(a) write the repeating decimal as a geometric series, and (b) write its sum as the ratio of two integers. 0.overline{81}

boitshupoO 2020-12-31 Answered
(a) write the repeating decimal as a geometric series, and (b) write its sum as the ratio of two integers. 0.81
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Expert Answer

Nathanael Webber
Answered 2021-01-01 Author has 117 answers
Given decimal: 0.81
(a) For the repeating decimal 0.81, we can write
0.81=0.818181...
=0.81+0.0081+0.000081+0.00000081+...
=81102+81104+81106+...
=n=081102(1102)n (b) Given Series: =n=081102(1102)n
Given series is a Geometric series with ratio r=1102 and a1=81102
So the sum is =a1(1r)
=81100(11100)
=8199
=911
Result
911
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