Scientific Notation

Allows a very large or small number to be expressed as a smaller number x power of 10.

Scientific notation for a large number. Example: 125 Move the decimal so that there is one number to the left of the decimal. 125. 1.25 Multiply by the power of 10 the number of spaces moved. 1.25 x 102

Example: 1700 Move the decimal. 1700 1.7 Multiply by power of 10. 1700 1.7 Multiply by power of 10. 1.7 x 103

Scientific Notation for a very small number Ex: 0.00058 Move the decimal so that there is only one number to the left of it. 0.00058 5.8 2. Multiply by a negative power of 10 for the number of places moved. 5.8 X 10-4

Example: 0.000074 0.000074 7.4 7.4 x 10-5

Practice problems (do in your comp book) Convert the following numbers to scientific notation. 56400 6,300,000 98224 0.0068 .00001874 (4 zeros) .0000000001 (9 zeros)

Convert from scientific notation to an ordinary number. Ex: 5.73 x 103 For positive powers of 10, move the decimal to the right that many places. 5.73 5730 Notice that you have to add a zero to get the right number of spaces.

Ex: 8.32 x 10-2 Move the decimal to the left when the exponent is negative. 8.32 .0832

Practice problems Convert the follow numbers into ordinary numbers. 1. 7.15 x 102 4.2 x 104 8.930 x 106 2.66 x 10-2 9.200 x 10-5 6.7 x 10-1

Multiplying in scientific notation Ex: 5.0 x 105 x 7.0 x 104 Multiply the numbers and add the exponents. 5.0 x 7.0 = 35.0 105+4 = 109 35.0 x 109

To divide in scientific notation. Ex: 6.0 x 102/ 2.0 x 103 Divide the number and subtract the exponent 6.0/2.0 = 3.0 102-3 = 10-1 3.0 x 10-1

Practice Problems 5.8 x 102 x 4.5 x 104 7.33 x 106 x 8.6 x 105

Homework p 148:1, 2, 3, 5,6, 8