What is the last digit of the decimal expansion of $\frac{1}{2^{10}}$?
I know that $\frac{1}{2}$ is 0.5, so I can start by dividing that by 2 to get $\frac{1}{2^2}$. That gives me 0.25, and I can divide that by 2 to get $\frac{1}{2^3}$. That gives me 0.125, and I can divide that by 2 to get $\frac{1}{2^4}$. That gives me 0.0625, and I can divide that by 2 to get $\frac{1}{2^5}$. That gives me 0.03125, and I can divide that by 2 to get $\frac{1}{2^6}$. That gives me 0.015625, and I can divide that by 2 to get $\frac{1}{2^7}$. That gives me 0.0078125, and I can divide that by 2 to get $\frac{1}{2^8}$. 