Post on 31-Dec-2015
description
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
4.4
Multiplying Decimals and Circumference of a Circle
Martin-Gay, Basic Mathematics, 4e 22
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 DecimalsStep 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.
Martin-Gay, Basic Mathematics, 4e 33
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Multiplying Decimals
Step Example
Step 1: Multiply the decimals as though they are whole numbers.
Multiply:
Step 2: The decimal point in the product is placed so that number of decimal places in the product is equal to the sum of the number of decimal places in the factors.
063
9.0
7.0
63.0
9.0
7.0
Total of 2 decimal places.
Decimal placed at two decimal places.
Martin-Gay, Basic Mathematics, 4e 44
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
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).
Martin-Gay, Basic Mathematics, 4e 55
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
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.
Martin-Gay, Basic Mathematics, 4ed 66
1. Multiply 45.9 X 0.42 2. Multiply 0.112 X 0.6
278.19 1836
Practice Problems
91842.0
9.45
Multiplying Decimals
P 275
1 decimal place
2 decimal places
1+2=3 decimal places
0672.06.0
112.0
3 decimal places
1 decimal place
3+1=4 decimal places
Martin-Gay, Basic Mathematics, 4ed 77
3. Multiply 0.0721 X 48
4608.3 2884
Practice Problems
576848
0721.0
Multiplying Decimals
P 276
4 decimal place
0 decimal places
4+0=4 decimal places
Martin-Gay, Basic Mathematics, 4e 88
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
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.
Martin-Gay, Basic Mathematics, 4ed 99
1748.90
27234
Estimating When Multiplying Decimals
Practice Problem 4
SOLUTION
Multiply:
Exact
Estimate
903
30
24208
98.2
26.30
98.2
26.30
Since 90.1748 is close to our estimate of 90, it is a reasonable answer.
P 276
6052
Round to the ones
Martin-Gay, Basic Mathematics, 4e 1010
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Multiplying by Powers of 10
Type Example
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.
0.501005.0
0006.001.006.0
Martin-Gay, Basic Mathematics, 4e 1111
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Example
Multiply.
a. 58.1 × 0.01
b. 85,624 × 0.1
c. 24.106 ×100
= 0.581 Move the decimal point 2 places to the left
= 8562.4 Move the decimal point 1 place to the left.
= 2410.6 Move the decimal point 2 places to the right.
Martin-Gay, Basic Mathematics, 4e 1212
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Problems Answers
5.
6.
7.
P 277
Practice Problems
107.23
Multiplying by Powers of 10
107.23 237
100004.203 100004.203 4.20300
100015.1 1000150.1 1150
Martin-Gay, Basic Mathematics, 4e 1313
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Problems Answers
8.
9.
10.
P 277
Practice Problems
1.62.7
Multiplying by Powers of 10
1.62.7 762.0
01.9.1 01.9.001 019.0
001.7682 001.7682 682.7
Martin-Gay, Basic Mathematics, 4e 1414
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Finding the Circumference of a Circle
Definition Example
Circumference: The distance around a circle.
diameter
radius
Circumference 2 radius Circumference diameter
The two common approximations for 22
are 3.14 and .7
Martin-Gay, Basic Mathematics, 4e 1515
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Example
Find the circumference of the following circle.
Circumference =
9.1 yards
2 9.1
2 r
yards 148.57
Martin-Gay, Basic Mathematics, 4e 1616
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
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.
Martin-Gay, Basic Mathematics, 4e 1717
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Finding the Circumference of a Circle
Practice Problem 12
SOLUTION
Find the circumference of a circle whose radius is 11 meters. Then use the approximations 3.14 for π to approximate this circumference. 11 meters
112 meters 08.69
P 278
Martin-Gay, Basic Mathematics, 4e 1818
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
DONE