Scientific Arithmetic

Scientific Arithmetic

Scientists use scientific notation to help with the arithmetic of large and small numbers

1000000 = 106
0.000001 = 1/1000000 = 10-6
1230000 = 1.23 x 106
0.00000123 = 1.23 x 10-6

The same number can take different forms

1230000 = 1.23 x 106 = 12.3 x 105 = 0.123 x 107
The form 1.23 x 106 is preferred.

To multiply, you add the exponents:

(1.2 x 106) x (2.0 x 105) = 2.4 x 1011

To divide, you subtract the exponents:

(4.2 x 1012) / (2.0 x 108) = 2.1 x 104

To add, you have to make the exponents the same first:

(1.2 x 106) + (2.0 x 105) = (1.2 x 106) + (0.2 x 106) = 1.4 x 106

Try it!

  1. The University of Oregon is located on which river?
  2. In a matchup between the UO and the OSU women's basketball teams, the likely winner is
  3. 456000000 =
  4. 888000 =
  5. (2.0 x 106) x (3.0 x 108) =
  6. (2.0 x 106) x (3.0 x 10-2) =
  7. (6.0 x 106) /(3.0 x 104) =
  8. (2.0 x 106)/ (3.0 x 10-2) =
  9. (2.00000 x 106) + (3.0 x 104) =
ASTR 122 course home page

Updated 27 September 2007

Davison E. Soper, Institute of Theoretical Science, University of Oregon, Eugene OR 97403 USA