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प्रश्न
Express the following recurring decimals as a rational number:
`4.bar18`
उत्तर
`4.bar18` = 4.181818…
= 4 + 0.18 + 0.0018 + 0.000018 + …
Here, 0.18, 0.0018, 0.000018, … are in G.P.
with a = 0.18 and r = 0.01
Since, | r | = |0.01| < 1
∴ Sum to infinity exists.
∴ Sum to infinity = `"a"/(1 - "r") = 0.18/(1 - (0.01)) = 0.18/0.99 = 18/99 = 2/11`
∴ `4.bar18 = 4 + 2/11 = 46/11`.
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