Exponents and Scientific Notation

53 Powers and Exponents The base is the number that is multiplied. The exponent tells how many times the base is used as a factor. 53 The number that is expressed using an exponent is called a power. “Five to the Third Power”

53 = 5×5×5=125 Standard Notation Expanded Notation Exponential Notation “five to the third power”

Place Value and Powers of Ten ____ ____ ____ , ____ ____ ____. ____ ____ ____ 105 104 103 102 101 100 10-1 10-2 10-3 100,000 105 = 1 x 10 x 10 x 10 x 10 x 10   104 1 x 10 x 10 x 10 x 10 103 1 x 10 x 10 x 10 102 1 x 10 x 10 101 1 x 10 100 1 1 x 1 x x 1 x x x 10,000 1,000 100 10 1 0.1 10-1 0.01 10-2 0.001 10-3

Any number to the power of zero is 1. Remember… 120 = 1 2340 = 1 560 = 1

You try… Express each number in both expanded and standard notation. 1) 73 1 x 7 x 7 x 7 343 2) 54 1 x 5 x 5 x 5 x 5 625 3) 26 1 x 2 x 2 x 2 x 2 x 2 x 2 64 4) 240 1 1 5) 35 1 x 3 x 3 x 3 x 3 x 3 243

Scientific Notation is a shorthand way of expressing very large or very small numbers.

An ordinary quarter contains about 97,700,000,000,000,000,000,000 atoms. The length of this number in standard notation makes it awkward to work with.

To express any number in scientific notation, write it as the product of a power of ten and a number greater than or equal to 1 but less than 10. . . 97,700,000,000,000,000,000,000 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 9.77 x 1022

The average size of an atom is about 0.00000003 centimeters across. Again, the length of this number in standard notation makes it awkward to work with.

To express any number in scientific notation, write it as the product of a power of ten and a number greater than or equal to 1 but less than 10. . . 0.00000003 1 2 3 4 5 6 7 8 3 x 10-8

A positive exponent means move the decimal to the right, and a negative exponent means move the decimal to the left. Helpful Hint

You try… Express each number in scientific notation. 1) 135,000 1.35 x 105 2) 0.00001653 1.653 x 10-5 3) 4,600,000 4.6 x 106 4) 0.007089 7.089 x 10-3 5) 0.000000021 2.1 x 10-8

Let’s try in reverse… 1) 7.02 x 104 70,200 2) 9.12 x 10-2 0.0912 Express each number in standard form. 1) 7.02 x 104 70,200 2) 9.12 x 10-2 0.0912 3) 6.4 x 107 64,000,000 4) 8.8 x 10-5 0.000088 5) 3.49 x 109 3,490,000,000