Express \(0.2\overline 7 \) in the form \(\frac{p}{q}\), where p and q are integers and q ≠ 0.

Question

Question

This question was previously asked in

RRB Group D 28 Sept 2022 Shift 3 Official Paper

Answer 1

Formula used:

If we have number in this form say \(0.a \bar b\)

Then, \(0.a \bar b\) = \(ab - a\over 90\)

In this the digit without bar is subtracted from the number

Now, this fraction is in the form of p/q

Calculation:

Here, we have \(0.2\bar7\)

As, here we have bar on only one digit

Also, 2 is without bar so it will get subtracted from 27 in numerator

So, \(0.2\bar7\) = \(27 -2\over90\) = 25/90 = 5/18

Now, 5/18 is is in the form of p/q

Hence, it can be expressed in the form of p/q is 5/18 .