1.01 Scientific Notation (Standard form)

Powers of 10

The most common number system we use is based on powers of 10

Power of 10
103
102
101
100
10-1
10-2
10-3


  = 1 x 10 x 10 x 10
  = 1 x 10 x 10
  = 1 x 10
  = 1
  = 1 ÷ 10
  = 1 ÷ 10 ÷ 10
  = 1 ÷ 10 ÷ 10 ÷ 10


   
   
   
   
    (= 1 ÷ 10)
    (= 1 ÷ 100)
    (= 1 ÷ 1000)

  Number
    = 1000
    = 100
    = 10
    = 1
    = 0.1
    = 0.01
    = 0.001

In science we have to deal with both very large and very small numbers which are cumbersome to express using conventional numbers. Scientific notation is a way of expressing numbers in a much more convenient format. Calculations can also be performed with simpler processes by using scientific notation (also referred to as standard form)

Expressing numbers in scientific notation

consider the following number 325,000

To convert a number from general format to scientific notation:

Examples

Important
When converting a number to scientific notation we need to decide whether to include the trailing zeros. See the examples above.( 670 = 6.70 x 102 and 9750 = 9.75 x 103)
Whether to include the trailing zeros or not depends on the precision of the number. This is explained in the section on measurement theory (chapter 7). (This is another advantage of using scientific notation, it gives us a convenient way of expressing the precision of a number.)
Unless you are justified in showing greater precision you should normally discard any trailing zeros.