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

After completing this chapter, students will be able to: Explain the place values of whole numbers and decimals; round decimals; convert decimal fractions to decimals, proper fractions to decimals, mixed numbers to decimals, and pure and mixed decimals to decimal fractions; add, subtract, multiply, and divide decimals; complete decimal applications in foreign currency; multiply and divide decimals by shortcut methods.

Chapter Three

Decimals

LU 3-1: Rounding Decimals; Fraction & Decimal Conversions

decimals

mixed numbers to decimals, and pure and mixed decimals to decimal fractions

Learning unit objectives

LU 3-2: Adding, Subtracting, Multiplying, and Dividing Decimals

Table 3.1 - Bag of M&M’s

Decimal Percent Color Fraction (hundredth) (hundredth)

Yellow 18 .33 32.73%

55

55

55

55

Brown 6 .11 10.91%

55

Green 5 .09 9.09%

55

3­4 Decimal place-value chart

Rounding Decimals

.337272

33

3272727

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

Step 3 Drop all digits to

the right of the identified digit

3 Steps

Rounding Decimals

Round to nearest cent: $1,196.885

Round to nearest hundredth: $38.563

$38.56

$1,196.89 $166

Converting Decimal Fractions

to Decimals

2 Steps

zeros in the denominator

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

10

3

100

3

1,000

3

10,000

Converting Proper Fractions

to Decimals

3

2 8 20 20 0

Converting Mixed Numbers

to Decimals

+ 4 = 8.4

2

2 0 0

8

4

Step 1

Step 2

8

24 1 24

24

100

2

.24

Step 1 Place the digits to the right 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

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

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

Converting Pure Decimals to Decimal

Fractions

Converting Mixed Decimals to

Decimal Fractions

45 1

45

17.45

Step 1

Step 3

Places

45 100 2

17.45

Step 1 Place the digits to the right 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

Step 3 Add the same number of zeros (as the

places) to the denominator of the fraction For

Places: The number of digits to the right

of the decimal point.

45

100

17

Adding Decimals

Add: 4 + 7.3 + 36.139 + 0007 + 8.22

4.0000 7.3000 36.1390 .0007 8.2200

55.6597

CHECK

4.0000 7.3000 36.1390 .0007 8.2200 55.6597

Subtracting Decimals

Subtract: 45.3 - 15.273

45.300

- 15.273 30.027

CHECK

45.300

- 15.273

= 30.027

Multiplying Decimals

2.36

x .016

1416

236

03776

57.084

(3 decimal places)

.03776

(5 decimal places)

8.52 (2 decimal places)

x 6.7 (1 decimal places)

= 5964

5112

57084

Need to add zero

Dividing Decimals

25 328.00

25 328.00

25

78

75

30

25

50

50

13.12

Step 1 Make the divisor a whole

number by moving the decimal point to the right

2.5 32.800

Example

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.

Step 3 Place the decimal point in the

quotient above the new decimal point in the dividend

Divide as usual

3 Steps

Decimals Applications in Foreign

Currency

CHECK $612.60 x $1.0210 = $600.00

Table factor from currency table

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)

Shortcuts for Multiples of 10

Multiplication

6.89 x 10 6.89 x 100

6890

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

Shortcuts for Multiples of 10

Division

6.89 / 10 6.89 / 100

.00689

.0689

Step 1 Count the zeros in the divisor

Step 2 Move the decimal point the same

number of spaces to the left