(0 . overline{09} times 7 . overline{3}) is e | vedclass

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(A) To solve $(0 . \overline{09} 	imes 7 . \overline{3})$,we first convert the repeating decimals into fractions.$1.$ Convert $0 . \overline{09}$ to

Vedclass · Accepted Answer

$0 . \overline{6}$

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(A) To solve $(0 . \overline{09} 	imes 7 . \overline{3})$,we first convert the repeating decimals into fractions.$1.$ Convert $0 . \overline{09}$ to a fraction:Let $x = 0 . \overline{09} = 0.090909...$$100x = 9.090909...$$100x - x = 9.090909... - 0.090909... = 9$$99x = 9 \implies x = \frac{9}{99} = \frac{1}{11}$.$2.$ Convert $7 . \overline{3}$ to a fraction:$7 . \overline{3} = 7 + 0 . \overline{3} = 7 + \frac{3}{9} = 7 + \frac{1}{3} = \frac{21+1}{3} = \frac{22}{3}$.$3.$ Multiply the fractions:$\frac{1}{11} 	imes \frac{22}{3} = \frac{1 	imes 22}{11 	imes 3} = \frac{22}{33} = \frac{2}{3}$.$4.$ Convert $\frac{2}{3}$ back to decimal:$\frac{2}{3} = 0.666... = 0 . \overline{6}$.

$(0 . \overline{09} \times 7 . \overline{3})$ is equal to

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