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Calculate the fraction of this recurring decimal. ​

Calculate the fraction of this recurring decimal. ​-example-1

1 Answer

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Answer: 76/4995

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Step-by-step explanation:

x = 0.0152152...

10x = 0.152152...

10000x = 152.152...

Subtract the last two equations to find that

  • 10000x-10x becomes 9990x on the left side
  • 152.152... - 0.152152... becomes 152 on the right side

We're left with the equation 9990x = 152 which solves to x = 152/9990

Divide both parts of that fraction by 2 so that the fraction fully reduces to 76/4995 which is the final answer

You can use your calculator to see that 76/4995 = 0.0152152152152... which confirms the answer.

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