Scientific Notation If numbers are very large, like the mass of the Earth kg If numbers are very large, like the mass of the Earth kg Or very small like the mass of an electron : kg Or very small like the mass of an electron : kg then standard decimal notation is very cumbersome, so we use scientific notation.

Scientific Notation A number in scientific notation has two parts: 1 st part: a number between 1 and 10 2 nd part: 10 to some power. A number in scientific notation has two parts: 1 st part: a number between 1 and 10 2 nd part: 10 to some power. Example: 5.9 x Means move the decimal 24 places to the right. Example: 6.2 x Means move the decimal 4 places to the left.

Examples – Put the number in Scientific Notation a b Answer: = 3.45 x 10 5 Answer: = 3.4 x 10 -4

Multiplication and Division RuleExample x m x n = x m+n x 2 x 3 = x 2+3 = x 5 x m /x n = x m-n x 6 /x 2 = x 6-2 = x 4 (x m ) n = x mn (x 2 ) 3 = x 2×3 = x 6 (xy) n = x n y n (xy) 3 = x 3 y 3 (x/y) n = x n /y n (x/y) 2 = x 2 / y 2 x -n = 1/x n x -3 = 1/x 3

Examples Simplify: (2 x 10 3 )(4 x 10 6 ) = (2)(4) x 10 3 (10 6 ) = 8 x 10 9 Simplify: (4 x 10 3 )/(2 x 10 6 ) = (4)/(2) x 10 3/ 10 6 = 2 x Simplify: (2 x 10 3 ) 3 = 2 3 x (10 3 ) 3 = 8 x 10 9