Show that 0.overline{076923} = frac{1}{13}. | vedclass

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(N/A) Let $x = 0.\overline{076923}$.This can be written as $x = 0.076923076923...$ (Equation $1$).Since there are $6$ repeating digits, multiply both

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(N/A) Let $x = 0.\overline{076923}$.This can be written as $x = 0.076923076923...$ (Equation $1$).Since there are $6$ repeating digits, multiply both sides by $10^6 = 1,000,000$:$1,000,000x = 76923.076923076923...$ (Equation $2$).Subtract Equation $1$ from Equation $2$:$1,000,000x - x = 76923.076923... - 0.076923...$$999,999x = 76923$.$x = \frac{76923}{999999}$.Dividing both numerator and denominator by $76923$:$x = \frac{76923 \div 76923}{999999 \div 76923} = \frac{1}{13}$.Thus, $0.\overline{076923} = \frac{1}{13}$.

Show that $0.\overline{076923} = \frac{1}{13}$.

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