Question

A bar over a sequence of digits in a decimal indicates that the sequence repeats indefinitely. What is the value of $({10}^4-{10}^2)\left(0.00\overline{12}\right)$

• A. 0
• B. $0.\overline{12}$
• C. 1.2
• D. 10
• E. 12

Answer 1

Answer: (E)

12

$({10}^4-{10}^2)\left(0.00\overline{12}\right)$

= $9900\times$ $0.00\overline{12}$

= $99$ $\times$ $0.\overline{12}$..................(1)

Also, we know that

$0.\overline{12}$ = X

$12.\overline{12}$= 100X

Thus, 99X = 12 or X = $\frac{12}{99}$

So, (1) becomes

$99\times \frac{12}{99}=12$ So, option E