Question

If $d=\frac{1}{2^3\times 5^7}$ is expressed as a terminating decimal, how many non zero digits will $d$ have?

• A. One
• B. Two
• C. Three
• D. Seven
• E. Ten

Answer 1

Answer: (B)

Two

Given, $d=\frac{1}{2^3\times 5^7}$.

Multiply by $\frac{2^4}{2^4}$,

$\Rightarrow d=\frac{2^4}{2^3\times 5^7\times 2^4}$

= $\frac{16}{2^7\times 5^7}$

= $\frac{16}{{10}^7}$

=$0.0000016$

Hence, $d$ will have two non-zero digits, $1$ and $6$, when expressed as a decimal.

Therefore, option $B$ is the correct answer.