Very Small Numbers

A human hair is about 0.00007 meters thick. A small number has many zeros after the decimal point, just as a large number has many zeros at the end. Scientific notation works for small numbers too. It uses the negative exponents from the last chapter.

$0.003$ is 3 thousandths, which is $\frac{3\cdot 1}{1000}$, which is $3\cdot 10^{-3}$. The decimal point moved three places to the right, so that it sits after the 3. The exponent is $-3$. The 3 counts the places the point moved, and the minus sign shows that the number is less than 1.

In scientific notation, the first part is at least 1 and less than 10. The sign of the exponent tells you the size of the number. A positive exponent gives a number that is at least 10. A negative exponent gives a number less than 1. An exponent of zero leaves a number between 1 and 10.