Definition
Power of ten
A power of ten is a number written as 10 raised to an integer exponent.
What it means
Powers of ten make a base-ten ladder. Move the exponent up by 1 and the value becomes 10 times as large. Move it down by 1 and the value becomes one tenth as large.
Remember it
Think of an exponent ladder: each step changes the value by a factor of 10.
Example
10^4 = 10 × 10 × 10 × 10 = 10,000. One step down is 10^3 = 1,000, which is one tenth as large.
Watch for
A number can contain a power of ten without being one. For example, 30 = 3 × 10, but 30 itself is not 10^n for any integer n.
Common mix-up
The exponent counts factors of 10; 10^3 means 10 × 10 × 10, not 10 × 3.
Exact meaning
A power of ten has the form 10^n, where n is an integer. Positive exponents give repeated factors of 10, 10^0 = 1, and negative exponents give reciprocals such as 10^-2 = 0.01.