Calculate the sum: 0.overline{35} + 0.overlin | vedclass

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Question

(A) Let $x = 0.\overline{35} = 0.353535...$ and $y = 0.\overline{28} = 0.282828...$To convert $0.\overline{35}$ to a fraction: $100x = 35.3535...$,so

Vedclass · Accepted Answer

$0.\overline{63}$

Vedclass · Answer

(A) Let $x = 0.\overline{35} = 0.353535...$ and $y = 0.\overline{28} = 0.282828...$To convert $0.\overline{35}$ to a fraction: $100x = 35.3535...$,so $99x = 35$,which gives $x = \frac{35}{99}$.To convert $0.\overline{28}$ to a fraction: $100y = 28.2828...$,so $99y = 28$,which gives $y = \frac{28}{99}$.Adding the two fractions: $x + y = \frac{35}{99} + \frac{28}{99} = \frac{63}{99}$.Dividing $63$ by $99$ gives $0.636363...$,which is $0.\overline{63}$.

Calculate the sum: $0.\overline{35} + 0.\overline{28}$.

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