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Express 0. 001 as a fraction in the si...

Express `0. 001 ` as a fraction in the simplest form.

Text Solution

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Let `x = 0.overline001`
Then, `x = 0.001001001… " "…(i)`
Since the repeating block 001 has 3 digits, we multiply x by 1000 to get
`1000x = 1.001001001….." "….(ii)`
Subracting (i) from (ii), we get
`999 x = 1 hArr x = (1)/(999)`.
Hence , `0.overline001= (1)/(999)`.
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