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

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(N/A) Let $x = 0.5 \overline{7}.$$	herefore x = 0.5777...$ $(1)$Multiply both sides by $10$ to shift the decimal point before the repeating part:$10x

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(N/A) Let $x = 0.5 \overline{7}.$$	herefore x = 0.5777...$ $(1)$Multiply both sides by $10$ to shift the decimal point before the repeating part:$10x = 5.777...$ $(2)$Now,multiply equation $(2)$ by $10$ to shift the decimal point after one repeating digit:$100x = 57.777...$ $(3)$Subtract equation $(2)$ from equation $(3)$:$100x - 10x = 57.777... - 5.777...$$90x = 52$$x = \frac{52}{90}$Simplify the fraction by dividing both numerator and denominator by $2$:$x = \frac{26}{45}$Thus,$0.5 \overline{7} = \frac{26}{45}.$

Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0.$
$0.5 \overline{7}$

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Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0.$$0.5 \overline{7}$