Express in the form of
Question:

Express in the form of $\frac{p}{q}: 0 . \overline{38}+1 . \overline{27}$.

 

 

Solution:

Let $0 . \overline{38}=x$

$1 . \overline{27}=y$

x = 0.3838…                                  …(i)
Multiply with 100 as there are 2 repeating digits after decimals
100x = 38.3838…                          …(ii)
Subtracting (i) from (ii) we get
99x = 38

$\Rightarrow x=\frac{38}{99}$

Similarly, we take 
y = 1.2727…                                  …(iii)
Multiply y with 100 as there are 2 repeating digits after decimal.
100y = 127.2727…                       …(iv)
Subtract (iii) from (iv) we get
99y = 126

$\Rightarrow y=\frac{126}{99}$

Now, $x+y=\frac{38}{99}+\frac{126}{99}=\frac{164}{99}$

 

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