Chapter ThreeDECIMALS

Copyright © 2014 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin

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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.

LEARNING UNIT OBJECTIVES

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.

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TABLE 3.1 - BAG OF M&M’S

Decimal PercentColor Fraction (hundredth)

(hundredth)

Yellow 18 .33 32.73% 55

Red 10 .18 18.18% 55

Blue 9 .16 16.36% 55Orange 7 .13 12.73%

55Brown 6 .11 10.91%

55Green 5 .09 9.09% 55Total 55 1.00 100.00% 55 = 1

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DECIMAL PLACE-VALUE CHART

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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

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ROUNDING DECIMALS

Round to nearest dollar: $166.39

Round to nearest cent: $1,196.885

Round to nearest hundredth: $38.563

Round to nearest thousandth: $1,432.9981 $1,432.998

$38.56

$1,196.89

$166

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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 10 3 100 3 1,000 3 10,000

.3 1

.03

2

.003 3

.0003 4

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CONVERTING PROPER FRACTIONS TO DECIMALS

34 4 3.00

2 8 20 20 0

.75 Decimal

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CONVERTING MIXED NUMBERS TO DECIMALS

+ .4 = 8.4

25 5 2.0

2 0 0

8 .4 Step 1

Step 2

8

3-10

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 numberof 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

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CONVERTING MIXED DECIMALS TO DECIMAL FRACTIONS

45 1

45

17.45

Step 1

Step 3

Places

45100

2

17.45Step 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.

45 100

17

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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

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SUBTRACTING DECIMALS

Subtract: 45.3 - 15.273

45.300

- 15.273

30.027 CHECK

45.300

- 15.273

= 30.027

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MULTIPLYING DECIMALS

2.36x .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

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DIVIDING DECIMALS

25. 328.00

25. 328.00 25 78 75 30 25 50 50

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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

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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).

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SHORTCUTS FOR MULTIPLES OF 10MULTIPLICATION

6.89 x 106.89 x 100

6.89 x 1000 68.96890

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.

689

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SHORTCUTS FOR MULTIPLES OF 10DIVISION

6.89 / 106.89 / 100

6.89 / 1000 .689.00689

.0689

Step 1. Count the zeros in the divisor.Step 2. Move the decimal point the

same number of spaces to the left.