Download Scientific Notation

e x p l o r at i o n
Georgia Performance
Standards
4D
Scientific Notation
M8N1.j
1. Complete the table of values for the powers of ten.
Exponent
Power
–6
10–6 –5
10–5 –4
10–4 –3
10–3 –2
0.01
10–2 2 10 10
–1
1
1
10
1
1
10–1 1 1
0.1
0
10
0
100 1
1
101 10
2
102 10 10 100
3
103 4
104 5
105 6
106 Think and Discuss
2. Discuss the pattern you see in the table of values for
powers of ten.
3. Explain how you know that 109 0.000000001.
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110
Holt Mathematics
Name
Date
LAB
Technology Lab
4D
Scientific Notation
Class
Some numbers are so big that even calculators use scientific
notation to display them. A scientific calculator displays numbers in
standard form up to a certain number of digits. Beyond that limit, the
calculator displays numbers in scientific notation. A scientific
calculator makes it easy to multiply numbers in scientific notation.
Activity 1
Using a scientific or graphing calculator, you can determine the
distance a ray of light travels in one day. The calculator will display
the answer in scientific notation when it exceeds the display limit.
Light travels at a constant speed of 186,000 miles
per second. To find out how far a ray of light
travels in 1 minute, multiply 186,000 by 60
(1 minute 60 seconds) to get 11,160,000.
To find out how far the light travels in an hour, multiply
11,160,000 by 60 (1 hour 60 minutes)
to get 669,600,000 miles.
Next, multiply 669,600,000 by 24 (24 hours 1 day).
The calculator automatically converts the final answer to scientific
notation. This number can be used for further calculations.
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
111
Holt Mathematics
Name
Date
LAB
Technology Lab
4D
Scientific Notation, continued
Class
Activity 2
A scientific calculator allows you to easily multiply numbers written
in scientific notation. Take the final answer from the previous activity
(1.60704E10) and multiply that number by 8.96 103.
Enter the first number in scientific notation with the following
EE
keystrokes: 1.60704
2nd
,
10. Then press the multiplication button.
EE
Enter the second number with the following keystrokes: 8.96
Then press “Enter” to obtain the product.
2nd
,
3.
Think and Discuss
1. Which of the following products is displayed in scientific notation
on your calculator?
9,217,400,938 • 385,474,609
771,247,792 • 7.6312345
Were both of them displayed in scientific notation? Why or why not?
Try This
Perform each operation using a scientific calculator.
1. (4.7 • 109) • (3.33 • 106)
2. (9.92415 • 103) • (8.3 • 107)
3. (4.3 • 102) (6.3 • 108)
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
112
Holt Mathematics
Name
LESSON
4D
Date
Class
Review for Mastery
Scientific Notation
Standard Notation
Scientific Notation
(
430,000
0.0000057
)(
)
1st factor is
between 1 and 10.
2nd factor is an
integer power of 10.
4.3 108
5.7 106
positive integer for large number
negative integer for small number
To convert from scientific notation, look at the power of 10 to tell
how many places and which way to move the decimal point.
Complete to write each in standard notation.
1. 4.12 106
2. 3.4 105
Is the exponent positive or negative?
Move the decimal point right or left?
How many places?
Write the number in standard notation.
Write each number in standard notation.
3. 8 105
4. 7.1 104
5. 3.14 108
To convert to scientific notation, determine the factor between 1 and
10. Then determine the power of 10 by counting from the decimal
point in the first factor to the decimal point in the given number.
Complete to write each in scientific notation.
6. 32,000,000
7. 0.0000000712
What is the first factor?
From its location in the first factor, which
way must the decimal move to its location
in the given number? How many places?
Write the number in scientific notation.
Write each number in scientific notation.
8. 41,000,000
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
9. 0.0000000643
113
10. 1,370,000,000
Holt Mathematics
Name
LESSON
4D
Date
Class
Homework and Practice
Scientific Notation
Write each number in standard notation.
1. 6.12 102
2. 7.9 103
3. 4.87 104
4. 9.3 102
5. 8.06 103
6. 5.7 104
7. 3.17 105
8. 9.00613 102
9. 9.85 105
10. 6.004 107
11. 8.23 104
12. 1.48 106
Write each number in scientific notation.
13. 108,000,000
14. 0.5943
15. 42
16. 0.0000673
17. 0.0056
18. 6004
19. 0.00852
20. 24,631,500
21. 89450
22. 0.005702
23. 8,005,000,000
24. 0.00012805
25. The mass of the Earth is 5,980,000,000,000,000,000,000,000
kilograms. Write this number in scientific notation.
26. The mass of a dust particle is 7.53 1010. Write this number in
standard notation.
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
114
Holt Mathematics