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$2.\overline{36}+0.\overline{23}=\text{x}+\text{y}=\frac{234}{99}+\frac{23}{99}=\frac{257}{99}$
$\text{y}=0.\overline{23} \ ...(\text{ii})$
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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