10th Class Mathematics Real Numbers Question Bank MCQs - Real Numbers

The rational form of \[0.2\overline{54}\]is in the form of \[\frac{p}{q}\]then \[(p+q)\] is:

A) 14

B) 55

C) 69

D) None of these

Correct Answer: C

Solution :

Sol. [c] Let. \[x=0.2\overline{54},\]

then \[x=0.2545454......\] ...(1)

Multiplying eq. (1) by 100. we get

\[100\text{x}=\text{25}.\text{4545}..........\] ...(2)

Subtracting eq. (1) from eq. (2). we get

\[99x=25.2\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,x=\frac{252}{990}=\frac{14}{55}\]

Comparing with \[\frac{p}{q},\]we get

\[p=14\]

and \[q=55\]

Hence, \[\text{p}+\text{q}=\text{14}+\text{55}=\text{69}\]