Express 1.23overline{4} in the form frac{p}{q | vedclass

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Question

(A) Let $x = 1.23444...$ (Equation $1$).Multiply by $100$ to shift the decimal point: $100x = 123.444...$ (Equation $2$).Multiply Equation $2$ by $10$

Vedclass · Accepted Answer

$\frac{1111}{900}$

Vedclass · Answer

(A) Let $x = 1.23444...$ (Equation $1$).Multiply by $100$ to shift the decimal point: $100x = 123.444...$ (Equation $2$).Multiply Equation $2$ by $10$ to shift the decimal point again: $1000x = 1234.444...$ (Equation $3$).Subtract Equation $2$ from Equation $3$:$1000x - 100x = 1234.444... - 123.444...$$900x = 1111$.Therefore,$x = \frac{1111}{900}$.

Express $1.23\overline{4}$ in the form $\frac{p}{q}$,where $p$ and $q$ are integers and $q \neq 0$.

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