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Chapter 5
Section 3
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
5.3
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An Application of Exponents:
Scientific Notation
Express numbers in scientific notation.
Convert numbers in scientific notation to
numbers without exponents.
Use scientific notation in calculations.
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Objective 1
Express numbers in scientific
notation.
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 5.3 - 3
Express numbers in scientific notation.
Numbers occurring in science are often extremely large (as the
distance from Earth to sun, 93,000,000 mi) or extremely small
(wavelength of yellow-green light, approx. 0.0000006 m). Due to the
difficulty of working with many zeros, scientists often express such
numbers with exponents, using a form called scientific notation.
A number is written in scientific notation when it is expressed in
the form
n
a 10 ,
where 1 ≤ |a| < 10 and n is an integer.
A number in scientific notation is always written with the
decimal point after the first nonzero digit an then multiplied by the
appropriate power of 10. For example 56,200 is written 5.62 × 104,
since
56, 200  5.62 10,000  5.62 104.
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 5.3 - 4
Writing a Number in Scientific Notation
To write a number in scientific notation, follow these steps.
Step 1: Move the decimal point to the right of the first
nonzero digit.
Step 2: Count the number of places you moved the decimal
point.
Step 3: The number of places in Step 2 is the absolute value of
the exponent on 10.
Step 4: The exponent on 10 is positive if the original number is
greater than the number in Step 1; the exponent is
negative if the original number is less than in Step 1.
If the decimal point is not moved, the exponent is 0.
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 5.3 - 5
EXAMPLE 1
Using Scientific Notation
Write in scientific notation.
0.0571
Solution:
 5.71102
2,140, 000, 000
 2.14 109
0.000062
 6.2  105
The exponent is positive if the original number is extremely “large”.
Likewise, the exponent will be negative if the original if the original
number is extremely “small”.
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 5.3 - 6
Objective 2
Convert numbers in scientific
notation to numbers without
exponents.
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 5.3 - 7
Convert numbers in scientific notation
to numbers without exponents.
To convert a number written scientific notation to a
number without exponents, work in reverse.
Multiplying a number by a positive power of 10 will
make the number greater; multiplying by a negative
power of 10 will make the number less.
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 5.3 - 8
EXAMPLE 2
Writing Numbers without
Exponents
Write without exponents.
Solution:
8.7 10
5
3.28 10
6
 870, 000
 0.00000328
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 5.3 - 9
Objective 3
Use scientific notation in
calculations.
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Slide 5.3 - 10
Multiplying and Dividing with
Scientific Notation
EXAMPLE 3
Perform each calculation. Write answers in scientific
notation and also without exponents.
Solution:
5
2
3
4
 15, 000
3

10
5

10

15

1
0

1.5

1
0



4.8 102
2.4 105
 2  10 3  0.002
Multiplying or dividing numbers written in scientific notation may produce
an answer in the form a × 100. Since 100 = 1, a × 100 = a. For example,
8 10 5 10   40 10
4
4
0
 40.
Also, if a =1, then a × 10n = 10n. For example, we could write 1,000,000
as 106 instead of 1 × 106.
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 5.3 - 11
EXAMPLE 4
Using Scientific Notation to
Solve an Application
The speed of light is approximately 3.0 × 105 km
per sec. How far does light travel in 6.0 × 101 sec?
(Source World Almanac and Book of Facts 2006.)
Solution: d  rt
d   3.0 10
5
 6.0 10 
1
d  18 106
d  1.8 10 or 18,000, 000
7
Light would travel 18,000,000 km in 6 seconds.
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 5.3 - 12
EXAMPLE 5
Using Scientific Notation to
Solve an Application
If the speed of light is approximately 3.0 × 105 km
per sec, how many seconds does it take light to travel
approximately 1.5 × 108 km from the sun to Earth?
(Source World Almanac and Book of Facts 2006.)
r
Solution: t 
d
1.5 108
t
3.0 105
t  0.5 103
t  5 102 or 500 sec
It would take 500 seconds for light from the sun
to reach Earth.
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Slide 5.3 - 13