Fractions to Decimals

In this lesson, we will look at how to convert fractions to decimals.

The following diagram gives some examples of converting between fractions and decimals. Scroll down the page for more examples and solutions.

 

The following diagrams show how to convert from a fraction to a decimal using long division. Scroll down the page for more examples and solutions.

 

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

How to convert a fraction to a decimal?
When we convert a fraction to a decimal, we divide the numerator of the fraction by the denominator. Use long division when necessary and round the decimal if needed.

1. Terminating Decimal
Example:
Convert \(\frac{3}{4} \) to a decimal.

Solution:
Divide 3 by 4
3 ÷ 4 = 0.75

Therefore, \(\frac{3}{4} \) = 0.75

2. Repeating Decimal
Example:
Convert \(\frac{2}{3} \) to a decimal

Solution:
Divide 2 by 3
2 ÷ 3 = 0.6666…
This is a repeating decimal. We write it with a bar over the repeating digit(s): \(0.\bar{6}\)

Therefore, \(\frac{2}{3} = 0.\bar{6} \)

3. Mixed Number
Example:
Convert the \(3 \frac{3}{8}\) to a decimal.

Solution:
Whole number: 3
Fraction: \(\frac{3}{8}\) = 0.375
Combined: 3 + 0.375 = 3.375

Therefore, \(3 \frac{3}{8}\) = 3.375

4. Fraction with a Denominator that’s a Power of 10
Convert the fraction to have a denominator of 10, 100, or 1000, then write as a decimal.
Example:
Convert the \(\frac{3}{5}\) to a decimal.

Solution:
\(\frac{3}{5} = \frac{6}{10} = 0.6 \)

Example:
Convert the \(\frac{7}{20}\) to a decimal.

Solution:
\(\frac{7}{20} = \frac{35}{100} = 0.35 \)

Check out this lesson on converting fractions (powers of 10)

More examples of converting fractions to decimals.

• Show Video Lesson

Converting Between Fractions and Decimals
Learn how to change any decimal value into its fraction equivalent in lowest terms. Review decimal place values in the process and how to reduce to lowest terms.

• Show Video Lesson

When allowed, you can use the calculator to get the decimal. However, for 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.\(\bar{3} \) = 0.33333 …

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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