SCIENTIFIC NOTATION
It’s usually much easier to write very large or very small numbers in scientific
notation. For example, the speed of light through empty space is approximately
300,000,000 meters per second. In scientific notation, this number would be written
as 3 × 10^8. Here’s another example: In standard units, Newton’s universal
gravitational constant is about 0.0000000000667; in scientific notation, this number
would be written as 6.67 × 10−11. In general, we say that a number is in scientific
notation when it’s written in the form a × 10n, where 1 ≤ a < 10 and n is an integer.
As the two examples above show, when a very large number is written in scientific
notation, the value of n is a large positive integer, and when a very small number is
written in scientific notation, n is a negative integer with a large magnitude. To
multiply or divide two numbers written in scientific notation, just remember that
10 m × 10n = 10m + n and 10m/10n = 10m − n. So, for example, (3 × 10^8 )(2.5 × 10−12)
= 7.5 × 10−4 and (8 × 10^9 )/(2 × 10−5) = 4 × 10^14.