Multiply and Divide with Scientific Notation
Mississippi Standard: Multiply and divide numbers written in scientific notation.
You can use scientific notation to simplify computations with very large and/or
very small numbers.
To multiply numbers in scientific notation, regroup to multiply the factors and
multiply the powers of ten. Then simplify. To multiply the powers of ten, use the
Product of Powers .
Product of Powers
Words
To multiply powers with the same base, add their exponents.
Symbols
Arithmetic
32
35
32 5
Algebra
or
37
xa
xb x a b
Multiplication with Scientific Notation
Evaluate the expression (1.3 102)(2.5 101).
(1.3 102)(2.5 101) (1.3 2.5)(102 101)
(3.25)(102 101)
3.25 Commutative and Associative Properties
Multiply 1.3 by 2.5.
102 1
Product of Powers
3.25 103
Add the exponents.
3.25 1,000
103 1,000
3,250
Move the decimal point 3 places.
Evaluate the expression (4.2 103)(1.6 104).
(4.2 103)(1.6 104) (4.2 1.6)(103 104)
(6.72)(103 104)
6.72 Commutative and Associative Properties
Multiply 4.2 by 1.6.
103 4
Product of Powers
6.72 107
Add the exponents.
6.72 10,000,000
107 10,000,000
67,200,000
Move the decimal point 7 places.
To divide numbers in scientific notation, regroup to divide the factors and
divide the powers of ten. Then simplify. To divide the powers of ten, use the
Quotient of Powers .
Quotient of Powers
Words
To divide powers with the same base, subtract their exponents.
Symbols
Arithmetic
48
43
48 3
600 Prerequisite Skills
or
Algebra
45
xa
xa b, x
xb
0
Division with Scientific Notation
9.45 106
2.1 10
Evaluate the expression 3 .
Associative Property
10
4.5 3
10 Divide 9.45 by 2.1.
4.5 106 3
Quotient of Powers
4.5 103
Subtract the exponents.
4.5 1,000
103 1,000
4,500
Move the decimal point 3 places.
9.45 106
9.45 106
3
3
2.1 10
2.1 10
6
Exercises
Multiply or divide. Express using exponents.
1. 51 54
25
2
4. 3
2. 65 64
3. 102 103
76
7
109
10
5. 5
6. 6
Evaluate each expression. Express the result in scientific notation and
standard form.
7. (2.6 105)(1.9 102)
8. (5.3 104)(0.9 103)
9. (3.7 102)(1.2 102)
10. (3.3 103)(2.1 102)
11. (8.5 103)(1.1 101)
12. (3.9 102)(2.3 106)
13. (6.45 105)(1.2 103)
14. (4.18 104)(0.9 105)
15. 3
8.37 108
2.7 10
16. 2
17. 5
9.72 109
1.8 10
18. 3
8.32 107
1.3 10
20. 6
4.2 108
1.68 10
22. 8
19. 5
21. 2
8.04 105
6.7 10
4.64 104
2.9 10
6.3 1010
1.5 10
9.0 1011
2.4 10
23. BASEBALL The table shows the 2007 salaries of
six Major League Baseball players. About how
many times greater is Alex Rodriguez’s salary
than Juan Castro’s salary?
24. ASTRONOMY The Sun burns about
4.4 106 tons of hydrogen per second. How
much hydrogen does the Sun burn in one year?
(Hint: one year 3.16 107 seconds)
25. OCEANS The area of the Pacific Ocean is
6.0 107 square miles. The area of the Atlantic
Ocean is 2.96 107 square miles. About how many
times greater is the area of the Pacific Ocean than
the Atlantic Ocean?
2007 Major League Baseball Salaries
Player
Team
Juan Castro
Coco Crisp
Nomar Garciaparra
Chipper Jones
Kazuo Matsui
Alex Rodriguez
Cincinnati Reds
Boston Red Sox
Los Angeles Dodgers
Atlanta Braves
Colorado Rockies
New York Yankees
Salary
(dollars)
9.25 105
3.83 106
8.52 106
1.23 107
1.5 106
2.27 107
Source: USA Today
Prerequisite Skills
601