Prerequisites: Reviewing Numbers

Powers of 10

Writing out very large and very small numbers such as the distance of Neptune from the Sun, 4,500,000,000 km, or the diameter of a typical atom, 0.00000001 cm, is inconvenient and prone to error. We make use of the "powers of 10" or exponential notation. The distance from Neptune to the Sun is then expressed as 4.5 x 109 km and the diameter of an atom is 1.0 x 10-8 cm. This way of writing numbers is based on the use of exponents, where an signifies a multiplied by itself n  times. For example, 104 = 10 x 10 x 10 x 10 = 10,000. Thus, 4.50 x 109 = 4.50 x 1,000,000,000 = 4,500,000,000. Notice that the exponent (9 in this case) is just the number of places the decimal point is moved to the right to obtain the fully written-out number.

For numbers less than 1, say 0.01, the exponent power of 10 is written with a negative sign: zero point zero one equals one divided by one hundred equals one divided by ten squared equals ten to the power of negative two . Similarly, 0.002 = 2 x 10-3. The decimal point has again been moved the number of places expressed in the exponent.