1. Powers of Ten and Scientific Notation
Warm Up
Lesson Presentation

2. Warm Up
Find each value.
1. 92
3. 152
5. 103 81
2. 122
144
225
4. 102
100
1,000
6. 104
10,000

3. Goal
Learn to express large numbers in scientific notation.

4. Vocabulary
standard form
scientific notation

5. The distance from Venus to the Sun is over 100,000,000 kilometers
The distance from Venus to the Sun is over 100,000,000 kilometers. You can write this number as a power of ten by using a base of ten and an exponent.
10 · 10 · 10 · 10 · 10 · 10 · 10 · 10 = 108
Power of ten

6. The table shows several powers of ten.
Power of 10
Meaning
Value
101 10 10
102
10 · 10
100
103
10 · 10 · 10
1,000
104
10 · 10 · 10 · 10
10,000

7. Additional Example 1: Multiplying by Powers of Ten
14 · 103 = 14 · (10 · 10 · 10)
Use 10 as a factor
3 times.
= 14 · 1,000
Multiply.
= 14,000

8. Try This: Example 1
Multiply 12 · 102.
12 · 102 = 12 · (10 · 10)
Use 10 as a factor
2 times.
= 12 · 100
Multiply.
= 1,200

9. You can also find the product of a number and a power of ten simply by moving the decimal point of the number. For powers of ten with positive exponents, move the decimal point to the right.

10. Additional Example 2: Multiplying by Powers of Ten Mentally
Find each product.
A. 212 · 104
4 places
212 · 104 =
Move the decimal point
4 places.
= 2,120,000
(You will need to add
4 zeros.)
B · 103
3 places
31.6 · 103 =
Move the decimal point
3 places.
= 31,600
(You will need to add
2 zeros.)

11. Insert Lesson Title Here
Try This: Example 2
Find each product.
A · 102
2 places
22.5 · 102 = 22.50
Move the decimal point
2 places.
= 2,250
(You will need to add
1 zero.)
B · 103
3 places
39.5 · 103 =
Move the decimal point
3 places.
= 39,500
(You will need to add
2 zeros.)

12. Numbers are usually written in standard form
Numbers are usually written in standard form. For example, 17,900,000 is in standard form. Scientific notation is a kind of shorthand that can be used to write large numbers. Numbers expressed in scientific notation are written as the product of two factors. In scientific notation, 17,900,000 is written as 7
1.79
x 10
A number greater than or equal to 1 but less than 10
A power of 10

13. Writing Math
In scientific notation, it is customary to use a multiplication cross () instead of a dot.

14. Additional Example 3A: Writing Numbers in Scientific Notation
Write the number in scientific notation.
A. 4,340,000
6 places
Move the decimal point to
get a number that is greater
than or equal to 1 and less
than 10.
4,340,000 = 4,340,000
The exponent is equal to
the number of places the
decimal point is moved.
= 4.34  106

15. Additional Example 3B: Writing Numbers in Scientific Notation
Write the number in scientific notation.
B. 327,000,000
8 places
Move the decimal point to
get a number that is greater
than or equal to 1 and less
than 10.
327,000,000 = 327,000,000
The exponent is equal to
the number of places the
decimal point is moved.
= 3.27  108

16. Insert Lesson Title Here
Try This: Example 3A
Write the number in scientific notation.
A. 8,421,000
6 places
Move the decimal point to
get a number that is greater
than or equal to 1 and less
than 10.
8,421,000 = 8,421,000
The exponent is equal to
the number of places the
decimal point is moved.
=  106

17. Insert Lesson Title Here
Try This: Example 3B
Write the number in scientific notation.
B. 327,000
5 places
Move the decimal point to
get a number that is greater
than or equal to 1 and less
than 10.
327,000 = 327,000
The exponent is equal to
the number of places the
decimal point is moved.
= 3.27  105

18. Additional Example 4: Writing Numbers in Standard Form
The population of China in the year 2000 was estimated to be about  109. Write this number in standard form.
Since the exponent is 9, move the decimal
point 9 places to the right.
1.262  109 =
= 1,262,000,000
The population of China was about 1,262,000,000
people.

19. Insert Lesson Title Here
Try This: Example 4
The distance from the Earth to the Sun is calculated to be 1.5  108 kilometers. Write this distance in standard form.
Since the exponent is
8, move the decimal
point 8 places to the
right.
1.5  108 =
= 150,000,000
The distance from the Earth to the Sun is about 150,000,000 kilometers.

20. Insert Lesson Title Here
Lesson Quiz: Part 1
Multiply.
1. 25  102
2,500
2. 18  104
180,000
Find each product.
 102
11,000
 103
3,742

21. Insert Lesson Title Here
Lesson Quiz: Part 2
Write each number in scientific notation..
5. 7,400,000
6. 45,000
7. Earth is about  107 miles from the Sun. Write this number in standard form.
7.4  106
4.5 104
92,920,000