Q. If $a,\ b,\ c$ are digits, then the rational number represented by 0. $cababab\ldots$ is
A) $\frac{cab}{990}$
B) $\frac{99c + 10a + b}{99}$
C) $\frac{99c + ba}{990}$
D) $\frac{99c + 10a + b}{990}$
Explanation
(d)
Let $x = 0.cababab\ldots$
$10x = c.ababab\ldots$ …(i)
And $100 \times 10x = cab.abab\ldots$ …(ii)
On subtracting Eq. (i) from Eq.(ii), we get
$990x = cab - c$
$\Rightarrow \ \ x = \frac{100c + 10a + b - c}{990}$
$= \frac{99c + 10a + b}{990}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.