(A) Let $x = 0.\overline{001} = 0.001001...$ $(1)$Since there are three repeating digits,multiply both sides by $1000$:$1000x = 1.001001...$ $(2)$Subt

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(A) Let $x = 0.\overline{001} = 0.001001...$ $(1)$Since there are three repeating digits,multiply both sides by $1000$:$1000x = 1.001001...$ $(2)$Subtracting equation $(1)$ from equation $(2)$:$1000x - x = 1.001001... - 0.001001...$$999x = 1$$x = \frac{1}{999}$Thus,the number $0.\overline{001}$ in the form $\frac{p}{q}$ is $\frac{1}{999}$.

Class 9 Mathematics Number Systems Real Numbers and their Decimal Expansions

Easy

Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0$ :
$0 . \overline{001}$

A
$\frac{1}{999}$
B
$\frac{1}{9999}$
C
$\frac{-1}{999}$
D
$\frac{1}{990}$

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Real Numbers and their Decimal Expansions

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Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0$ :$0 . \overline{001}$

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