8.4 Scientific Notation

Scientific notation is used to write very large and very small numbers in powers of 10.

Decimal form Power of 10 Name

1,000,000,000 109 one billion

1,000,000 106 one million

1,000 103 one thousand

100 102 one hundred

10 101 ten

1 100 one

.1 10-1 one tenth

.01 10-2 one hundredth

.001 10-3 one thousandth

Form: c 10n where c is a number > 1 and <10

Change decimals to scientific notation:

93,000,000

.00000625

9.3 107

6.25 10-6

Scientific Notation to decimal form:

2.83 105

1.5 10-7

283,000

0.00000015

Multiplying Scientific notation:

(3.2 106) ( 4.2 104)

3.2 4.2 106 104

13.44 1010

1.344 1011

Combine like terms

Multiply numbers and add exponents

Pull out another positive power of 10, so 1010 + 101 = 1011!

Dividing with scientific notation:

4.5 10-7

9.0 10-4

.5 10-7-(-4)

.5 10-3

5 10-4 .0005

Divide numbers

Subtract exponents

Simplify.

or