The last digit in the decimal representation of $\left(\frac{1}{5}\right)^{2000}$ is
(a)2
(b)4
(c)5
(d)6
Answer
Answer (as printed): D
Explanation
$\frac{1}{5}=0.2 ;\left(\frac{1}{5}\right)^{2}=(0.2)^{2}=0.04;\left(\frac{1}{5}\right)^{3}=(0.2)^{3}=0.008$; $$\left(\frac{1}{5}\right)^{4}=(0.2)^{4}=0.0016$$ Clearly, for every power which is a multiple of 4, the expression would have 6 as the last digit. So, $\left(\frac{1}{5}\right)^{2000}$ would have 6 as the last digit.
Explanation as extracted from the printed page; notation may be imperfect.