Powers of Ten

With base 10, every exponent is easy to see. A positive exponent counts the zeros: $10^{2} = 100$, $10^{3} = 1000$, and $10^{6}$ is a million. Each step up multiplies by 10 and adds one zero.

A negative power of ten is a reciprocal: $10^{-1} = \frac{1}{10} = 0.1$, $10^{-2} = \frac{1}{100} = 0.01$, and $10^{-3} = \frac{1}{1000} = 0.001$. Each step down in the exponent divides the value by 10.

Powers of ten are the base of scientific notation, which the next chapter covers. In scientific notation, a number is written as a number times a power of ten.