Convert Repeating Decimals to Fractions

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There are three sets of converting decimals worksheets.
Convert Decimals to Fractions
Convert Decimals to Mixed Numbers
Convert Repeating Decimals to Fractions

Examples, solutions, videos, and worksheets to help Grade 6 students learn how to repeating decimals to fractions. Include dividing decimals word problems.

How to convert a repeating decimal to a fraction?

Condition 1: Single repeating digit (e.g., 0.333…)

Identify the repeating digit(s) and assign it to a variable (e.g., x).
Set up an equation where x represents the repeating part: x = 0.333…
Multiply both sides of the equation by a power of 10 that matches the number of decimal places in the repeating part. In this case, we multiply by 10 because there is one repeating digit after the decimal point: 10x = 3.333…
Subtract the original equation from the multiplied equation: 10x - x = 3.333… - 0.333…
Simplifying the right side gives: 9x = 3
Solve for x by dividing both sides of the equation by 9: x = 3/9
Simplify the fraction if possible: x = 1/3

Condition 2: Repeating block of digits (e.g., 0.126126126…)

Identify the repeating block of digits and assign it to a variable (e.g., x).
Set up an equation where x represents the repeating block: x = 0.126126126…
Multiply both sides of the equation by a power of 10 that matches the number of decimal places in the repeating block. In this case, we multiply by 1000 because there are three repeating digits after the decimal point: 1000x = 126.126126…
Subtract the original equation from the multiplied equation: 1000x - x = 126.126126… - 0.126126126…
Simplifying the right side gives: 999x = 126
Solve for x by dividing both sides of the equation by 999: x = 126/999
Simplify the fraction if possible: x = 14/111

Condition 3: Repeating pattern with non-repeating digits (e.g., 0.12666…)

Identify the non-repeating part and the repeating block of digits.
Set up an equation where x represents the entire repeating pattern: x = 0.12666…
Multiply both sides of the equation by a power of 10 that matches the number of decimal places in the repeating block. In this case, we multiply by 100 because there are two non-repeating digits after the decimal point: 100x = 12.666…
Subtract the original equation from the multiplied equation: 100x - x = 12.666… - 0.12666…
Simplifying the right side gives: 99x = 12.54
Solve for x by dividing both sides of the equation by 99: x = 12.54/99
Simplify the fraction if possible: x = 19/150

Remember to simplify the fractions obtained in the final steps if possible.

The following figure gives steps that will work for any repeating decimals.

Convert Repeating Decimals to Fractions

Have a look at this video if you need to review how to convert repeating decimals to fractions.

Convert Repeating Decimal Numbers to Fractions

Have a look at this video if you want to use a shortcut trick to convert repeating decimals to fractions.

Convert Repeating Decimal Numbers to Fractions (Shortcut)

Click on the following worksheet to get a printable pdf document.
Scroll down the page for more Convert Repeating Decimals to Fractions Worksheets.

More Convert Repeating Decimals to Fractions Worksheets

Printable
(Answers on the second page.)
Convert Repeating Decimals to Fractions #1 (1 repeating digit)
Convert Repeating Decimals to Fractions #2 (2 or more repeating digits)
Convert Repeating Decimals to Fractions #3 (repeating pattern with non-repeating digits)
Convert Repeating Decimals to Fractions #4 (mixed)

Online
Decimals to Fractions
Decimals to Mixed Numbers