Unit 9 L-3 Math 8
Aim: Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very
large or very small quantities, and to express how many times as much one is than the other. Perform
operations with numbers expressed in scientific notation. (8.EE.3 and 8.EE.4)
Multiplication and Division of Numbers in Scientific Notation
Vocabulary:
product
factors
product of powers property
quotient
quotient of powers property
Multiplying Numbers in Scientific Notation
To multiply numbers written in scientific notation, you ______________ the first
factors, and then ____________ the exponents of the powers of ten using the product
of powers property. After finding the product, be sure your answer is in scientific
notation.
To Multiply Numbers in Scientific Notation:
1. Multiply the first numbers.
2. Add the exponents of the powers of 10.
3. Be sure answer is in Scientific Notation.
(Product of Powers Property)
Example 1:
Find the product and express your answer in scientific notation:
(4 x 104)(2 x 106)
Example 2:
Find the product and express your answer in scientific notation:
(3 x 10-5)(5 x 10-2)
Example 3:
The world population is about 7 billion. There are 4.6 x 107 ants for every human on the
planet. About how many ants are there in the world?
2014-2015
Dividing Numbers in Scientific Notation
To divide numbers written in scientific notation, you ______________ the first factors,
and then __________ the exponents of the powers of ten using the quotient of powers
property. After finding the quotient, be sure your answer is in scientific notation. You can
check your answer by converting the numbers to standard form and then dividing them.
To Divide Numbers in Scientific Notation:
1. Divide the first numbers.
2. Subtract the exponents of the powers of 10.
3. Be sure answer is in Scientific Notation.
(Quotient of Powers Property)
Example 4:
Find the quotient and express your answer in scientific notation:
(8 x 108)
(2 x 103)
Example 5:
Find the quotient and express your answer in scientific notation:
(15 x 10-5)
(2 x 107)
Example 6:
A social media company processes about 990 billion “likes” per year. If the company has
approximately 8.9 x 108 users of the social media, about how many “likes” is each user
responsible for per year. Write your answer in scientific and standard notation.
2014-2015
Practice: Multiply or Divide. Show all work. Write your answer in scientific notation.
1. (2.5 x 108)(2 x 103)
2.
(2 x 10-4)(8 x 10-4)
3.
(8 x 109)(4 x 10-2)
4.
(3 x 10-4)(1.4 x 10-9)
5.
18 x 1021
6 x 1014
6.
4.6 x 1017
2 x 109
7.
1.6 x 1010
8 x 106
8.
1.8 x 10-11
3 x 10-2
9. (5 x 103)(2,000)
10.
(720)(8 x 103)
12.
(0.3 x 104)(1.5 x 103)
11.
(4.1 x 107)(23,000)
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13.
12 x 103
600
14.
9,500
5 x 102
15.
2.4 x 108
0.6 x 103
16.
1.4 x 105
70,000
For each problem, show your work. Write your answer in scientific notation.
17. A music download Web site announced that over 4 x 109 songs were downloaded by
5 x 107 registered users. What is the average number of downloads per user?
18. Find the area of the rectangle. Write your answer in scientific notation.
6 x 106 cm
9 x 107 cm
19. Human hair grows at an average rate of about 4 x 10-2 centimeters per day. If Mr.
Kunz has not cut his hair in a year (365 days), how many centimeters has it grown?
2014-2015