Relating Fractions and Decimals

An error occurred trying to load this video.

Try refreshing the page, or contact customer support.

Coming up next: How to Find Least Common Denominators

You're on a roll. Keep up the good work!

Take Quiz Watch Next Lesson
Your next lesson will play in 10 seconds
  • 0:01 Fractions & Decimals
  • 1:36 Changing to a Fraction…
  • 3:22 Changing to a Decimal…
  • 4:00 Choosing Between…
  • 5:39 Lesson Summary
Save Save Save

Want to watch this again later?

Log in or sign up to add this lesson to a Custom Course.

Log in or Sign up

Speed Speed
Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Watch this video lesson to learn how to use both fractions and decimals to help you solve problems. Learn how to change between the two to use the best one for your problem.

Fractions and Decimals

Did you know that in math, fractions and most decimals are related to each other? Yes, indeed they are. In this video lesson, you will learn about this relationship and how you can use it to your advantage in helping you to solve your problems. You will learn how to choose between the two to make your problem-solving life that much easier. So, are you ready to get going? Let's go!

We begin with a brief definition of a fraction and a decimal. A fraction is a part of a whole. It is written with a number on top, the numerator, and a number on bottom, the denominator, with either a slanted slash or a horizontal slash between the two numbers. You can think of fractions in terms of pies. The fraction 3/4, for example, means that if you cut a piece of pie into 4 slices, then 3 of those slices are yours.

A decimal is a number with a decimal point. If you go shopping at all, you will see decimal numbers everywhere. How much does lipstick cost? $7.99. That's a decimal. How much do your favorite running shoes cost? $89.99. That's a decimal.

Earlier I said that most decimals are related to fractions. The only decimals that are not related to fractions are the ones that keep on going and going and going - the ones that never end. For example, the number pi (not the pie you eat, but the mathematical constant) is not related to a fraction because it keeps going and going and never ends. Decimals and fractions are related to each other in that you can easily convert one to the other. So, let's see how this is done.

Changing to a Fraction from a Decimal

First, let's see how to go from a decimal to a fraction. It's actually quite simple. Let's try converting 7.89.

We first write the number before the decimal point down. Now we convert the number after the decimal point into a fraction. The number after the decimal point will be our top number, our numerator. Our denominator, our bottom number, will be a 1 followed by zeroes. The number of zeroes will equal the number of decimal spaces we have.

So, we count the number of digits we have after the decimal point. We count 2, so we will have 2 zeroes on the bottom following our 1. So, our decimal 7.89 turned into a fraction is 7 89/100. This is a mixed fraction.

We can turn it into an improper fraction by multiplying our whole number with the denominator and adding the numerator part of our fraction part. This will become our new numerator. So, the new numerator of 7 89/100 is 7 * 100 + 89 = 789. So, 7 89/100 turned into an improper fraction is 789/100.

See if you can turn 0.3 into a fraction. How many decimal spaces do we have? We have 1. So, how many zeroes will we have after the 1 in our denominator? We will have 1 zero. So, our fraction is 3/10.

We left our fractions as they are in both of these cases because they are already as reduced as they can be. If, however, we ended up with a fraction such as 8/10, we could reduce it to 4/5.

Changing to a Decimal from a Fraction

Now let's see how we change fractions into decimals. Let's try changing 1/8 into a decimal. Notice that the slash is the same slash that we use to mean division in algebra. Remember that part and you will know how to turn a fraction into a decimal.

Yes, you guessed it! We will divide to find our decimal. Dividing 1 by 8, we get 0.125, and there we have our decimal.

Why don't you try turning 3/4 into a decimal? What do you do? Yes, you divide 3 by 4. What do you get? 0.75. You got it!

To unlock this lesson you must be a Member.
Create your account

Register to view this lesson

Are you a student or a teacher?

Unlock Your Education

See for yourself why 30 million people use

Become a member and start learning now.
Become a Member  Back
What teachers are saying about
Try it risk-free for 30 days

Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Transferring credit to the school of your choice

Not sure what college you want to attend yet? has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

Create an account to start this course today
Try it risk-free for 30 days!
Create an account