How to Convert Decimals to Fractions

The numbers we use in our daily lives can be broken up into two main groups: rational and irrational numbers. Irrational numbers cannot be written out exactly in decimal form since you’d need an infinite number of decimal digits to do so. Rational numbers can be written as decimal numbers that either stop after some number of digits or keep repeating some pattern of digits forever.

In today’s article, we’re going to learn how to take a decimal representation of a rational number and turn it into an equivalent fraction.

What are Terminating and Repeating Decimals?

Before we get into the details of how to actually convert terminating and repeating decimals into fractions, we’d better make sure we understand what it means for a rational number to be a “terminating” or “repeating” decimal in the first place. To see what the difference is, let’s take a look at a few examples of decimal representations of rational numbers:

• 1/4 = 0.25 is a terminating decimal since it has a finite number of decimal digits

• 1/3 = 0.3333… is a repeating decimal since the number 3 goes on forever

• 3/5 = 0.6 is another terminating decimal number

• 7/9 = 0.7777… is a repeating decimal since 7 goes on forever

• 9/11 = 0.818181… is another repeating decimal since the pattern of digits “81” repeat forever.

So a repeating decimal is a rational number whose decimal representation has some repeating pattern, and a terminating decimal is a rational number whose decimal representation eventually stops. (Remember, a decimal that just goes on and on with no repeating pattern is irrational.)

Can a Terminating Decimal Be Written as a Repeating Decimal?

If you think about it though, you’ll see that any terminating decimal number can actually be written as a repeating decimal too. How? Well, since you can always attach an infinite number of zeros to the very end of a number without changing its value, you can put an infinitely long string of zeros on the end of an otherwise terminating decimal…and you’ll have turned it into a repeating decimal!

For example, you can think of the terminating decimal 0.25 as 0.25000… instead. But in this case, none of this really matters since the value of the number is exactly the same no matter how it’s written. And that’s why usually when we say “repeating decimal...

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