Express 0.overline{4} in the form frac{p}{q}, | vedclass

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Question

(A) Let $x = 0.\overline{4} = 0.4444...$ (Equation $1$).Since there is one repeating digit after the decimal point, multiply both sides by $10$:$10x =

Vedclass · Accepted Answer

$\frac{4}{9}$

Vedclass · Answer

(A) Let $x = 0.\overline{4} = 0.4444...$ (Equation $1$).Since there is one repeating digit after the decimal point, multiply both sides by $10$:$10x = 4.4444...$ (Equation $2$).Subtract Equation $1$ from Equation $2$:$10x - x = 4.4444... - 0.4444...$$9x = 4$$x = \frac{4}{9}$.Thus, $0.\overline{4}$ expressed in the form $\frac{p}{q}$ is $\frac{4}{9}$.

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

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