find the reduced value of this repeating decimals?

2009-11-17 6:48 am
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2.101
= 2.101 101 101 101 101......

I'm not sure how to construct the geometric series/summation to find the answer.

回答 (1)

2009-11-17 6:55 am
✔ 最佳答案
whatever the repeating decimals are, in this case it is the
digits 101, you divide by 999.

so,
0.101 101 101 101 is 101/999
since 2 = 2(999)/999
=1998/999

2.101 101 101 101
= 2099 / 999


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