Let D be a recurring decimal of the form D=0.a1 a2 a1 a2....

Two ways to solve this question:

1) When there is a recurring number i.e non-terminating number, the number can be expressed in the below form

Suppose N = 0.abababababab......

N can be written as
===> __
==>0.ab


To convert any recurring number to fraction form, divide the number by 9,99,999,9999, depending on the no. of recurring digits.

Here we have two recurring digits, so N=ab/99,
Similarly if we have,
====> _____
M = 0.abcde, them M = abcde/99999

NOTE: this is only for numbers in the form of 0.abcdef..... , not for normal recurring number 123123123....

Now in this question, we have
===> ____
D= 0.a1a2

Therefore, D=a1a2/99

Lets try each option and multiple it by D

For C, we have (a1a2/99)*198 => 2* a1a2, this will be an integer.

So option C is correct, for other option we are getting fractional terms.

2) Second way

D= 0.a1a2a1a2a1a2.......
===> ____
D=0.a1a2

Now,
=========> ____
100D= a1a2.a1a2

Now, 100D - D => a1a2 ( Both recurring parts will be subtracted)
99D = a1a2
D = a1a2/99

Rest same as explained 1st way.


Thanks,
Jai

KUDOS if it Helped..!!!