Question

If $0.\overline{27}$ is written in simplest fractional form $\frac{p}{q}$, then find $p\times q.$

• A. 35
• B. 23
• C. 33
• D. 37

Answer 1

The correct option is C 33

$x=0.\overline{27}$ ..........(I)

Here the periodicity of the decimal is two.
So multiply both sides of (i) by 100, we have
$100x=27.\overline{27}$ ......….(II)

Subtracting (I) from (II), we get

$99x=27$

$x=\frac{27}{99}=\frac{3}{11}$
i.e., p = 3, q = 11
So, $p\times q=3\times 11=33$