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Chapter 03 Decimals McGraw-Hill/Irwin Copyright © 2011 by the McGraw-Hill Companies, Inc. All rights reserved.

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

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

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3-4 Table 3.1 - Bag of M&M’s Decimal Percent ColorFraction (hundredth)(hundredth) Yellow Yellow 18.33 32.73% 55 Red Red 10.18 18.18% 55 Blue Blue 9.16 16.36% 55 Orange Orange 7.13 12.73% 55 Brown Brown 6.11 10.91% 55 Green Green 5.09 9.09% 55 Total Total 55 1.00 100.00% 55 = 1

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3-5 Decimal place-value chart Figure 3.1 HundredsThousandsTensOnes Hundredths Tenths Ten Thousandths Thousandths Hundred Thousandths 1,000100101 1 10 1. 100 1. 1,000 1. 10,000 1. 100,000 Decimal Point and Whole Number Groups Decimal Place Values

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3-6 Rounding Decimals.3272727.337272 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.33

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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

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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 3.31 10 3.032 100 3.0033 1,000 3.00034 10,000

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3-9 Converting Proper Fractions to Decimals 3434 4 3.00 2.8 20 0.75 EQUALS.75 Step 1

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3-10 Converting Mixed Numbers to Decimals 2525 5 2.0 2.0 0 8.4.4 8 8 +.4 (Step 2) (Step 1)

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3-11 Converting Pure Decimals to Decimal Fractions 24 1 24 100 2.24 Step 1 Step 2 Step 3 Places

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3-12 Converting Mixed Decimals to Decimal Fractions 45 1 45 45 45 100 2 17.45 Step 1 Step 2 Step 3 Places =17

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3-13 Adding Decimals Add: 4 + 7.3 + 36.139 +.0007 + 8.22 4.0000 7.3000 36.1390.0007 8.2200 55.6597

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3-14 Subtracting Decimals Subtract: 45.3 - 15.273 45.300 - 15.273 30.027

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3-15 Multiplying Decimals 2.36 x.016 5708457.084 3 decimal places 3776.03776 5 decimal places 8.52 (2 decimal places) x 6.7 (1 decimal places) Need to add zero

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3-16 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. 2.5 32.800 25. 328.00 25 78 75 30 25 50 13.12 Example

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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

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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 Multiplication

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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 Division

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3-20 Problem 3-62: $24,000 x.6157 = 14,776.8 pounds Solution: Check: 14,776.8 x 1.6241 = $23,999

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3-21 Problem 3-69: 2 x $29.95 = $59.90 $0.145 x 410.85 = + $59.57 $119.47 Solution:

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3-22 Problem 3-74: $14.99 + $3.10 + $3.75 = $ 21.84 110.8 sq. yards + 31.8 sq. yards + 161.9 sq. yards = x 304.5 $6,650.28 Solution:

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3-23 Problem 3-76: Laundry Detergent A $2.00 for 37 ounces $2.00 ÷ 37 = $.05 Laundry Detergent B $2.37 for 38 ounces $2.37 ÷ 38 = $.06 Mustard A $.88 for 6 ounces $.88 ÷ 6 = $.15 Mustard B $1.61 for 12.5 ounces $1.61 ÷ 12.5 = $.13 Canned Tuna A $1.09 for 6 ounces $1.09 ÷ 6 = $.18 Canned Tuna B $1.29 for 8.75 ounces $1.29 ÷ 8.75 = $.15 Solution:

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