Transcript Scientific Notation

Measurements
1.2
Scientific Notation
Copyright © 2009 by Pearson Education, Inc.
Scientific Notation
Scientific Notation
• is used to write very large
or very small numbers.
• for the width of a human
hair of 0.000 008 m is
written 8 x 10-6 m.
• of a large number such
as 4 500 000 s is written
4.5 x 106 s.
Copyright © 2009 by Pearson Education, Inc.
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Numbers in Scientific Notation
A number written in scientific notation contains a
• coefficient.
• power of 10.
Examples:
coefficient
1.5
power of ten
x
102
coefficient
7.35
power of ten
x
10-4
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Writing Numbers in
Scientific Notation
To write a number in scientific notation,
• move the decimal point to give a number 1-9.
• show the spaces moved as a power of 10.
Examples:
52 000. = 5.2 x 10 4
4 spaces left
0.00178 = 1.78 x 10-3
3 spaces right
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Some Powers of 10
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Comparing Numbers in Standard
and Scientific Notation
Here are some numbers written in standard format
and in scientific notation.
Number in
Number in
Standard Format
Scientific Notation
Diameter of the Earth
12 800 000 m
1.28 x 107 m
Mass of a typical human
68 kg
6.8 x 101 kg
Length of a pox virus
0.000 03 cm
3 x 10-5 cm
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Study Tip: Scientific Notation
In a number 10 or larger, the decimal point
• is moved to the left to give a positive power of 10
In a number less than 1, the decimal point
• is moved to the right to give a negative power of 10
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Learning Check
Select the correct scientific notation for each.
A. 0.000 008 m
1) 8 x 106 m,
2) 8 x 10-6 m, 3) 0.8 x 10-5 m
B. 72 000 g
1) 7.2 x 104 g, 2) 72 x 103 g, 3) 7.2 x 10-4 g
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Solution
Select the correct scientific notation for each.
A. 0.000 008 m
2) 8 x 10-6 m
B. 72 000 g
1) 7.2 x 104 g
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Learning Check
Write each as a standard number.
A. 2.0 x 10-2 L
1) 200 L,
2) 0.0020 L,
3) 0.020 L
B. 1.8 x 105 g
1) 180 000 g,
2) 0.000 018 g,
3) 18 000 g
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Solution
Write each as a standard number.
A. 2.0 x 10-2 L
3) 0.020 L
B. 1.8 x 105 g
1) 180 000 g
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