Transcript Multiplying Decimals

Chapter 4
Decimals
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
4.4
Multiplying Decimals and
Circumference of a Circle
Copyright © 2011 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.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Developmental Mathematics, 2e
3
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.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Developmental Mathematics, 2e
4
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).
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Developmental Mathematics, 2e
5
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.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Developmental Mathematics, 2e
6
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.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Developmental Mathematics, 2e
7
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
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Developmental Mathematics, 2e
8
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.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Developmental Mathematics, 2e
9
Finding the Circumference of a Circle
Definition
Circumference: The
distance around a circle.
Example
radius
diameter
Circumference  2   radius
Circumference 
 diameter
22
The two common approximations for  are 3.14 and .
7
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Developmental Mathematics, 2e
10
Example
Find the circumference of the following circle.
9.1 yards
Circumference = 2    r
 2  9.1  
 57.148 yards
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Developmental Mathematics, 2e
11
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.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Developmental Mathematics, 2e
12