Chapter 3 Decimals McGraw-Hill/Irwin ©2011 The McGraw-Hill Companies, All Rights Reserved

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

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

Table 3.1 - Bag of M&M’s Decimal Percent Color Fraction (hundredth) (hundredth) Yellow 18 .33 32.73% 55 Red 10 .18 18.18% Blue 9 .16 16.36% Orange 7 .13 12.73% Brown 6 .11 10.91% Green 5 .09 9.09% Total 55 1.00 100.00% 55 = 1

Decimal place-value chart Figure 3.1 Whole Number Groups Decimal Place Values Hundredths Ten Thousandths Thousands Hundreds Tens Ones Decimal Point Tenths Thousandths Hundred Thousandths 1 10 1 . 100 1 . 1,000 1 . 10,000 1 . 100,000 1,000 100 10 1 and

Rounding Decimals .3272727 .337272 .33 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 .33

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

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 .3 1 10 3 .03 2 100 3 .003 3 1,000 3 .0003 4 10,000

Converting Proper Fractions to Decimals .75 4 3.00 2.8 20 EQUALS 3 4 Step 1 .75

Converting Mixed Numbers to Decimals .4 5 2.0 2.0 (Step 1) 2 5 8 8 + .4 (Step 2) 8.4

Converting Pure Decimals to Decimal Fractions Step 1 24 Step 2 24 1 .24 Places 2 Step 3 24 100

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

Adding Decimals Add: 4 + 7.3 + 36.139 + .0007 + 8.22 4.0000 7.3000 36.1390 .0007 8.2200 55.6597

Subtracting Decimals Subtract: 45.3 - 15.273 45.300 - 15.273 30.027

Multiplying Decimals 8.52 (2 decimal places) x 6.7 (1 decimal places) 57084 57.084 5 decimal places 3776 .03776 Need to add zero 2.36 x .016

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. Example 2.5 32.800 25. 328.00 13.12 25. 328.00 25 78 75 30 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

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 68.9 6.89 x 10 6.89 x 100 689

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 .689 6.89 / 1000 6.89 / 10 6.89 / 100 .0689