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# Decimals

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Let $y = 0.(\overline{123}) + (\overline{345})$.  When y is written out as a repeating decimal, what is the sum of the digits in a single repeating period? (In other words, what is the sum of the digits covered by the repeat bar?)

Apr 2, 2021

If by $(\overline{345})$ you meant $0.(\overline{345})$, then the answer would be $0.(\overline{123+345})=0.(\overline{468})$. This means the sum of the digits in one repeating period is $4+6+8=\boxed{18}$