How do you convert decimals to fractions?

Fractions and decimals represent the same things: numbers that are not whole numbers. Any terminating decimal can be converted to a fraction by counting the number of decimal places and putting the decimal's digits over 1. Then move the decimal to the right to the end of the number and add the same number of zeros to the 1. For example:

Start by writing this as .78/1, and then move the decimal places two steps to the right and add two zeros to the 1, so it becomes


Simplified, this fraction would be 39/50.

A terminating decimal is that simple. ("Terminating" means that it ends.) A "repeating" decimal is a little trickier. For example, the decimal for 1/3 is 0.333333 and the 3s go on forever. You should probably just memorize the fractions for the most common repeating decimals, like 1/3 and 2/3 (0.6666666).

To get as close as possible to a correct fraction for a repeating decimal, follow these steps. Suppose you have a number like 0.27777777 . . . This number equals a fraction, and let's call it "x".

 x = 0.27777777 

There is one repeating digit in this decimal, so multiply x by 1, followed by one zero. (In simpler terms, just multiply by 10.):

 10x = 2.7777777 

Now subtract the former from the latter

 10x = 2.7777777 - x = 0.27777777 9x = 2.5 

So 9x = 2.5 (which equals 25/10). Solving this, you'll see that x = 25/90.