How we can express 0-001 with BAR on 001 in the form of p - q- where q is not equal to 0

Let x=0.001 bar=0.001001001....... and 1000x = 1.001001001............. subtract x from 1000x 1000x = 1.001001001......... x = 0.001001001......... 999x ...

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Standard IX

Mathematics

Irrational Numbers

How we can ex...

Question

How we can express $0. ¯ ¯¯¯¯¯¯ ¯ 001$ in the form of $\frac{p}{q}$ ,where $q \neq 0$

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Solution

Let $x = 0. ¯ ¯¯¯¯¯¯ ¯ 001$
$\Rightarrow x = 0.001001001....$ ...(1)
Multiplying both sides by $1000$ , we get,
$\Rightarrow 1000 x = 1. ¯ ¯¯¯¯¯¯ ¯ 001$ ...(2)
Subtracting (1) from (2), we get,
$\Rightarrow 1000 x - x = 1. ¯ ¯¯¯¯¯¯ ¯ 001 - 0. ¯ ¯¯¯¯¯¯ ¯ 001$
$\Rightarrow 999 x = 1$
$\Rightarrow x = \frac{1}{999}$

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How we can express 0.¯¯¯¯¯¯¯¯001 in the form of pq ,where q≠0

Let x=0.¯¯¯¯¯¯¯¯001⇒x=0.001001001.... ...(1)Multiplying both sides by 1000, we get,⇒1000x=1.¯¯¯¯¯¯¯¯001...(2)Subtracting (1) from (2), we get,⇒1000x−x=1.¯¯¯¯¯¯¯¯001−0.¯¯¯¯¯¯¯¯001⇒999x=1⇒x=1999

How we can express $0. ¯ ¯¯¯¯¯¯ ¯ 001$ in the form of $\frac{p}{q}$ ,where $q \neq 0$