Scientific Arithmetic

These notes use superscripts, as in 3 x 108. The 8 is supposed to be above and to the right of the 10. If this looks like 2 x 10 8 to you, then your web browser is not yet supporting superscripts. There is another version of this that I wrote last quarter that might work better for you in this case.

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?
    • The Willammette.
    • The Wilammette.
    • The Willamette.
    • The Wilamette.
    • The Willammete.
    • The Wilammete.
    • The Willamete.
    • The Wilamete.
  2. In a matchup between the UO and the OSU women's basketball teams, the likely winner is
    • OSU.
    • UO.
  3. The UO football team is most likely to go to which bowl game next year?
    • The Rose Bowl.
    • The Huka Bowl.
  4. 456000000 =
    • 4.56 x 101.
    • 4.56 x 102.
    • 4.56 x 103.
    • 4.56 x 104.
    • 4.56 x 105.
    • 4.56 x 106.
    • 4.56 x 107.
    • 4.56 x 108.
    • 4.56 x 109.
    • 4.56 x 1010.
    • 4.56 x 1011.
    • 4.56 x 1012.
  5. 888000 =
    • 0.888 x 104.
    • 8.88 x 104.
    • 88.8 x 104.
    • 888 x 104.
    • 8880 x 104.
    • 88800 x 104.
    • 888000 x 104.
  6. (2.0 x 106) x (3.0 x 108) =
    • 6.0 x 106.
    • 6.0 x 108.
    • 6.0 x 1010.
    • 6.0 x 1012.
    • 6.0 x 1014.
    • 6.0 x 1016.
    • 6.0 x 1032.
    • 6.0 x 1048.
  7. (2.0 x 106) x (3.0 x 10-2) =
    • 6.0 x 10-12 .
    • 6.0 x 10-4 .
    • 6.0 x 10-2 .
    • 6.0 x 102.
    • 6.0 x 104.
    • 6.0 x 106.
    • 6.0 x 108.
    • 6.0 x 1010.
    • 6.0 x 1012.
  8. (6.0 x 106) /(3.0 x 104) =
    • 2.0 x 10-6.
    • 2.0 x 10-4.
    • 2.0 x 10-2.
    • 2.0 x 100.
    • 2.0 x 102.
    • 2.0 x 104.
    • 2.0 x 106.
    • 2.0 x 108.
    • 2.0 x 1010.
  9. (2.0 x 106)/ (3.0 x 10-2) =
    • 6.67 x 10-8 .
    • 6.67 x 10-7 .
    • 6.67 x 10-6 .
    • 6.67 x 104.
    • 6.67 x 106.
    • 6.67 x 107.
    • 6.67 x 108.
    • 6.67 x 109.
    • 6.67 x 1010.
  10. (2.00000 x 106) + (3.0 x 104) =
    • 5.000000 x 106 .
    • 2.300000 x 106 .
    • 2.030000 x 106 .
    • 2.003000 x 106 .
    • 2.000300 x 106 .
Davison E. Soper, Institute of Theoretical Science, University of Oregon, Eugene OR 97403 USA soper@bovine.uoregon.edu