Calculate the fraction of this recurring decimal.
1 answer:
<h3>
Answer: 76/4995</h3>
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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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