Topic 4
Math 8
Scientific Notation
Name: ____________________
Period: _________
Vocabulary
Unit B – Topic 4
TERM
SCIENTIFIC
NOTATION
DEFINITION
EXAMPLE
A product of two factors,
one greater than or equal to
1and less than 10, and the
other is a power of ten.
A number using digits and
place value.
STANDARD FORM
MULTIPLY BY
NEGATIVE
POWERS OF TEN
MULTIPLY BY
POSITIVE
POWERS OF TEN
MULTIPLY
NUMBERS IN
SCIENTIFIC
NOTATION
The power tells you how
many place values you move
the decimal to the LEFT.
56.789 ·10 -3 = .056789
The power tells you how
many place values you move
the decimal to the RIGHT.
56.789 ·10 5 = 5,678,900
Multiply the factors first
then keep the power of 10
and add the exponents.
DIVIDE NUMBERS Divide the factors first then
keep the power of 10 and
IN SCIENTIFIC
subtract the exponents.
NOTATION
2
ADD NUMBERS IN
SCIENTIFIC
NOTATION
SUBTRACT
NUMBERS IN
SCIENTIFIC
NOTATION
Make sure they have the
same power of 10, then add
the first factors and keep the
same power of ten and the
exponent.
Make sure they have the
same power of 10, then
subtract the first factors and
keep the same power of ten
and the exponent.
3
Lesson 4-1
Exploring Scientific Notation
Part I
4
Key Concept
5
Part II
Part III
6
Lesson 4-1
Homework
7
Lesson 4-2
Using Scientific Notation to Describe Very Large Quantities
Key Concept
Part I
Part II
Part III
9
Lesson 4-2
Homework
10
Lesson 4-3
Using Scientific Notation to Describe Very Small Quantities
Key Concept
Part I
11
Part II
12
Part III
13
Lesson 4-3
Homework
14
Lesson 4-4
Operating with Numbers Expressed in Scientific Notation
Part I
15
16
17
Part II
18
19
Part III
20
21
Lesson 4-4
Homework
22
Lesson 4-5
Problem Solving
Part II
23
ADDITIONAL PRACTICE
GOES WITH LESSON 4-1/4-2/4-3
COMPARE NUMBERS IN SCIENTIFIC NOTATION
WRITING NUMBERS IN SCIENTIFIC NOTATION AND STANDARD FORM
IDENTIFYING NUMBERS WRITTEN CORRECTLY
24
GOES WITH LESSON 4-4
ADD/SUBTRACT AND MULTIPLY /DIVIDE
25
26
27
CHAPTER WRAP UP
28
29
TOPIC 4 Test REVIEW
Quizlet http://quizlet.com/_9a4x9
1. Which of the following numbers is written in scientific notation?
32 ´ 10 3
3.2 ´ 10 -2
3.2
32
2. Write the following numbers in order from least to greatest.
7.25 ´ 10-4
7.25 ´ 10-6
7.25 ´ 100
7.25 ´ 10 3
3. Suppose your calculator display shows 5.32E+12. Express this result in scientific
notation.
5.32E+12=
4. Express the following numbers in scientific notation.
102,000 =
8,456,000 =
67 million =
5. Express the following numbers in standard form.
5 ´10 4 =
9.32 ´ 106 =
1.045 ´107 =
6. Use the table to find a pattern.
Number
5000
500
50
5
0.5
0.05
0.005
Powers of 10
5 x 103
5 x 102
5 x 101
5 x 100
5 x 10-1
5 x 10-2
5 x 10-3
Which of the following is a pattern in the table?
a) Negative exponents make the number increase.
b) Negative exponents make the value equal to 0.
c) Positive exponents make the number decrease.
30
d) Positive exponents make the number increase.
7a. Think About The Process A young man and an old man are having the follicles of
hair on their head measured by a machine. The young man has 72,000,000 hair follicles
and the old man has 1.2 ´ 10 7 follicles on his head. Please write the number of follicles on
the young man’s head in scientific notation.
7b. The young man has more hair on his head. How many times more hair follicles does
the young man have when compared to the old man?
8. Which number is greater, 7 ´ 105 or 9 ´ 10 4 ?
9. Express the following numbers in scientific notation:
0.0004 =
0.0125 =
0.0000834 =
10. Write the following numbers in standard form:
6.92 ´ 10-3 =
3.078 ´10-2=
7.74 ´10-7=
11. Multiple Representations The numbers below represent 0.0005 as a product of two
factors. Which product is written in scientific notation?
0.5 ´ 10-3
5 ´ 10 -4
5 ´ 10 4
50 ´ 10-5
12. Subtract and write your answer in scientific notation.
(4.2 ´ 10 4 ) - (2.7 ´ 10 4 )
13. Simplify the expression. Write the answer in scientific notation.
31
(7 ´ 10 -4 )(6 ´ 10-5 )
14. Divide. Express your answer in scientific notation.
15 ´ 10 -7
6 ´ 10 -5
15. Grocery Shopping: A recent study shows that the average person buys 160 bottles
of water a year. If there are 270 million people in the United States, how many bottles of
water are purchased by Americans each year?
16. Two planets are 9.26 x 1015 miles apart. 1 light year is about 4.76 x 1012 miles.
How many light years are the planets apart? Express your answer in scientific notation.
17. The diameter of a cheek cell is 6 ´10-5 m. The diameter of a white blood cell is
1´10-5m. A cheek cell is how many times as large as a white blood cell?
18. What is the value of n?
(5.8 ´ 10 7 ) = (2 ´ 10 2 )(2.9 ´ 10n )
æ x2ö
19. Use the properties of exponents to simplify ç ÷
è 4ø
3
32
3a 5b 4
20. Simplify the expression:
18a 5b
33