Question

If $x=0.\overline{7}$, what is the value of $2x$?

• A. $1.\overline{4}$
• B. $1.\overline{5}$
• C. $1.\overline{54}$
• D. $1.\overline{45}$

Answer 1

Answer: (B)

$1.\overline{5}$

We have $x=0.\overline{7}$ ...(1)

Multiplying both sides by 10 we have,

$10x=7.\overline{7}$ ...(2)

Subtracting eq (2) from eq (1) we have:

$10x-x=7.\overline{7}-0.\overline{7}$

or, $x=\frac{7}{9}$

Now $2x=2\times \frac{7}{9}=\frac{14}{9}=1.\overline{5}$