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Express the recurring decimal 0.125125125 … as a rational number.

1 Answer

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Best answer

Given:

0.125125125

So, 0.125125125 =

= 0.125 + 0.000125 + 0.000000125 + …

This can be written as

125/103 + 125/106 + 125/109 + …

125/103 [1 + 1/103 + 1/106 + …]

By using the formula,

S = a/(1 – r)

125/103 [1 / (1 – 1/1000)]

125/103 [1 / ((1000 – 1)/1000))]

125/103 [1 / (999/1000)]

125/1000 (1000/999)

125/999

∴ The decimal 0.125125125 can be expressed in rational number as 125/999

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