. Since we’re multiplying 5 times x, we’re going to divide to solve the equation. To get x by itself, we’re going to divide each side by 5. That step looks like this:
Now that each side is divided by 5, we only have x left on the left side of the equation. On the right side, we have 300 divided by 5, which is 60. Therefore, we have x = 60.
Now, we’re almost done! We just need to finish up one more step in making this fraction a percent. You need to take the number 60, and add a percent sign after it, like this: 60%. Then, you’re done! You’ve solved the problem by changing the fraction 3/5 into a percent, which is 60%.
There is another way to solve this problem that doesn’t involve a proportion or cross multiplication. In fact, it uses two conversions we’ve learned already: converting a fraction to a decimal, and converting a decimal to a percent. Just to make sure this makes sense, we’ll go through one to see what it would look like:
Take our fraction from before, 3/5. In order to convert it to a decimal, we need to do long division. Set up and work through the long division; when you’re done, check it with our answer:
We came up with an answer of 0.6—now we need to convert that decimal into a percent. In order to convert a decimal into a percent, we need to move the decimal point two places to the right. For this problem, moving the decimal looks like this:
Notice that we had to add a zero after the 6 in order to move the decimal place. You may have to do this to any numbers that are single digits, as .6 is. Now, we have 60. so all we have to do is add a percent sign to the end, like this: 60%.
There you go! Your fraction is now a percent. And, this answer is the same as the answer from the proportion problem. Either method you use will give you the same answer.