Question

Represent 0.353535… in a rational form. How will you verify whether the obtained fraction is reccurring or non-recurring? [4 MARKS]

Answer 1

Concept : 2 Marks
Calculation : 2 Marks

Let x = 0.353535...

100x = 35.35353535...

99x = 35

$Hence,x=\frac{35}{99}$

In order to identify whether a rational number is non-recurring, the denominator should be of the form $2^n\times 5^m$(where n and m are whole numbers), otherwise it is recurring.
Since the denominator of x is not of the form $2^n\times 5^m$(where n and m are whole numbers), the obtained fraction is recurring.