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Question
Express the following recurring decimal as a rational number:
`0.bar(7)`
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Solution
`0.bar(7)` = 0.7777 ...
= 0.7 + 0.07 + 0.007 + …
The terms are in G.P.
∴ a = 0.7, r = `0.07/0.7` = 0.1
Since |r| = |0.1| < 1
∴ Sum to infinity exists.
∴ Sum to infinity = `"a"/(1 - "r")`
= `0.7/(1 - 0.1)`
= `0.7/0.9`
= `7/9`
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