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.

0.000001 = 1/1,000,000 = 10

1,230,000 = 1.23 × 10

0.00000123 = 1.23 × 10

The same number can take different forms:

To multiply, you add the exponents:

To divide, you subtract the exponents:

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

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

- What is 456,000,000 in scientific notation?
- What is 8.88 × 10
^{3}in ordinary notation? - What is (2 × 10
^{6}) × (3 × 10^{8})? - What is (3 × 10
^{6}) × (3 × 10^{-4})? - What is (6 × 10
^{7}) ÷ (3 × 10^{5})? - What is (3 × 10
^{6}) ÷ (2 × 10^{-2})? - What is (2 × 10
^{6}) + (3 × 10^{4})?

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

Last modified: August 15, 2001

`http://www.ifa.hawaii.edu/~barnes/ast110/scinote.html`