Chapter 3

DecimalsDecimals

McGraw-Hill/Irwin ©2011 The McGraw-Hill Companies, 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