Express 0.7overline{39} in the form frac{p}{q | vedclass

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Question

(B) Let $x = 0.7\overline{39} = 0.7393939...$ (Equation $1$).Multiply both sides by $10$ to shift the decimal point: $10x = 7.393939...$ (Equation $2$

Vedclass · Accepted Answer

$\frac{122}{165}$

Vedclass · Answer

(B) Let $x = 0.7\overline{39} = 0.7393939...$ (Equation $1$).Multiply both sides by $10$ to shift the decimal point: $10x = 7.393939...$ (Equation $2$).Multiply Equation $2$ by $100$ to shift the decimal point past the repeating part: $1000x = 739.393939...$ (Equation $3$).Subtract Equation $2$ from Equation $3$:$1000x - 10x = 739.393939... - 7.393939...$$990x = 732$.$x = \frac{732}{990}$.Simplify the fraction by dividing both numerator and denominator by their greatest common divisor,which is $6$:$x = \frac{732 \div 6}{990 \div 6} = \frac{122}{165}$.

Express $0.7\overline{39}$ in the form $\frac{p}{q}$,where $p$ and $q$ are integers and $q \neq 0$.

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