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Copyright © 2005 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. 1 Chapter 3 Decimals Prepared by Dr. Elena Skliarenko Copyright © 2005 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. 2 #3 LU3.1 Fractions Learning Unit Objectives Rounding Decimals; Fractions & 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 Copyright © 2005 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. 3 #3 LU3.2 Fractions Learning Unit Objectives Adding, Subtracting, Dividing, and Multiplying Decimals • Add, subtract, multiply, and divide decimals • Multiply and divide decimals by shortcut methods • Complete decimal applications in foreign currency Copyright © 2005 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. 4 #3 LU3.3 Fractions Learning Unit Objectives Using a Calculator to perform operations with Decimals • Converting fractions to decimals and decimals to fractions • Adding, subtracting, multiplying, and dividing decimals Copyright © 2005 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. 5 Decimal place-value chart and 1 10 1 . 100 1 . 1,000 1 . 10,000 Copyright © 2005 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. Hundred Thousandths 1 Ten Thousandths Ones 10 Thousandths Tens 100 Hundredths Hundreds 1,000 Tenths Thousands Figure 3.1 1 . 100,000 6 Rounding Decimals 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 .3272727 .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 Copyright © 2005 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. .33 7 Converting Proper Fractions to Decimals .75 4 3.00 2.8 20 20 0 3 4 .75 Copyright © 2005 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. 8 Converting Pure Decimals to Decimal Fractions Step 1 Step 2 .24 Places Step 3 Copyright © 2005 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. 24 24 1 2 24 100 9 Converting Mixed Decimals to Decimal Fractions Step 1 .54 1 2 Step 2 Places Step 3 Copyright © 2005 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. 545 545 1 3 545 1000 10 Adding and Subtracting Decimals Add: 7 + 5.3 + 24.139 + .0003 + 5.02 7.0000 5.3000 24.1390 .0003 5.0200 41.4593 Copyright © 2005 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. 11 Multiplying Decimals 9.09 x 3.8 34542 17275 3 decimal places 5 decimal places 34.542 .17275 6.91 x .025 Copyright © 2005 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. 12 Dividing Decimals Question 3 Steps 4.5 82.89 •Make the divisor a whole number by moving the decimal point to the right •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. •Place the decimal point in the quotient above the new decimal point in the dividend. Divide as usual. Answer 45. 828.9 18.42 45. 828.90 45 378 360 189 180 90 90 Copyright © 2005 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. 13 Decimals Applications in Foreign Currency Key Currency Cross Rates US$ Yen Euro C$ U.K. Aust $ Sfranc US $ 1 122 1.002 1.558 0.64 1.784 1.464 Yen 0.008199 1 0.008213 0.01277 0.005249 0.01463 0.012 Euro 0.9983 121.8 1 1.555 0.6391 1.781 1.462 C$ U.K.Pound Aust $ Sfranc 0.6418 1.562 0.5606 6831 78.28 190.5 68.37 83.31 0.6429 1.565 0.5616 0.6842 1 2.434 0.8734 1.064 0.4109 1 0.3589 0.4373 1.145 2.786 1 1.218 0.9397 2.287 0.8207 1 Copyright © 2005 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. 14 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 68.9 6.89 x 100 689 Copyright © 2005 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. 15 Shortcuts for Multiples of 10 Division •Count the zeros in the divisor •Move the decimal point the same number of spaces to the right .00689 6.89 / 1000 6.89 / 10 .689 6.89 / 100 .0689 Copyright © 2005 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. 16 Proper use of the calculator Copyright © 2005 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. 17 Converting mixed numbers to decimals and decimals to mixed numbers a b/c For example , to convert 1 ¾ into decimal you have to follow these steps. Step 1. Enter 1 ¾ in your calculator 1 a b/c 3 a b/c 4 1 r 3 r 4 Step 2. Press equal sign button = Step 3. Press the “magic” button a b/c 1.75 To convert decimal number into mixed number or fraction undertake the following steps: Step 1. Enter decimal number in your calculator Step 2. Press equal sign button Step 3. Press the “magic” button a b/c Copyright © 2005 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. 18