The value of 1.999 .... in the form frac{p}{q | vedclass

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Question

Let $x=1.999 \ldots=1 . \overline{9}..........(1)$

Then, $10 x=19.999 \ldots=19 . \overline{9}...........(2)$

Subtracting $(1)$ and $(2),$ we ge

Vedclass · Accepted Answer

$2$

Vedclass · Answer

Let $x=1.999 \ldots=1 . \overline{9}..........(1)$

Then, $10 x=19.999 \ldots=19 . \overline{9}...........(2)$

Subtracting $(1)$ and $(2),$ we get

$9 x=18 \Rightarrow x=18 \div 9=2$

$	herefore$ The value of $1.999 \ldots$ in the form $\frac{p}{q}$ is 2 or $\frac{2}{1}$

Hence, $(b)$ is the correct answer.

The value of $1.999 ....$ in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0,$ is

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