Decimal Fraction Equivalents

Fraction and decimal equivalents are different ways of representing the same value. Fractions express a part of a whole as a ratio of two integers (e.g., 1/2), while decimals express the same value in base-10 notation (e.g., 0.5). Understanding how to convert between fractions and decimals is essential in math.

Common Fraction and Decimal Equivalents
The following diagram gives some common fraction and decimals equivalents. Scroll down the page for examples and explanations on how to convert repeating decimals to fractions.

 

Fraction & Decimal Worksheets
Practice your skills with the following worksheets:
Fraction Worksheets
Decimal Worksheets

How to Convert Fractions to Decimals

1. Division Method:
   Divide the numerator by the denominator.
   Example: \(\frac{3}{4} = 3 ÷ 4 = 0.75 \)
   
2. Denominator of 10, 100, etc.:
   Convert the fraction to have a denominator of 10, 100, or 1000.
   Example: \(\frac{1}{5} = \frac{2}{10} = 0.2\)
   
3. Repeating Decimals:
   Some fractions result in repeating decimals.
   Example: \(\frac{1}{3} = 0.\bar{3}\)
   Check out this lesson on converting fractions to decimals

How to Convert Decimals to Fractions

1. Terminating Decimals:
   Write the decimal as a fraction with a denominator of 10, 100, etc., and simplify.
   Example: \(0.25 = \frac{25}{100} = \frac{1}{4}\)
   Check out this lesson on converting decimals to fractions
   
2. Repeating Decimals:
   Use algebra to convert repeating decimals to fractions.
   Example: \(0.\bar{6} = \frac{2}{3}\)
   Check out this lesson on converting repeating decimals to fractions

What are the decimal equivalent of fractions that you will need to know for the SAT?
How to Convert a Recurring Decimal Into a Fraction?

When allowed, you can use a calculator to convert between decimals and fractions. However, for the SAT, the College Board recommends that you know the decimal equivalent of the following fractions:

Fraction
Decimal

The bar notation indicates that the 3 and the 6 repeat infinitely, ie: = 0.33333 …

Converting Between Fractions and Decimals
Fractions to Decimals and Decimals to Fractions

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Converting Repeating Decimal Numbers to Fractions
Decimal numbers with an infinitely repeating sequence of digits after the decimal point can be converted into fractions. This chapter explains why.

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Math Lessons & Study Tips : How to Convert a Recurring Decimal Into a Fraction
In order to convert a recurring decimal into a fraction, understand that 1/3 is equal to .333 repeating. Find out how to use a bar to denote a recurring decimal.

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Try out our new and fun Fraction Concoction Game.

Add and subtract fractions to make exciting fraction concoctions following a recipe. There are four levels of difficulty: Easy, medium, hard and insane. Practice the basics of fraction addition and subtraction or challenge yourself with the insane level.

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