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?
• 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. 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.
4. 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.
5. (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.
6. (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.
7. (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.
8. (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.
9. (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 .