Express the following in the form frac{p}{q}, | vedclass

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(C) Let $x = 0.1\overline{34} = 0.1343434... \quad ....(1)$Multiply both sides by $10$ to shift the non-repeating part:$10x = 1.343434... \quad ....(2

Vedclass · Accepted Answer

$\frac{133}{990}$

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(C) Let $x = 0.1\overline{34} = 0.1343434... \quad ....(1)$Multiply both sides by $10$ to shift the non-repeating part:$10x = 1.343434... \quad ....(2)$Multiply equation $(2)$ by $100$ to shift the repeating part:$1000x = 134.343434... \quad ....(3)$Subtract equation $(2)$ from equation $(3)$:$1000x - 10x = 134.343434... - 1.343434...$$990x = 133$Therefore,$x = \frac{133}{990}$.

Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0$ :
$0.1\overline{34}$

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Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0$ :$0.1\overline{34}$