How to Convert Decimals that Don’t Go On Forever Into Fractions

Learn how to convert this type of decimal into a fraction.

Jason Marshall, PhD
1-minute read

The first digit to the right of a decimal point is the number of tenths (or 1/10s), the next digit to the right is the number of hundredths (or 1/100s), the next is the number of thousandths (1/1000s), and so on. Which means that any decimal that doesn’t go on and on forever can be turned into a fraction that consists of some number of tenths, hundredths, thousands, or whatever, depending on the number of digits in the decimal.

For example, how do you convert the decimal 0.5 into a fraction? Well, since the first digit to the right of the decimal point represents the number of tenths, we know that 0.5 is the same thing as 5 tenths, or 5 x 1/10 = 5/10 = 1/2. How about a longer decimal like 0.312? In this case, since the final digit of the decimal is in the thousandths place, 0.312 is the same thing as 312 thousandths, or 312 x 1/1000 = 312/1000. We can reduce the fraction 312/1000 by dividing the top and bottom by 8 to find that 0.312 = 39/125.
For more, see How To Convert Decimals to Fractions

Math image courtesy of Shutterstock

About the Author

Jason Marshall, PhD

Jason Marshall is the author of The Math Dude's Quick and Dirty Guide to Algebra. He provides clear explanations of math terms and principles, and his simple tricks for solving basic algebra problems will have even the most math-phobic person looking forward to working out whatever math problem comes their way.