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yaroslaw [1]
3 years ago
11

Calculate the fraction of this recurring decimal. ​

Mathematics
1 answer:
Agata [3.3K]3 years ago
8 0
<h3>Answer:  76/4995</h3>

========================================================

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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