1. MAT111 epw 9/18/06 The Decimal Number System or The Power of the Powers of 10

2. MAT111 epw 9/18/06 The Powers of 10 Definition: 10 0 = 1, otherwise… Powers of 10 indicate how many times a ten appears when multiplying 10 by itself 10 1 = 10 10 2 = 10  10 = 100 10 3 = 10  10  10 = 1,000 · · · 10 6 = 10  10  10  10  10  10 = 1,000,000

3. MAT111 epw 9/18/06 Positive Powers (Positive Exponents) A positive exponent tells how many 0s to follow the 1. Examples:  10 0 is a 1 followed by no 0s  10 1 is a 1 followed by one 0 · · · 10 8 is a 1 followed by eight 0s

4. MAT111 epw 9/18/06 Negative Powers (Negative Exponents) Negative powers indicate reciprocals of corresponding positive powers

5. MAT111 epw 9/18/06 Negative Powers (Negative Exponents) A negative exponent tells how many places are to the right of the decimal point, including the 1 Examples:  10 -1 = 0.1  10 -6 = 0.000001

6. MAT111 epw 9/18/06 Multiplying Powers of 10 Easy… Just add exponents!

7. MAT111 epw 9/18/06 Dividing Powers of 10 Easy… Just subtract exponents!

8. MAT111 epw 9/18/06 Powers of Powers of 10 Use multiplication and division rules to raise powers of 10 to other powers

9. MAT111 epw 9/18/06 Adding and Subtracting Powers of 10 There is no shortcut Values must be written in longhand notation 10 6 + 10 2 = 1,000,000 + 100 = 1,000,100 10 8 + 10 -3 = 100,000,000 + 0.001 = 100,000,000.001 10 7 – 10 3 = 10,000,000 – 1,000 = 9,999,000

10. MAT111 epw 9/18/06 Summary To multiply powers of 10, add exponents 10 n  10 m = 10 n+m To divide powers of 10, subtract exponents To raise powers of 10 to other powers, multiply exponents (10 n ) m = 10 n  m

11. MAT111 epw 9/18/06 Decimal Numbers What is this number (value)? 123