Decimals to Fractions

Fractions are a way of demonstrating how whole things (such as pizza or money) can be divided into smaller things. Decimals are the same thing, only shown in a slightly different way.

Let’s see how to change a decimal into a fraction.

Simply put, a decimal is a number with a period in it. Here are some examples of decimals:

• 1.3
• 23.01
• 5.25

The decimal has two parts. The number to the left of the period (or decimal point, as it’s called) is the whole number. The number to the right of the decimal point is the fractional number, the part that’s smaller than one.

Let’s look at dollars and cents, because that’s how I learned about decimals and fractions. In the third example above, 5.25 would be five dollars and 25 cents — 5 being the whole number, and 25 being the fractional number.

A fraction has two parts. The numerator is the number on top, and the denominator is the number on the bottom. In the fraction 1/2, the numerator is 1 and the denominator is 2.

For decimals, the numerator and denominator will take a couple of steps to find.

To convert the fractional number part of a decimal just follow these steps:

1. Start with the fractional number part — in our first example, it is .3
2. Count how many spots you have to move the decimal point to the right in order to put it after all the numbers — in our first example, that’s one spot to make 3.
3. For your denominator, start with a 1 and add one zero for each spot from step #2 — in our first example, that’s 1 spot, so the denominator is 10.
4. Your numerator is the number to the right of the original decimal — in the first example, that’s 3
5. You now have your numerator and denominator, but don’t forget to include your whole number! In this case, the whole number is 1.
6. Your decimal of 1.3 is the fraction 1 and 3/10

Let’s look at more examples to make sure we understand, following the steps from above. To change the decimal 12.75:

1. The fractional number is .75
2. It takes two spots to move the decimal point past the number — one spot to 7.5, and another spot to 75.
3. The denominator is 1 and two zeroes, or 100.
4. The numerator is 75
5. The whole number is 12
6. The decimal becomes the fraction 12 and 75/100

Let’s try another example. To change the decimal 0.003:

1. The fractional number is .003
2. It takes three spots to move the decimal point past the number — one spot to 0.03, another spot for 00.3, and another spot to 003 (or just 3; you can safely get rid of leading zeroes in a whole number).
3. The denominator is 1 and three zeroes, or 1000.
4. The numerator is 3
5. The whole number is 0 (with no whole number, you can just show the fraction)
6. The decimal becomes the fraction 3/1000

Get More Help!

Click one of these links to get more help from another Cramlet in this same chapter:

• Decimals to Fractions
• Working With Radicals
• Rational Exponents
• Radicals and Roots
• Properties of Real Numbers
• Properties of Exponents
• Multiplying and Dividing Fractions
• Fractions, Decimals, and Percents
• Adding and Subtracting Un-Like Fractions
• Adding and Subtracting Like Fractions
• About Real Numbers
• About Exponents