The number 0.121212 ldots in the form frac{p} | vedclass

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Question

(C) Let $x = 0.121212 \ldots$ (Equation $1$)Since there are two repeating digits,multiply both sides by $100$:$100x = 12.121212 \ldots$ (Equation $2$)

Vedclass · Accepted Answer

$\frac{4}{33}$

Vedclass · Answer

(C) Let $x = 0.121212 \ldots$ (Equation $1$)Since there are two repeating digits,multiply both sides by $100$:$100x = 12.121212 \ldots$ (Equation $2$)Subtract Equation $1$ from Equation $2$:$100x - x = 12.121212 \ldots - 0.121212 \ldots$$99x = 12$$x = \frac{12}{99}$Dividing both numerator and denominator by their greatest common divisor,which is $3$:$x = \frac{12 \div 3}{99 \div 3} = \frac{4}{33}$

The number $0.121212 \ldots$ in the form $\frac{p}{q}$ is equal to

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