Question

0.001bar change into fraction​

Answer 1

Let x=0.001

 bar=0.001001001....... and

1000x = 1.001001001.............

subtract x from 1000x

 999x = 1.000000000..........

 999x = 1

     x  =   1/999


           

Answer 2

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Convert 0.001bar into fractional form.

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$\sf let \: us \: consider \: the \: number \: as \: x \\\sf x = 0.001001001.... \\\sf the \: periodicity \: is \: 3. \: it \: means \: there \: are \: 3 \: digits \:\\\sf after \: the \: decimal \: point \\\sf multiply \: both \: the \: sides \: by \: 1000 \\\sf 1000x = 001.001001... \\ \sf = 1000x - x = 001.001.... - 0.001001... \\ \sf = 999x = 1 \\\sf x = \frac{1}{999}$