Common Fractions with Decimal and Percent Equivalents

Updated April 13, 2021 | Factmonster Staff

How to convert fractions to decimals.

Fractions and decimals are two common ways to write out partial numbers. Here's who to turn one into the other.

How to tackle fractions

Fractions are a common way of writing out partial numbers. A fraction usually means a number of equal parts like "one half" and "two thirds." This is written as one whole number over another whole number. "Two thirds" would be written out as 1/3.

To use fractions, we need to figure out what number goes on top, and what goes on bottom. The number on top is called the numerator; this is the number of parts we have (Two thirds). The number on bottom is called the denominator; this is how many of those parts make one whole (Two thirds).

Because a fraction means a "part" of something, we call fractions "proper" if the number on top is smaller than the number on bottom (this means that it is less than 1). If the number on top is larger we call it an improper fraction.

Improper fractions can also be written out as a mix of a whole number and a fractions. These are called mixed numbers.

Sometimes fractions can be written differently but have the same value. 1/3 is the same as 2/6. These are called equivalent fractions. The way to get equivalent fractions is the multiply or divide the top and bottom numbers by the same number. In general you want to divide down to the smallest numbers you can; this is called simplifying fractions.

How to handle decimals

A decimal is another way of showing a partial number. It's called a "decimal" because it's done in groups of ten ("dec-" in Latin), like normal numbers. With a decimal, though, the numbers go after the 1s place instead of before. The number of places we go beyond 1 are called decimal places. To keep things simple, we mark off the start of these decimal numbers with a decimal point or period. An example would be 1.1 or 5.6

The best way to calculate decimals is using long division. That's a bit of an involved process, so we won't go over that step by step here. The important thing to know is that, most of the time, you only want to write out to the second decimal place (or the "hundredths" place).

Converting fractions into decimal numbers

Converting fractions to decimals is simple once you know your division. To turn a fraction into a decimal, divide the numerator by the denominator. So if you have 3/4, divide 3 by 4.

The result won't always have a simple answer. In some cases, there is no easy way to divide. 1/3, for example, comes out to .33 (with more 3s going on forever). These are called repeating decimals. You show that a decimal repeats by drawing a line over the last two numbers.

Convert decimals to fractions

To convert a decimal into a fraction, you just have to do the same process in reverse. Create a fraction with the decimal as the numerator and "1" as the denominator. Then multiply them both by ten as many times as you need to get whole numbers on top and bottom. This will give you a fraction.

For example, .63/1 will become 63/100 after we multiply the top and bottom by 100.

.05/1 will become 5/100. In this case, we can simplify the fraction down to 1/20. So, .05 = 1/20

Some common decimals and fractions