NAME _____________________________________________ DATE __________________ PERIOD _________
Lesson 7 Reteach
Compute with Scientific Notation
You can use the Product of Powers and Quotient of Powers properties to multiply and divide numbers
written in scientific notation.
Example 1
Evaluate (3.4 × 105)(2.3 × 103). Express the result in scientific notation.
(3.4 × 105)(2.3 × 103) = (3.4 × 2.3)(105 × 103)
Commutative and Associative Properties
= (7.82)(105 × 103)
Multiply 3.4 by 2.3.
= 7.82 × 105 + 3
Product of Powers
= 7.82 × 108
Add the exponents.
Example 2
2.325 × 104
Evaluate −−−−−−−−
. Express the result in scientific notation.
2
3.1 × 10
2.325
2.325 × 104
= −−−−
−−−−−−−
3.1
3.1 × 102
10
) (−−−
10 )
Associative Property
104
= (0.75) −−−
2
( 10 )
Divide 2.325 by 3.1.
= 0.75 × 104 – 2
Quotient of Powers
= 0.75 × 102
Subtract the exponents.
Copyright © The McGraw-Hill Companies, Inc. Permission is granted to reproduce for classroom use.
(
4
2
= 0.75 × 10
2
Write 0.75 × 102 in scientific notation.
= 7.5 × 10
Since the decimal point moved 1 place to the right,
subtract 1 from the exponent.
Example 3
Evaluate (5.24 × 105) + (8.65 × 106). Express the result in
scientific notation.
(5.24 × 105) + (8.65 × 106) = (5.24 × 105) + (86.5 × 105) Write 8.65 × 106 as 86.5 × 105.
= (5.24 + 86.5) × 105
Distributive Property
= 91.74 × 105
Add 5.24 and 86.5.
= 9.174 × 106
Write 91.74 × 105 in scientific
notation.
Exercises
Evaluate each expression. Express the result in scientific notation.
1. (6.7 × 104)(2.9 × 105) 1.943 × 1010
2. (4.3 × 104) + (5.21 × 105) 5.64 × 105
5.46 × 105
3. −−−−−−−
6.5 × 10
3
4. (9.6 × 105) – (3.7 × 103) 9.563 × 105
8.4 × 10
Course 3 • Chapter 1 Real Numbers
15
NAME _____________________________________________ DATE __________________ PERIOD _________
Lesson 7 Skills Practice
Compute with Scientific Notation
Evaluate each expression. Express the result in scientific notation.
1. (5.8 × 105)(6.4 × 102)
3.712 × 10
8
2. (3.92 × 106)(2.2 × 104)
8.624 × 1010
2.952 × 106
3. −−−−−−−
3
2.052 × 107
4. −−−−−−−
4
8.2 × 102
3.8 × 102
3.6 × 10
5. (6.9 × 107) + (2.12 × 105)
6.9212 × 107
7. (8.4 × 107) – (6.3 × 106)
7.77 × 107
6.8 × 10
9.2 × 10
3
11. (3.68 × 103)(2.4 × 106)
8.832 × 109
13. (6.78 × 104) – (4.13 × 102)
6.7387 × 104
15. (5.9 × 108) + (2.6 × 106)
5.926 × 108
17. (8.33 × 103) + (4.1 × 105)
4.1833 × 105
16
6. (1.78 × 104) + (5.35 × 103)
2.315 × 104
8. (9.62 × 105) – (2.58 × 103)
9.5942 × 105
2.888 × 105
10. −−−−−−−
2
7.22 × 10
4 × 102
12. (7.2 × 107)(1.82 × 102)
1.3104 × 1010
3.024 × 106
14. −−−−−−−
2
4.8 × 10
6.3 × 103
16. (3.45 × 107)(1.68 × 104)
5.796 × 1011
18. (6.82 × 105) – (3.11 × 104)
6.509 × 105
Course 3 • Chapter 1 Real Numbers
Copyright © The McGraw-Hill Companies, Inc. Permission is granted to reproduce for classroom use.
6.256 × 108
9. −−−−−−−
4
5.4 × 10