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Chapter 03
DecimalsDecimals
McGraw-Hill/Irwin Copyright © 2011 by the McGraw-Hill Companies, Inc. All rights reserved.
1. Explain the place values of whole numbers and decimals; round decimals
2. Convert decimal fractions to decimals, proper fractions to decimals, mixed numbers to decimals, and pure and mixed decimals to decimal fractions
Decimals#3#3Learning Unit ObjectivesRounding Decimals; Fraction and Decimal Conversions
LU3.1LU3.1
3-2
1. Add, subtract, multiply, and divide decimals
2. Multiply and divide decimals by shortcut methods
3. Complete decimal applications in foreign currency
Decimals#3#3Learning Unit ObjectivesAdding, Subtracting, Multiplying, and Dividing Decimals
LU3.2LU3.2
3-3
3-4
Table 3.1 - Bag of M&M’s
Decimal PercentColor Fraction (hundredth) (hundredth)
YellowYellow 18 .33 32.73% 55
RedRed 10 .18 18.18% 55
BlueBlue 9 .16 16.36% 55OrangeOrange 7 .13 12.73%
55BrownBrown 6 .11 10.91%
55GreenGreen 5 .09 9.09% 55TotalTotal 55 1.00 100.00% 55 = 1
3-5
Decimal place-value chart
Figure 3.1H
undr
eds
Tho
usan
ds
Ten
s
One
s
Hun
dred
ths
Ten
ths
Ten
Tho
usan
dths
Tho
usan
dths
Hu
nd
red
Th
ousa
nd
ths
1,000 100 10 1 110
1 . 100
1 . 1,000
1 . 10,000
1 . 100,000
Dec
imal
Poi
nt
and
Whole Number Groups Decimal Place Values
3-6
Rounding Decimals
.3272727 .337272
Step 1. Identify the place value of the digit you wantto round
Step 2. Identify the digit to the right.If 5 or more, increase the identified digit
by 1. If less than 5 do not change
Step 3. Drop all digits to the rightof the identified digit
.33
3-7
Rounding Decimals
Round to nearest dollar: $166.39 $166
Round to nearest cent: $1,196.885 $1,196.89
Round to nearest hundredth: $38.563 $38.56
Round to nearest thousandth: $1,432.9981 $1,432.998
3-8
Converting Decimal Fractions to Decimals
2 Steps
1. Count the number of zeros in the denominator.
2. Place the numerator of the decimal fraction to the right of the decimal point the same number of places as you have zeros in the denominator. Do not go over the total number of denominator zeros.
Fraction Decimal # of places
3 .3 110
3 .03 2100
3 .003 31,000
3 .0003 410,000
3-9
Converting Proper Fractions to Decimals
34
4 3.00
2.8
20
20
0
.75
EQUALS
.75
Step 1
3-10
Converting Mixed Numbers to Decimals
25
5 2.0 2.0 0
8.4
.4
88 + .4 (Step 2)
(Step 1)
3-11
Converting Pure Decimals to Decimal Fractions
24 1
24
24100
2
.24
Step 1
Step 2
Step 3
Places
3-12
Converting Mixed Decimals to Decimal Fractions
45 1
45
45 45100 100
217.45
Step 1
Step 2
Step 3
Places
=17
3-13
Adding DecimalsAdd: 4 + 7.3 + 36.139 + .0007 + 8.22
4.0000
7.3000
36.1390
.0007
8.2200
55.6597
3-14
Subtracting Decimals
Subtract: 45.3 - 15.273
45.300
- 15.273
30.027
3-15
Multiplying Decimals
2.36x .016
57084 57.0843 decimal places
3776 .037765 decimal places
8.52 (2 decimal places)
x 6.7 (1 decimal places)
Need to add zero
3-16
Dividing DecimalsStep 1. Make the divisor a
whole number by moving the decimal point to the right
Step 2. Move the decimal point in the dividend to the right the same number of places as in step 1. If there are not enough places, add zeros to the right of the dividend.
Step 3. Place the decimal point in the quotient above the new decimal point in the dividend. Divide as usual.
2.5 32.800
25. 328.00
25. 328.00 25 78 75 30 25 50 50
13.12
Example
3-17
Decimals Applications in Foreign Currency
Check $29.11 x 6.8348 = 198.96 yuan
Each 1 equal 6.8348 yuan
The Wall Street Journal clip shows in China the price of Microsoft Office was reduced to 199 yuan from an original price of 699 yuan. Using the currencies table lets us see what the original as well as sales price is in U.S. dollars. In the table on page 74 1 yuan equals $.1463. To find the original selling price you multiply the number of yuan (699) times $.1463.
699 yuan x $.1463 = $102.26
The original selling price in U.S. Dollars is $102.26. To find the new selling price in U.S. dollars, you multiply the number of yuan 199 times $.1463. The new selling price in U.S. dollars is $29.11.
$199 x $.1463 = $29.11 Table factor from currency table on page 74
3-18
Shortcuts for Multiples of 10
6.89 x 10
6.89 x 100
6.89 x 1000 68.96890
689
•Count the zeros in the multiplier
•Move the decimal point the same
number of spaces to the right
MultiplicationMultiplication
3-19
Shortcuts for Multiples of 10
6.89 / 10
6.89 / 100
6.89 / 1000 .689.00689
.0689
•Count the zeros in the divisor
•Move the decimal point the same
number of spaces to the left
DivisionDivision
3-20
Problem 3-62:
$24,000 x .6157 = 14,776.8 pounds
Solution:
Check:
14,776.8 x 1.6241 = $23,999
3-21
Problem 3-69:
2 x $29.95 = $59.90
$0.145 x 410.85 = + $59.57
$119.47
Solution:
3-22
Problem 3-74:
$14.99 + $3.10 + $3.75 = $ 21.84
110.8 sq. yards + 31.8 sq. yards + 161.9 sq. yards = x 304.5
$6,650.28
Solution:
3-23
Problem 3-76:
Laundry Detergent A
$2.00 for 37 ounces$2.00 ÷ 37 = $.05
Laundry Detergent B
$2.37 for 38 ounces$2.37 ÷ 38 = $.06
Mustard A$.88 for 6 ounces$.88 ÷ 6 = $.15
Mustard B
$1.61 for 12.5 ounces$1.61 ÷ 12.5 = $.13
Canned Tuna A$1.09 for 6 ounces$1.09 ÷ 6 = $.18
Canned Tuna B$1.29 for 8.75 ounces$1.29 ÷ 8.75 = $.15
Solution: