Decimals Chapter Three McGraw-Hill/Irwin Copyright © 2014 by The McGraw-Hill 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.

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

Rounding Decimals .3272727 .337272 3 Steps Step 1. Identify the place value of the digit you want to round. 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. .337272 Step 3. Drop all digits to the right of the identified digit. .33

Rounding Decimals Round to nearest dollar: $166.39 $166 Round to nearest cent: $1,196.885 Round to nearest hundredth: $38.563 Round to nearest thousandth: $1,432.9981 $166 $1,196.89 $38.56 $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 10 100 1,000 10,000 .3 1 .03 2 .003 3 .0003 4

Converting Proper Fractions to Decimals 3 4 4 3.00 2 8 20 .75

Converting Mixed Numbers to Decimals .4 Step 1 2 5 8 5 2.0 2 0 Step 2 8 + .4 = 8.4

Converting Pure Decimals to Decimal Fractions Step 1. Place the digits to the right of the decimal point in the numerator of the fraction. Omit the decimal point. 24 Step 2. Put a 1 in the denominator of the fraction. 24 1 .24 Places: The number of digits to the right of the decimal point. 2 Step 3. 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

Converting Mixed Decimals to Decimal Fractions Step 1. Place the digits to the right of the decimal point in the numerator of the fraction. Omit the decimal point. Step 1 45 17.45 Step 2. Put a 1 in the denominator of the fraction. 45 1 17.45 Places: The number of digits to the right of the decimal point. Places 2 45 100 Step 3. 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. 17 45 100 Step 3

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

Subtracting Decimals Subtract: 45.3 - 15.273 45.300 - 15.273 30.027 CHECK 45.300 - 15.273 = 30.027

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)

Dividing Decimals Step 1. Make the divisor a whole number by moving the decimal point to the right. 2.5 32.800 Example 3 Steps Step 2. 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 25. 328.00 25 78 75 30 50 13.12 Step 3. Place the decimal point in the quotient above the new decimal point in the dividend. Divide as usual.

Decimals Applications in Foreign Currency The price of an Apple iPad 2 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 2 would sell for in Canadian dollars. In the table on page 74, 1 U.S. Dollar equals $1.0210 Canadian dollars . To find the cost in Canadian dollars: 1. You multiply the number of U.S. dollars ($600) times $1.0210. $600 x $1.0210 = $612.60 2. To check your calculations, take the $612.60 Canadian dollars cost of the iPad 2 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). CHECK $612.60 x $1.0210 = $600.00 Table factor from currency table

Shortcuts for Multiples of 10 Multiplication 6.89 x 10 6.89 x 100 6.89 x 1000 68.9 6890 Step 1. Count the zeros in the multiplier. Step 2. Move the decimal point in the multiplicand the same number of places to the right as you have zeros in the multiplier. 689

Shortcuts for Multiples of 10 Division 6.89 / 10 6.89 / 100 6.89 / 1000 .689 .00689 .0689 Step 1. Count the zeros in the divisor. Step 2. Move the decimal point the same number of spaces to the left.