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Find the exact value of the repeating de...

Find the exact value of the repeating decimal 0.4545…

Text Solution

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This can be represented by a geometric series, `0.45+0.0045+0.000045+..,` with `t_(1)=0.45` and r = 0.01
Since `|r| lt1,`
`S=(0.45)/(1-0.01)=(0.45)/(0.99)=(45)/(99)=(5)/(11)`
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