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**Chapter 3 Decimals McGraw-Hill/Irwin**

©2011 The McGraw-Hill Companies, All Rights Reserved

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**Learning Unit Objectives**

#3 Decimals Learning Unit Objectives Rounding Decimals; Fraction and Decimal Conversions LU3.1 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 3-2

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**Learning Unit Objectives**

#3 Decimals Learning Unit Objectives Adding, Subtracting, Multiplying, and Dividing Decimals LU3.2 Add, subtract, multiply, and divide decimals Multiply and divide decimals by shortcut methods Complete decimal applications in foreign currency 3-3

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**Table 3.1 - Bag of M&M’s Decimal Percent**

Color Fraction (hundredth) (hundredth) Yellow % 55 Red % Blue % Orange % Brown % Green % Total % 55 = 1

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**Decimal place-value chart**

Figure 3.1 Whole Number Groups Decimal Place Values Hundredths Ten Thousandths Thousands Hundreds Tens Ones Decimal Point Tenths Thousandths Hundred Thousandths 1 10 1 . 100 1 . 1,000 10,000 100,000 1,000 100 10 1 and

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**Rounding Decimals .3272727 .337272 .33 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 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 .33

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**Rounding Decimals Round to nearest dollar: $166.39 $166**

Round to nearest cent: $1, $1,196.89 Round to nearest hundredth: $ $38.56 Round to nearest thousandth: $1, $1,

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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 10 100 1,000 10,000

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**Converting Proper Fractions to Decimals**

.75 2.8 20 EQUALS 3 4 Step 1 .75

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**Converting Mixed Numbers to Decimals**

.4 2.0 (Step 1) 2 5 8 (Step 2) 8.4

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**Converting Pure Decimals to Decimal Fractions**

Step 1 24 Step 2 24 1 .24 Places 2 Step 3 24 100

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**Converting Mixed Decimals to Decimal Fractions**

45 Step 1 45 1 Step 2 17.45 Places 2 Step 3 =17

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

.0007 8.2200

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Subtracting Decimals Subtract: 45.300 30.027

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**Multiplying Decimals 8.52 (2 decimal places) x 6.7 (1 decimal places)**

57084 57.084 5 decimal places 3776 .03776 Need to add zero 2.36 x

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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. Example 13.12 25 78 75 30 50

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**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 $ 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 $ To find the new selling price in U.S. dollars, you multiply the number of yuan 199 times $ 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 = yuan Each 1 equal yuan

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**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 68.9 6.89 x 10 6.89 x 100 689

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**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 .689 6.89 / 1000 6.89 / 10 6.89 / 100 .0689

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