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How to Convert a Repeating Decimal into a Fraction

Example 1

Convert the decimal 0.47474747 ... into a fraction.

1. Use a letter to represent the decimal 0.47474747 ...

= 0.4747474747 ... ( 1)

2. Multiply both sides of the equation by 100, because the decimal has 2 repeating digits. When

multiplying the right side by 100, move the decimal point two places to the right.

100() = 100(0.4747474747 ... )

100 = 47.4747474747 ... ( 2)

3. Subtract equation 1 from equation 2.

100 = 47.4747474747 ...

= 0.4747474747 ...

99 = 47

4. Solve the equation for .

99 = 47

99 47

99 = 99

= 47

99

So, we converted the repeating decimal into a fraction.

0.47474747474747 ... = 47

99

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Example 2

Convert the decimal 0.222222 ... into a fraction.

1. Use a letter to represent the decimal 0.222222 ...

= 0.222222 ... ( 1)

2. Multiply both sides of the equation by 10, because the decimal has 1 repeating digit. When

multiplying the right side by 10, move the decimal point one place to the right.

10() = 10(0.222222 ... )

10 = 2.22222 ... ( 2)

3. Subtract equation 1 from equation 2.

10 = 2.22222 ...

= 0.222222 ...

9 = 2

4. Solve the equation for .

9 = 2

9 2

9 =9

=2

9

So, we converted the repeating decimal into a fraction.

0.222222 ... = 2

9

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Example 3

Convert the decimal 0.285714285714 ... into a fraction.

1. Use a letter to represent the decimal 0.285714285714 ...

= 0.285714285714 ... ( 1)

2. Multiply both sides of the equation by 1,000,000, because the decimal has 6 repeating digits. When

multiplying the right side by 1,000,000, move the decimal point six places to the right.

1,000,000() = 1,000,000(0.285714285714 ... )

1,000,000 = 285,714.285714 ... ( 2)

3. Subtract equation 1 from equation 2.

1,000,000 = 285,714.285714 ...

= 0.285714285714 ...

999,999 = 285,714

4. Solve the equation for .

999,999 = 285714

999,999 285,714

999,999 = 999,999

= 285,714

999,999

Reduce the fraction.

= 285,714 ? 142,857 2

999,999 ? 142,857 = 7

So, we converted the repeating decimal into a fraction.

0.285714285714 ... = 2

7

How do you turn decimals into a fraction? Convert Decimals to Fractions. Step 1: Write down the decimal divided by 1, like this: decimal 1. Step 2: Multiply both top and bottom by 10 for every number after the decimal point. (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.) Step 3: Simplify (or reduce) the fraction.

Author: Elena Belinski

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CreationDate: Sun Feb 4 07:50:40 2018

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