Transcript 5.3 Multiplying Decimals and Circumference of a Circle Martin

5.3
Multiplying Decimals
and Circumference of a
Circle
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Multiplying Decimals
Multiplying decimals is similar to multiplying
whole numbers. The difference is that we place a
decimal point in the product.
0.7  0.03 =
7
10
1 decimal
place

21
3
100
2 decimal
places
=
1000
= 0.021
3 decimal places
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra, 6ed
2
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.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra, 6ed
3
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.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra, 6ed
4
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.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra, 6ed
5
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.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra, 6ed
6
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
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra, 6ed
7
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  0.01
Since there are two decimal places in 0.01, move the decimal
place two places to the left.
8.57  0.01 =
008.57 =
0.0857
Notice that zeros had to be inserted.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra, 6ed
8
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.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra, 6ed
9
The Circumference of a Circle
r
d
Circumference = 2·p ·radius
or
Circumference = p ·diameter
C = 2 p r or C = p d
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra, 6ed
10
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 .
7
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra, 6ed
11
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.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra, 6ed
12