After completing this chapter, students will be able to: 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.
Decimals Chapter Three McGrawHill/Irwin Copyright © 2014 by The McGrawHill Companies, Inc. All rights reserved Learning unit objectives LU 3-1: Rounding Decimals; Fraction & 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 LU 3-2: Adding, Subtracting, Multiplying, and Dividing Decimals Add, subtract, multiply, and divide decimals Complete decimal applications in foreign currency Multiply and divide decimals by shortcut methods 32 Table 3.1 - Bag of M&M’s Color Yellow Red Blue Orange Brown Green Total Decimal Percent Fraction (hundredth) (hundredth) 55 10 55 55 55 18 33 18 32.73% 18.18% 55 16 16.36% 13 12.73% 11 10.91% 55 55 55 = 09 9.09% 1.00 100.00% 33 Decimal place-value chart 34 Rounding Decimals Steps Step Identify the place value of the digit you want to round Step Identify the digit to the right If or more, increase the identified digit by If less than 5, not change .3272727 337272 Step Drop all digits to the right of the identified digit .33 35 Rounding Decimals $166 Round to nearest dollar: $166.39 Round to nearest cent: $1,196.885 $1,196.89 $38.563 $38.56 Round to nearest hundredth: Round to nearest thousandth: $1,432.9981 $1,432.998 36 Converting Decimal Fractions to Decimals Steps Fraction Count the number of zeros in the denominator 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 10 100 1,000 10,000 Decimal # of places 03 003 0003 37 Converting Proper Fractions to Decimals 75 Decimal 3.00 28 20 20 38 Converting Mixed Numbers to Decimals Step 2.0 20 Step + = 8.4 39 Converting Pure Decimals to Decimal Fractions Step Place the digits to the right of the decimal point in the numerator of the fraction Omit the decimal point 24 Step Put a in the denominator of the fraction 24 Places: The number of digits to the right of the decimal point 24 Step 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 24 100 310 Converting Mixed Decimals to Decimal Fractions 17.45 Step Place the digits to the Stepright of the decimal point in the numerator of the fraction Omit the decimal point Step Put a in the denominator of the fraction 17.45 17 45 100 45 45 Places: The number of digits toPlaces the right of the decimal point Step Add the same number of zeros (as the Step places) to the denominator of the3fraction For mixed decimals, add the fraction to the whole number 45 100 311 Adding Decimals Add: + 7.3 + 36.139 + 0007 + 8.22 4.0000 7.3000 36.1390 CHECK 0007 4.0000 8.2200 7.3000 55.6597 36.1390 0007 8.2200 55.6597 312 Subtracting Decimals Subtract: 45.3 - 15.273 45.300 - 15.273 30.027 CHECK 45.300 - 15.273 = 30.027 313 Multiplying Decimals 8.52 (2 decimal places) x 6.7 (1 decimal places) = 5964 5112 57084 57.084 (3 decimal places) 2.36 x 016 1416 236 03776 Need to add zero 03776 (5 decimal places) 314 Dividing Decimals Example Steps Step Make the divisor a whole number by moving the decimal point to the right 2.5 32.800 Step 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 25 328.00 Step Place the decimal point in the quotient above the new decimal point in the dividend Divide as usual 13.12 25 328.00 25 78 75 30 25 50 50 315 Decimals Applications in Foreign Currency The price of an Apple iPad 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 would sell for in Canadian dollars In the table on page 74, U.S Dollar equals $1.0210 Canadian dollars To find the cost in Canadian dollars: You multiply the number of U.S dollars ($600) times $1.0210 $600 x $1.0210 = $612.60 To check your calculations, take the $612.60 Canadian dollars cost of the iPad 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) Table factor from currency table CHECK $612.60 x $1.0210 = $600.00 316 Shortcuts for Multiples of 10 Multiplication Step Count the zeros in the multiplier Step Move the decimal point in the multiplicand the same number of places to the right as you have zeros in the multiplier 6890 6.89 x 1000 6.89 x 100 689 6.89 x 10 68.9 317 Shortcuts for Multiples of 10 Division Step Count the zeros in the divisor Step Move the decimal point the same number of spaces to the left .00689 6.89 / 1000 6.89 / 100 6.89 / 10 689 0689 318 ... LU 3-1 : Rounding Decimals; Fraction & 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 LU 3-2 : Adding, Subtracting, Multiplying, and Dividing Decimals Add, subtract, multiply, and divide decimals Complete... 36.1390 0007 8.2200 55.6597 312 Subtracting Decimals Subtract: 45.3 - 15.273 45.300 - 15.273 30.027 CHECK 45.300 - 15.273 = 30.027 313 Multiplying Decimals 8.52 (2 decimal places) x 6.7 (1 decimal