Scientific Notation
Joshua Barnes  Fall 1999
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 = 10^{6}
0.000001 = 1/1,000,000 = 10^{6}
1,230,000 = 1.23 × 10^{6}
0.00000123 = 1.23 × 10^{6}
The same number can take different forms:
1,230,000 = 1.23 × 10^{6} = 12.3 × 10^{5}
= 0.123 × 10^{7}
(The form 1.23 × 10^{6} is usually preferred,
because the constant in front (1.23) is between 1 and 10.)
To multiply, you add the exponents:
(1.2 × 10^{6}) × (2 × 10^{5}) =
(1.2 × 2) × 10^{(6+5)} = 2.4 ×
10^{11}
To divide, you subtract the exponents:
(4.2 × 10^{12}) ÷ (2 × 10^{8})
= (4.2 ÷ 2) × 10^{(128)} = 2.1 ×
10^{4}
To add or subtract numbers in scientific notation,
you have to make the exponents the same first:
(1.2 × 10^{6}) + (2 × 10^{5}) = (1.2
× 10^{6}) + (0.2 × 10^{6}) = 1.4 ×
10^{6}
Test yourself: Select the right answer to each question, and
click on it to check.
 What is 456,000,000 in scientific notation?

4.56 × 10^{3}

4.56 × 10^{4}

4.56 × 10^{6}

4.56 × 10^{8}

4.56 × 10^{9}
 What is 8.88 × 10^{3} in ordinary notation?

88.8

888

8,880

88,800

888,000
 What is (2 × 10^{6}) ×
(3 × 10^{8})?

6 × 10^{6}

6 × 10^{8}

6 × 10^{10}

6 × 10^{12}

6 × 10^{14}
 What is (3 × 10^{6}) ×
(3 × 10^{4})?

9 × 10^{2}

9 × 10^{0}

9 × 10^{2}

9 × 10^{4}

9 × 10^{6}
 What is (6 × 10^{7}) ÷
(3 × 10^{5})?

2 × 10^{2}

2 × 10^{3}

2 × 10^{4}

2 × 10^{5}

2 × 10^{6}
 What is (3 × 10^{6}) ÷
(2 × 10^{2})?

6 × 10^{8}

1.5 × 10^{8}

6 × 10^{4}

1.5 × 10^{4}

5 × 10^{8}
 What is (2 × 10^{6}) +
(3 × 10^{4})?

5 × 10^{6}

2.03 × 10^{10}

2.3 × 10^{6}

2.03 × 10^{6}

2.003 × 10^{6}
Joshua E. Barnes
(barnes@ifa.hawaii.edu)
Last modified: August 27, 1999
http://www.ifa.hawaii.edu/~barnes/ast110_99/scinote.html