$$1.\overline {27} $$ in the from $$\frac{p}{q}$$ is equal to : Options: A . &nbsp$$\frac{127}{100}$$ B . &nbsp$$\frac{14}{11}$$ C . &nbsp$$\frac{73}{100}$$ D . &nbsp$$\frac{11}{14}$$

$$1.\overline {27} $$ in the from $$\frac{p}{q}$$ is equal to :

Question

$$1.\overline {27} $$ in the from $$\frac{p}{q}$$ is equal to :

Options:

A . $$\frac{127}{100}$$

B . $$\frac{14}{11}$$

C . $$\frac{73}{100}$$

D . $$\frac{11}{14}$$

Answer: Option B
$$\eqalign{
& = 1.\overline {27} \cr
& = 1 + 0.\overline {27} \cr
& = 1 + \frac{{27}}{{99}} \cr
& = 1 + \frac{3}{{11}} \cr
& = \frac{{11 + 3}}{{11}} \cr
& = \frac{{14}}{{11}} \cr} $$

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