Transcript Chapter 5: Decimals

Section 5.3
Multiplying Decimals and
Circumference of a Circle
Multiplying Decimals
Multiplying decimals is similar to
multiplying whole numbers. The
difference is that we place a decimal
point in the product.
0.7 x 0.03 =
1 decimal
place
7
10
x
3
100
2 decimal
places
=
21
1000
= 0.021
3 decimal places
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Multiplying Decimals
Step 1. Multiply the decimals as though
they were whole numbers.
Step 2. The decimal point in the product
is placed so the number of
decimal places in the product is
equal to the sum of the number of
decimal places in the factors.
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Estimating when Multiplying
Decimals
Multiply 32.3 x 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 Decimals by
Powers of 10
76.543 x 10 = 765.43
1 zero
Decimal point moved 1
place to the right.
76.543 x 100 = 7654.3 Decimal point moved 2
places to the right.
2 zeros
76.543 x 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 by Powers of 10 such
as 10, 100, 1000 or 10,000, . . .
Move the decimal point to the right the
same number of places as there are zeros
in the power of 10.
Multiply: 3.4305 x 100
Since there are two zeros in 100, move the
decimal place two places to the right.
3.4305 x 100 = 3.4305 = 343.05
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Multiplying by Powers of 10 such
as 0.1, 0.01, 0.001, 0.0001, . . .
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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Finding 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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Circumference of a Circle
r
d
Circumference = 2·p ·radius
or
Circumference = p ·diameter
C = 2pr
or
C = pd
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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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4 inches
Find the circumference of a circle
whose radius is 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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