Express 0.5overline{7} in the form frac{p}{q} | vedclass

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Question

(A) Let $x = 0.5\overline{7} = 0.5777...$ (Equation $1$).Multiply both sides by $10$ to shift the decimal point:$10x = 5.777...$ (Equation $2$).Multip

Vedclass · Accepted Answer

$\frac{26}{45}$

Vedclass · Answer

(A) Let $x = 0.5\overline{7} = 0.5777...$ (Equation $1$).Multiply both sides by $10$ to shift the decimal point:$10x = 5.777...$ (Equation $2$).Multiply Equation $2$ by $10$ again to shift the decimal point past the repeating digit:$100x = 57.777...$ (Equation $3$).Subtract Equation $2$ from Equation $3$:$100x - 10x = 57.777... - 5.777...$$90x = 52$.$x = \frac{52}{90}$.Simplify the fraction by dividing the numerator and denominator by their greatest common divisor,$2$:$x = \frac{26}{45}$.

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

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