29:006 Notes on Scientific notation

• In physics we often deal with very small and very large numbers. For example the speed of light is approximately 300,000,000 m/s. The size of an atom is roughly 0.0000000001 m. Rather than writing out all of the zeros, we express these numbers in scientific notation – a decimal number followed by the factor 10 raised to some power.
  
  In scientific notation then:
   

  • The speed of light is roughly 3 x10⁸ m/s (or more precisely  2.99 x10⁸ m/s.
     

  • Small numbers (numbers less than 1) are handled using negative exponents on the 10.
     

  • The size of the atom would be written as 1 x 10^-10 m. 

  ---

  
   

• Examples:

        4, 500,000 = 4.5 x10⁶

        0.000789 = 7.89 x10^-4

• big numbers (greater than 1)

•         10 = 101

•         100 = 10 x 10 = 102

•         1,000 = 10 x 10 x 10 = 103

•         1,000,000 = 10x10x10x10x10x10 = 106

•         1,000,000,000,000 = 1012  (trillion)

•         2000 = 2 x 1000 = 2 x 106

•         2500 = 2.5 x 1000 = 2.5 x 106   

 

• small numbers (less than 1)

29:006 – Practice Problems on Scientific Notation

1.         Express the following numbers in scientific notation.

            (a)                    2,530,000

            (b)                    0.0000072

            (c)                    859

            (d)                    0.001

            (e)                    300,000,000

2.         Express the following in standard notation.

            (a)                    7.35 X 10⁴

            (b)                    8.6 X10^-5

            (c)                    1.87 X10⁵

            (d)                    6 X10⁸

Answers

1.

(a) 2.53 x 10⁶

(b) 7.2 x 10^–6

(c) 8.59 x10²

(d) 1x10^-3

(e) 3 x 10⁸

2. 

(a)       73,500

(b)       0.000086

(c)       187000

(d)       600,000,000