Express 0.12 overline{3} in the form frac{p}{ | vedclass

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Question

(B) Let $x = 0.12333\ldots$ (Equation $1$)Multiply by $10$ to shift the decimal point: $10x = 1.2333\ldots$ (Equation $2$)Multiply Equation $1$ by $10

Vedclass · Accepted Answer

$\frac{37}{300}$

Vedclass · Answer

(B) Let $x = 0.12333\ldots$ (Equation $1$)Multiply by $10$ to shift the decimal point: $10x = 1.2333\ldots$ (Equation $2$)Multiply Equation $1$ by $100$ to shift the decimal point past the non-repeating part: $100x = 12.333\ldots$ (Equation $3$)Subtract Equation $2$ from Equation $3$:$100x - 10x = 12.333\ldots - 1.2333\ldots$$90x = 11.1$$x = \frac{11.1}{90} = \frac{111}{900}$Simplify the fraction by dividing both numerator and denominator by $3$:$x = \frac{111 \div 3}{900 \div 3} = \frac{37}{300}$Thus,$0.12 \overline{3} = \frac{37}{300}$.

Express $0.12 \overline{3}$ in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0$.

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