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Pure recurring decimals to fractions

Let equal the recurring decimal. Multiply by a power of 10 that shifts one complete repeating block.

  • Let equal the recurring decimal. Multiply by a power of 10 that shifts one complete repeating block.
  • Subtract the original equation so the identical infinite tails cancel.
  • Solve for and simplify. A one-digit block uses ; a two-digit block uses .

Example 1

Write the recurring decimal as a fraction in simplest form.

Let be the decimal.Two digits recur, so multiply by 100.Subtract from .Divide both sides by 99.

Example 2

Write the recurring decimal as a fraction in simplest form.

Let be the decimal.Two digits recur, so multiply by 100.Subtract from .Divide both sides by 99.

Remember
Use the worked steps to check your method, not just the final answer.

Your turn

Question 1

Write the recurring decimal as a fraction in simplest form.

Check answer
Let be the decimal.Two digits recur, so multiply by 100.Subtract from .Divide both sides by 99.
Question 2

Write the recurring decimal as a fraction in simplest form.

Check answer
Let be the decimal.Two digits recur, so multiply by 100.Subtract from .Divide both sides by 99.
Question 3

Write the recurring decimal as a fraction in simplest form.

Check answer
Let be the decimal.Two digits recur, so multiply by 100.Subtract from .Divide both sides by 99.
Question 4

Write the recurring decimal as a fraction in simplest form.

Check answer
Let be the decimal.Two digits recur, so multiply by 100.Subtract from .Divide both sides by 99.
Question 5

Write the recurring decimal as a fraction in simplest form.

Check answer
Let be the decimal.Two digits recur, so multiply by 100.Subtract from .Divide both sides by 99.
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