# Scientific Notation

Adapted from `Scientific Arithmetic' by Davison E. Soper at the University of Oregon.

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

1,000,000 = 106
0.000001 = 1/1,000,000 = 10-6
1,230,000 = 1.23 × 106
0.00000123 = 1.23 × 10-6

The same number can take different forms:

1,230,000 = 1.23 × 106 = 12.3 × 105 = 0.123 × 107
(The form 1.23 × 106 is usually preferred, because the constant in front (1.23) is between 1 and 10.)

To multiply, you add the exponents:

(1.2 × 106) × (2 × 105) = (1.2 × 2) × 10(6+5) = 2.4 × 1011

To divide, you subtract the exponents:

(4.2 × 1012) ÷ (2 × 108) = (4.2 ÷ 2) × 10(12-8) = 2.1 × 104

To add or subtract numbers in scientific notation, you have to make the exponents the same first:

(1.2 × 106) + (2 × 105) = (1.2 × 106) + (0.2 × 106) = 1.4 × 106

Test yourself: Select the right answer to each question, and click on it to check.

1. What is 456,000,000 in scientific notation?
2. What is 8.88 × 103 in ordinary notation?
3. What is (2 × 106) × (3 × 108)?
4. What is (3 × 106) × (3 × 10-4)?
5. What is (6 × 107) ÷ (3 × 105)?
6. What is (3 × 106) ÷ (2 × 10-2)?
7. What is (2 × 106) + (3 × 104)?

Joshua E. Barnes (barnes@ifa.hawaii.edu)