Chapter 3: Decimals

Chapter 3DecimalsMcGraw-Hill/Irwin©2011 The McGraw-Hill Companies, All Rights ReservedExplain the place values of whole numbers and decimals; round decimalsConvert decimal fractions to decimals, proper fractions to decimals, mixed numbers to decimals, and pure and mixed decimals to decimal fractionsDecimals#3Learning Unit ObjectivesRounding Decimals; Fraction and Decimal ConversionsLU3.13-2Add, subtract, multiply, and divide decimalsMultiply and divide decimals by shortcut methodsComplete decimal applications in foreign currencyDecimals#3Learning Unit ObjectivesAdding, Subtracting, Multiplying, and Dividing DecimalsLU3.23-3Table 3.1 - Bag of M&M’s Decimal PercentColor Fraction (hundredth) (hundredth)Yellow 18 .33 32.73% 55Red 10 .18 18.18% 55Blue 9 .16 16.36% 55Orange 7 .13 12.73% 55Brown 6 .11 10.91% 55Green 5 .09 9.09% 55 Total 55 1.00 100.00% 55 = 1Decimal place-value chartFigure 3.1HundredsThousandsTensOnesHundredthsTenthsTen ThousandthsThousandthsHundred Thousandths1,000100101 110 1 . 100 1 . 1,000 1 . 10,000 1 . 100,000Decimal PointandWhole Number GroupsDecimal Place ValuesRounding Decimals .3272727 .337272Step 1. Identify the place value of the digit you wantto roundStep 2. Identify the digit to the right.If 5 or more, increase the identified digit by 1. If less than 5 do not changeStep 3. Drop all digits to the rightof the identified digit .33Rounding DecimalsRound to nearest dollar: $166.39 $166Round to nearest cent: $1,196.885 $1,196.89Round to nearest hundredth: $38.563 $38.56Round to nearest thousandth: $1,432.9981 $1,432.998Converting Decimal Fractions to Decimals2 Steps1. 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 410,000Converting Proper Fractions to Decimals344 3.00 2.8 20 20 0.75EQUALS.75Step 1Converting Mixed Numbers to Decimals255 2.0 2.0 0 8.4.488 + .4 (Step 2)(Step 1)Converting Pure Decimals to Decimal Fractions24 124 241002.24Step 1Step 2Step 3PlacesConverting Mixed Decimals to Decimal Fractions45 145 45 45100 100217.45Step 1Step 2Step 3Places=17Adding DecimalsAdd: 4 + 7.3 + 36.139 + .0007 + 8.22 4.0000 7.300036.1390 .0007 8.220055.6597Subtracting DecimalsSubtract: 45.3 - 15.273 45.300- 15.27330.027Multiplying Decimals 2.36x .0165708457.0843 decimal places3776.037765 decimal places 8.52 (2 decimal places)x 6.7 (1 decimal places)Need to add zeroDividing DecimalsStep 1. Make the divisor a whole number by moving the decimal point to the rightStep 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 32.80025. 328.0025. 328.00 25 78 75 30 25 50 5013.12ExampleDecimals Applications in Foreign CurrencyCheck $29.11 x 6.8348 = 198.96 yuan Each 1 equal 6.8348 yuanThe 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 = $102.26The 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 = $29.11Table factor from currency table on page 74Shortcuts for Multiples of 10 6.89 x 106.89 x 1006.89 x 100068.96890689Count the zeros in the multiplierMove the decimal point the same number of spaces to the rightMultiplicationShortcuts for Multiples of 10 6.89 / 106.89 / 1006.89 / 1000.689.00689.0689Count the zeros in the divisorMove the decimal point the same number of spaces to the leftDivision