Question
Express $2.\overline{36}+0.\overline{23}$ as a fraction in simplest form.
✓
Answer
Given: $2.\overline{36}+0.\overline{23}$
Let $\text{x}=2.\overline{36} \ ...(\text{i})$
$\text{y}=0.\overline{23} \ ...(\text{ii})$
First we take $x$ and convert it into $\frac{\text{p}}{\text{q}}$$100x = 236.3636 ...(iii)$
Subtracting $(i)$ from $(iii)$ we get $99\text{x}=234$
$\Rightarrow\text{x}=\frac{234}{99}$
Similarly, multiply $y$ with $100$ as there are $2$ decimal places which are repeating themselves.
$100y = 23.2323 ...(iv) $
Subtracting $(ii)$ from $(iv$) we get $99\text{y}=23$
$\Rightarrow\text{y}=\frac{23}{99}$
Adding $x$ and $y$ we get $2.\overline{36}+0.\overline{23}=\text{x}+\text{y}=\frac{234}{99}+\frac{23}{99}=\frac{257}{99}$
Let $\text{x}=2.\overline{36} \ ...(\text{i})$
$\text{y}=0.\overline{23} \ ...(\text{ii})$
First we take $x$ and convert it into $\frac{\text{p}}{\text{q}}$$100x = 236.3636 ...(iii)$
Subtracting $(i)$ from $(iii)$ we get $99\text{x}=234$
$\Rightarrow\text{x}=\frac{234}{99}$
Similarly, multiply $y$ with $100$ as there are $2$ decimal places which are repeating themselves.
$100y = 23.2323 ...(iv) $
Subtracting $(ii)$ from $(iv$) we get $99\text{y}=23$
$\Rightarrow\text{y}=\frac{23}{99}$
Adding $x$ and $y$ we get $2.\overline{36}+0.\overline{23}=\text{x}+\text{y}=\frac{234}{99}+\frac{23}{99}=\frac{257}{99}$
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