Chapter 3 - Decimals. After reading this chapter, you should have a good understanding of the following learning objectives: 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; add, subtract, multiply, and divide decimals; complete decimal applications in foreign currency; multiply and divide decimals by shortcut methods.
Chapter 3 Decimals McGrawHill/Irwin ©2011 The McGrawHill Companies, All Rights Reserved #3 Decimals Learning Unit Objectives Rounding Decimals; Fraction and LU3.1 Decimal Conversions 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 32 #3 Decimals Learning Unit Objectives Adding, Subtracting, Multiplying, and LU3.2 Dividing Decimals Add, subtract, multiply, and divide decimals Multiply and divide decimals by shortcut methods Complete decimal applications in foreign currency 33 Table 3.1 Bag of M&M’s Decimal Color Yellow Fraction (hundredth) 18 .33 55 Red 10 .18 55 Blue 9 .16 Blue 55 Orange 7 .13 55 Brown 6 .11 55 Green 5 .09 55 Total 55 1.00 55 = 1 34 Percent (hundredth) 32.73% 18.18% 16.36% 12.73% 10.91% 9.09% 100.00% Decimal placevalue chart Figure 3.1 35 Tenths and 1 10 Hundred Thousandths Decimal Point Ten Thousandths Ones 10 Thousandths Tens Hundreds Thousands 1,000 100 Hundredths Decimal Place Values Whole Number Groups 1 . 1 . 1 . 1 . 100,000 1,000 10,000 100 Rounding Decimals Step 1. Identify the place value of the digit you want to round .3272727 Step 3. Drop all digits to the right of the identified digit .337272 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 36 .33 Rounding Decimals 37 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 Converting Decimal Fractions to Decimals 2 Steps 38 Fraction Decimal # of places 1. Count the number of zeros 3 in the denominator 10 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 3 100 03 3 1,000 003 3 10,000 0003 Converting Proper Fractions to Decimals S L A U EQ 1 p Ste 75 39 75 4 3.00 2.8 20 20 0 Converting Mixed Numbers to Decimals 85 ( ) p e t S 8.4 310 5 2.0 2.0 0 8 + .4 (Step 2) Converting Pure Decimals to Decimal Fractions Step 1 Step 2 24 1 Places 24 Step 3 311 24 24 100 Converting Mixed Decimals to Decimal Fractions Step 1 17.45 Step 2 45 1 Places Step 3 312 45 45 45 =17 100 100 Adding Decimals Add: 4 + 7.3 + 36.139 + .0007 + 8.22 4.0000 7.3000 36.1390 .0007 8.2200 55.6597 313 Subtracting Decimals Subtract: 45.3 15.273 45.300 15.273 30.027 314 Multiplying Decimals 8.52 (2 decimal places) x 6.7 (1 decimal places) 57084 3776 3 decimal places 5 decimal places 57.084 03776 Need to add zero 2.36 x .016 315 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 316 Example 2.5 32.800 25. 328.00 13.12 25. 328.00 25 78 75 30 25 50 50 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 $.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 Check $29.11 x 6.8348 = 198.96 yuan Each 1 equal 6.8348 yuan 317 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 6.89 x 10 6.89 x 100 318 689 68.9 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 6.89 / 1000 6.89 / 10 6.89 / 100 319 0689 689 ... 45 1 Places Step 3 312 45 45 45 =17 100 100 Adding Decimals Add: 4 + 7 .3 + 36 . 139 + .0007 + 8.22 4.0000 7 .30 00 36 . 139 0 .0007 8.2200 55.6597 3 13 Subtracting Decimals... Subtract: 45 .3 15.2 73 45 .30 0 15.2 73 30.027 3 14 Multiplying Decimals 8.52 (2 decimal places) x 6.7 (1 decimal places) 57084 37 76 3 decimal places 5 decimal places 57.084 037 76 Need to add zero... by 1. If less than 5 do not change 3 6 .33 Rounding Decimals 3 7 Round to nearest dollar: $166 .39 $166 Round to nearest cent: $1,196.885 $1,196.89 Round to nearest hundredth: $38 .5 63 $38 .56 Round to nearest thousandth: $1, 432 .9981