Download Decimals - Bakersfield College

Chapter 03
Decimals
McGraw-Hill/Irwin
Copyright © 2011 by the McGraw-Hill Companies, Inc. All rights reserved.
#3 Decimals
Learning Unit Objectives
Rounding Decimals; Fraction and
LU3.1
Decimal Conversions
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
3-2
#3 Decimals
Learning Unit Objectives
Adding, Subtracting, Multiplying, and
LU3.2
Dividing Decimals
1. Add, subtract, multiply, and divide
decimals
2. Multiply and divide decimals by shortcut
methods
3. Complete decimal applications in foreign
currency
3-3
Table 3.1 - Bag of M&M’s
Color
Yellow
Red
Blue
Orange
Brown
Green
Total
3-4
Fraction
18
55
10
55
9
55
7
55
6
55
5
55
55
55 = 1
Decimal
(hundredth)
Percent
(hundredth)
.33
32.73%
.18
18.18%
.16
16.36%
.13
12.73%
.11
10.91%
.09
9.09%
1.00
100.00%
Decimal place-value chart
Figure
3.1
3-5
and
1
10
1 .
100
1 .
1,000
Hundred Thousandths
Thousandths
1
Hundredths
Ones
10
Tenths
Tens
Hundreds
Thousands
1,000 100
Ten Thousandths
Decimal Place Values
Whole Number Groups
1 .
1 .
10,000 100,000
Rounding Decimals
Step 1. Identify the place
value of the digit you want
to round
Step 3. Drop all digits to the right
of the identified digit
.3272727
.337272
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
3-6
.33
Rounding Decimals
3-7
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
Converting Decimal Fractions to Decimals
2 Steps
Fraction
1. Count the number of zeros 3
in the denominator.
10
2. Place the numerator of the
3
decimal fraction to the
100
right of the decimal point
the same number of
3
places as you have zeros
1,000
in the denominator. Do
3
not go over the total
10,000
number of denominator
zeros.
3-8
Decimal
# of places
.3
1
.03
2
.003
3
.0003
4
Converting Proper Fractions to Decimals
.75
4 3.00
2.8
20
20
0
3
4
.75
3-9
Converting Mixed Numbers to Decimals
.4
5 2.0
2.0
0
2
85
8 + .4 (Step 2)
8.4
3-10
Converting Pure Decimals to Decimal Fractions
Step 1
Step 2
24
1
Places
2
.24
Step 3
3-11
24
24
100
Converting Mixed Decimals to
Decimal Fractions
Step 1
17.45
Step 2
45
1
Places
2
Step 3
3-12
45
45
45
=17
100
100
Adding Decimals
Add: 4 + 7.3 + 36.139 + .0007 + 8.22
4.0000
7.3000
36.1390
.0007
8.2200
55.6597
3-13
Subtracting Decimals
Subtract: 45.3 - 15.273
45.300
- 15.273
30.027
3-14
Multiplying Decimals
8.52 (2 decimal places)
x 6.7 (1 decimal places)
3 decimal places
57084
3776
57.084
5 decimal places
.03776
Need to add zero
2.36
x .016
3-15
Dividing Decimals
Step 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.
3-16
Example
2.5 32.800
25. 328.00
13.12
25. 328.00
25
78
75
30
25
50
50
Decimals Applications in Foreign Currency
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
Check $29.11 x 6.8348 = 198.96 yuan
Each 1 equal 6.8348 yuan
3-17
Shortcuts for Multiples of 10
Multiplication
•Count the zeros in the multiplier
•Move the decimal point the same
number of spaces to the right
6890
6.89 x 1000
6.89 x 10
6.89 x 100
3-18
689
68.9
Shortcuts for Multiples of 10
Division
•Count the zeros in the divisor
•Move the decimal point the same
number of spaces to the left
.00689
6.89 / 1000
6.89 / 10
6.89 / 100
3-19
.0689
.689
Problem 3-62:
Solution:
$24,000 x .6157 = 14,776.8 pounds
Check:
14,776.8 x 1.6241 = $23,999
3-20
Problem 3-69:
Solution:
2 x $29.95 =
$59.90
$0.145 x 410.85 = + $59.57
$119.47
3-21
Problem 3-74:
Solution:
$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
3-22
Problem 3-76:
Solution:
Mustard A
$.88 for 6 ounces
$.88 ÷ 6 = $.15
Mustard B
$1.61 for 12.5 ounces
$1.61 ÷ 12.5 = $.13
Laundry Detergent A
$2.00 for 37 ounces
$2.00 ÷ 37 = $.05
Canned Tuna A
$1.09 for 6 ounces
$1.09 ÷ 6 = $.18
Laundry Detergent B
$2.37 for 38 ounces
$2.37 ÷ 38 = $.06
Canned Tuna B
$1.29 for 8.75 ounces
$1.29 ÷ 8.75 = $.15
3-23