Transcript mgbmi2e_ppt_04_03

4.3
Multiplying Decimals and
Circumference of a Circle
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.
Multiplying Decimals
Multiplying decimals is similar to whole numbers. The
only difference is that we place a decimal point in the
product.
Multiplying Decimals
Step 1: Multiply the decimals as though they are
whole numbers.
Step 2: The decimal point in the product is placed so
that the number of decimal places in the
product is equal to the sum of the number of
decimal place in the factors.
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Multiplying Decimals
Step
Example
0 .7
Step 1: Multiply the decimals Multiply:
 0 .9
as though they are whole
063
numbers.
Step 2: The decimal point in
Total of 2 decimal
the product is placed so that
0 .7
places.
number of decimal places in
 0 .9
Decimal placed at
the product is equal to the
0.63
two decimal places.
sum of the number of decimal
places in the factors.
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Example
Multiply: 15.9 × 0.62
15.9
 0.62
318
9540
9.858
1 decimal place
2 decimal places
Insert the decimal point in the product so that
there are 3 decimal places (1 + 2 = 3).
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Example
Multiply: 0.648 × 0.5
0.648

0.5
0.3240
3 decimal places
1 decimal place
Insert the decimal point in the product so that
there are 4 decimal places.
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Estimating when Multiplying Decimals
We can estimate when multiplying decimals to check
for reasonableness.
Example:
Exact
5.3
 4.2
106
2120
22.26
Estimate
5
4
20
Since 22.26 is close to our
estimate of 20, it is a
reasonable answer.
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Estimating when Multiplying Decimals
Multiply 32.3  1.9.
Exact
32.3
1.9
290.7
323.0
61.37
Estimate
rounds to
rounds to
32
2
64
This is a reasonable answer.
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Multiplying Decimals by Powers of 10
There are some patterns that occur when
we multiply a number by a power of
ten, such as 10, 100, 1000, 10,000, and
so on.
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Multiplying by Powers of 10
Type
Multiplying Decimals by Powers of 10
such as 10, 100, 1000 . . .: Move the
decimal point to the right the same
number of places as there are zeros in
the power of 10.
Multiplying Decimals by Powers of 10
such as .1, .01, .001 . . .:
Move the decimal point to the left the
same number of places as there are
decimal places in the power of 10.
Example
0.5 100  50.
0.06  0.01  0.0006
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Multiplying Decimals by Powers of 10
Move the decimal point to the right the same number
of places as there are zeros in the power of 10.
Multiply: 3.4305  100
Since there are two zeros in 100, move the decimal place
two places to the right.
3.4305  100 =
3.4305 =
343.05
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Multiplying Decimals by Powers of 10
76.543  10 = 765.43
1 zero
76.543  100 = 7654.3
2 zeros
Decimal point moved 1
place to the right.
Decimal point moved 2
places to the right.
76.543  100,000 = 7,654,300
5 zeros
Decimal point moved 5
places to the right.
The decimal point is moved the same number of places as
there are zeros in the power of 10.
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Multiplying Decimals by Powers of 10
Move the decimal point to the left the same number of
places as there are decimal places in the power of 10.
Multiply: 8.57 x 0.01
Since there are two decimal places in 0.01, move the decimal
place two places to the left.
8.57 x 0.01 =
008.57 =
0.0857
Notice that zeros had to be inserted.
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Example
Multiply.
a. 58.1 × 0.01 = 0.581
Move the decimal point 2 places to the left.
b. 85,624 × 0.1 = 8562.4
Move the decimal point 1 place to the left.
c. 24.106 ×100 = 2410.6
Move the decimal point 2 places to the
right.
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The Circumference of a Circle
The distance around a polygon is called its perimeter.
The distance around a circle is called the
circumference.
This distance depends on the radius or the diameter of
the circle.
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The Circumference of a Circle
r
d
Circumference = 2·p ·radius
or
Circumference = p ·diameter
C = 2 p r or C = p d
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p
The symbol p is the Greek letter pi,
pronounced “pie.” It is a constant between 3
and 4. A decimal approximation for p is 3.14.
A fraction approximation for p is 22 .
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The Circumference of a Circle
Find the circumference of a circle
whose radius is 4 inches.
4 inches
C = 2pr = 2p ·4 = 8p inches
8p inches is the exact circumference of this circle.
If we replace p with the approximation 3.14, C = 8p 
8(3.14) = 25.12 inches.
25.12 inches is the approximate circumference of the
circle.
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Example
Find the circumference of the following circle.
9.1 yards
Circumference = 2  p  r
 2  9.1  p
 57.148 yards
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Solving Problems by Multiplying Decimals
Jose Severos, an electrician for Central Power and Light,
worked 40 hours last week. Calculate his pay before taxes
for last week if his hourly wage is $13.88.
13.88
 40
0
55520
555.20
Jose Severos’ pay before taxes for last week is $555.20.
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