Decimals to Fractions

Decimals and Fractions
Decimals are fractions with denominators that are powers of 10 (like 10, 100, 1000, etc.). When you convert a decimal to a fraction, you are writing it in this fractional form and then simplifying it.

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

 

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

Convert a Terminating Decimal to a Fraction

1. The digits after the decimal point become the numerator.
2. Count the number of decimal places; that’s how many zeros will be in your power of 10 denominator.
3. Simplify the fraction to its lowest terms.

Example:
Convert 0.6 and 0.09 to fractions.

Solution:
\(0.6 = \frac{6}{10} = \frac{3}{5}\)
\(0.09 = \frac{9}{100}\)

Convert a Decimal with a Whole Number
If the decimal has a whole number part, you can convert it to a mixed number.

1. Keep the whole number separate.
2. Convert the decimal part to a fraction.
3. Combine the whole number and the fraction

Example:
Convert 3.12 to a fraction

Solution:
\(3.12 = 3\frac{12}{100} = 3\frac{3}{25}\)

Convert a Repeating Decimal to a Fraction
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

How to change any decimal value into its fraction equivalent in lowest terms?
It also reviews decimal place values in the process and how to reduce to lowest terms.

Example:
Convert the following decimals to fractions
0.8
0.15
0.725

• Show Video Lesson

Decimal to simplified fraction
Here’s an example of how we convert a decimal to a simplified fraction.

Example:
Write 2.75 as a simplified fraction.

• Show Video Lesson

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