### Instruction: What is the last digit of the decimal expansion of $\frac{1}{2^{10}}$?### Response: 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 $\frac{1}{2^8}$.
That gives me 0.00390625, and I can divide that by 2 to get $\frac{1}{2^9}$.
That gives me 0.001953125, and I can divide that by 2 to get $\frac{1}{2^{10}}$.
That gives me 0.0009765625, and I can see that the last digit is 5.