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

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(D) Let $x = 0.00323232 \ldots = 0.00\overline{32} \quad \dots(1)$Multiply equation $(1)$ by $100$ to shift the decimal point:$100x = 0.323232 \ldots

Vedclass · Accepted Answer

$\frac{8}{2475}$

Vedclass · Answer

(D) Let $x = 0.00323232 \ldots = 0.00\overline{32} \quad \dots(1)$Multiply equation $(1)$ by $100$ to shift the decimal point:$100x = 0.323232 \ldots = 0.\overline{32} \quad \dots(2)$Multiply equation $(2)$ by $100$ again to shift the decimal point past the repeating part:$10000x = 32.323232 \ldots = 32.\overline{32} \quad \dots(3)$Subtracting equation $(2)$ from equation $(3)$:$10000x - 100x = 32.\overline{32} - 0.\overline{32}$$9900x = 32$$x = \frac{32}{9900}$Simplifying the fraction by dividing both numerator and denominator by $4$:$x = \frac{32 \div 4}{9900 \div 4} = \frac{8}{2475}$

Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0$ :
$0.00323232 \ldots$

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Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0$ :$0.00323232 \ldots$