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0.6+0. bar(7)+0.3 bar(7) in form of
(p)/(q)

$5$ . $0.6+0 . \overline{7}+0.3 \overline{7}$ in form of $\frac{p}{q}$

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Evaluate expression when two complex numbers are given

Full solution

Q.

5

.

0.6+0 . \overline{7}+0.3 \overline{7}

in form of

\frac{p}{q}

Convert to fraction: Step $1$ : Convert $0.\overline{7}$ to a fraction. $\newline$ $0.\overline{7}$ means $0.7777...$ , which is a repeating decimal. $\newline$ Let $x = 0.7777...$ $\newline$ $10x = 7.7777...$ $\newline$ Subtract the first equation from the second: $\newline$ $10x - x = 7.7777... - 0.7777...$ $\newline$ $9x = 7$ $\newline$ $x = \frac{7}{9}$
Convert to fraction: Step $2$ : Convert $0.3\overline{7}$ to a fraction. $\newline$ $0.3\overline{7}$ means $0.37777...$ $\newline$ Let $y = 0.37777...$ $\newline$ $10y = 3.7777...$ $\newline$ Subtract the first equation from the second: $\newline$ $10y - y = 3.7777... - 0.37777...$ $\newline$ $9y = 3.4$ $\newline$ $y = \frac{3.4}{9}$

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