Lecture Practical business math procedures (11/e) - Chapter 3: Decimals

Decimals
Chapter Three

McGraw­Hill/Irwin

Copyright © 2014 by The McGraw­Hill Companies, Inc. All rights reserved.


Learning unit objectives
LU 3-1: Rounding Decimals; Fraction & 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.
LU 3-2: Adding, Subtracting, Multiplying, and Dividing Decimals
1.
Add, subtract, multiply, and divide decimals.
2.
Complete decimal applications in foreign currency.
3.
Multiply and divide decimals by shortcut methods.

3­2


Table 3.1 - Bag of M&M’s

Color

Yellow
Red
Blue
Orange
Brown
Green
Total

Decimal Percent
Fraction
(hundredth) (hundredth)
55
10
55

55
55

18

.33
.18

32.73%
18.18%

9
55
7

.16

16.36%

.13

12.73%

6

.11

10.91%

5
55
55
55 = 1

.09

9.09%

1.00

100.00%

3­3

Decimal place-value chart

3­4


Rounding Decimals
3 Steps
Step 1. Identify the place
value of the digit you
want to 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.

.3272727

.337272
Step 3. Drop all digits to
the right of the
identified digit.

.33

3­5


Rounding Decimals

$166

Round to nearest dollar:

$166.39

Round to nearest cent:

$1,196.885

$1,196.89

$38.563

$38.56

Round to nearest hundredth:
Round to nearest thousandth:

$1,432.9981

$1,432.998

3­6


Converting Decimal Fractions
to Decimals
2 Steps

Fraction

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.

3
10
3
100
3
1,000
3
10,000

Decimal

# of places

.3

1

.03

2

.003

3

.0003

4

3­7


Converting Proper Fractions
to Decimals
.75
3
4

Decimal

4 3.00
28

20
20
0

3­8


Converting Mixed Numbers
to Decimals
8 2
5

Step 1

.4
5 2.0
20
0

Step 2

8

+ .4 = 8.4

3­9


Converting Pure Decimals to Decimal
Fractions

Step 1. Place the digits to the right of the
decimal point in the numerator of the
fraction. Omit the decimal point.

24

Step 2. Put a 1 in the
denominator of the fraction.

24
1

Places: The number of digits to the
right of the decimal point.

2

.24
Step 3. Add the same number
of zeros (as the places) to the denominator of the
fraction. For mixed decimals, add the fraction to
the whole number.

24
100

3­10


Converting Mixed Decimals to

Decimal Fractions
17.45

Step 1. Place the digits to the
Stepright
1 of the
decimal point in the numerator of the fraction.
Omit the decimal point.

Step 2. Put a 1 in the denominator of the
fraction.
17.45

17 45
100

45

45
1

Places: The number of digits toPlaces
the right
of the decimal point.

2

Step 3. Add the same number of zeros (as the
Step
places) to the denominator of

the3fraction. For
mixed decimals, add the fraction to the whole
number.

45
100

3­11


Adding Decimals
Add: 4 + 7.3 + 36.139 + .0007 + 8.22
4.0000
7.3000
36.1390

CHECK

.0007

4.0000

8.2200

7.3000

55.6597

36.1390
.0007

8.2200
55.6597

3­12


Subtracting Decimals
Subtract: 45.3 - 15.273
45.300
- 15.273
30.027

CHECK
45.300
- 15.273
= 30.027

3­13


Multiplying Decimals
8.52 (2 decimal places)
x 6.7 (1 decimal places)
= 5964
5112
57084
57.084
(3 decimal places)
2.36
x .016

1416
236
03776

Need to add zero

.03776
(5 decimal places)
3­14


Dividing Decimals
Example

3 Steps
Step 1.

Make the divisor a whole
number by moving the
decimal point to the right.

2.5 32.800

Step 2.

Move the decimal point in the
dividend to the right the same
number of places as in the
divisor (step 1). If there are
not enough places, add zeros

to the right of the dividend.

25. 328.00

Step 3. Place the decimal point in the
quotient above the new
decimal point in the dividend.
Divide as usual.

13.12
25. 328.00
25
78
75
30
25
50
50

3­15


Decimals Applications in Foreign
Currency
The price of an Apple iPad 2 can be bought in Canada for $600 U.S. dollars.
Using the currencies table from the Wall Street Journal let us see what the iPad 2
would sell for in Canadian dollars. In the table on page 74, 1 U.S. Dollar equals
$1.0210 Canadian dollars . To find the cost in Canadian dollars:
1. You multiply the number of U.S. dollars ($600) times $1.0210.
$600 x $1.0210 = $612.60

2. To check your calculations, take the $612.60 Canadian dollars cost of the
iPad 2 and multiply it by $0.9794. This is what the Canadian dollar is worth
against the U.S. dollar. It equals $599.98 (this amount is off .02 due to
rounding).
Table factor from currency table

CHECK $612.60 x $1.0210 = $600.00

3­16


Shortcuts for Multiples of 10
Multiplication
Step 1. Count the zeros in the multiplier.
Step 2. Move the decimal point in the multiplicand the same
number of places to the right as you have zeros in the
multiplier.

6890

6.89 x 1000

6.89 x 100

689

6.89 x 10

68.9

3­17


Shortcuts for Multiples of 10
Division
Step 1. Count the zeros in the divisor.
Step 2. Move the decimal point the same
number of spaces to the left.

.00689

6.89 / 1000

6.89 / 100

6.89 / 10

.689

.0689
3­18