Multiplying Decimals by 10, 100, or 1,000 6-1 You can use patterns to multiply decimals mentally by 10, 100, and 1,000. Andrew starts selling his baseball cards for $0.10 each. After selling 10 cards, he has made $1.00. After selling 100 cards, he has made $10.00. 6-1 $.0.10 $.0.10 10 $1.00 $0.10 100 $10.00 When you multiply by Move the decimal point 10 1 place to the right 100 2 places to the right 1,000 3 places to the right If Andrew sold 1,000 cards, how much money would he make? For questions 1 4, find the product using mental math. 1. 6.1 10 2. 100 37.98 3. 92.3 1,000 4. 0.418 100 5. Myla has an antique flower vase that she bought for $15.75 many years ago. The vase s value is now 1,000 times as great. What is the value of the vase? 6. Raul can hit a golf ball 26.4 yards. A.J. can hit a golf ball 10 times as far. How far can A.J. hit the ball? Reasonableness 7. Is 0.018 a reasonable answer for 1.8 100? Topic 6 21
Multiplying a Whole Number and a Decimal 6-2 Travis can read a book chapter in 2.6 hours. The book has 18 chapters. How long will it take Travis to read the book? 6-2 Step 1. Multiply as with whole numbers. 2.6 18 208 260 468 Step 2. Count the total decimal places in both factors. 2.6 1 decimal place 18 0 decimal places It will take Travis 46.8 hours to read the book. Step 3. Since there is a total of 1 decimal place in the factors, there is 1 decimal place in the product. 46.8 For questions 1 3, find the product. 1. 2.3 2. 71.7 3. 0.894 6 12 21 4. Sara is multiplying two factors, one is a whole number and one with two decimal places. She says that the product should have two decimal places. Is this correct? Explain. Critical Thinking 5. Light bulbs usually cost $2. They are on sale for 0.50 off the regular price. What is the sale price? Is this a better price than if the sale price were 0.35 off the regular price? 28 Topic 6
Estimating the Product of a Whole Number and a Decimal 6-3 You can estimate when you are multiplying a whole number by a decimal to check the reasonableness of your product. Zane needs to buy 27 lb of roast beef for the company party. The roast beef costs $2.98 per pound. About how much will the roast beef cost? There are two ways to estimate. Round both numbers Adjust your factors to compatible numbers you can multiply mentally. $2.98 27 $2.98 27 $3 30 $90 $3 25 $75 The roast beef will cost about $90. The roast beef will cost about $75. Estimate each product. 1. 0.8 22 2. 19.3 6 3. 345 5.79 4. 966 0.46 Use the chart to answer questions 5 7. Number Sense 5. About how much would it cost for Angelina and her 4 sisters to get a shampoo and a haircut? Treatment Cost Shampoo $7.95 Haircut $12.95 Coloring $18.25 Perm $22.45 6-3 6. Could 3 of the sisters get their hair colored for less than $100? 7. Angelina gets 9 haircuts per year. About how much does she spend on haircuts for the year? Topic 6 35
Multiplying Two Decimals 6-4 Caroline earns $2.40 per hour for babysitting her brother. She babysat last night for 3.25 hours. How much did she earn? First, estimate your product so you can check for reasonableness. $2.40 3.25 $2 3 6 Caroline earned about $6.00. Step 1: Multiply as with whole numbers. 3.25 2.40 000 13,000 65,000 78,000 Step 2: Count the total number of decimal places in both factors. 3.25 2 decimal places 2.40 2 decimal places So, 4 decimal places total. Step 3: Place the decimal point in the product with the correct total number of decimal places following it. 6-4 7.8000 $7.80 Caroline earned $7.80 last night. Because $7.80 is close to your estimate of $6, your answer is reasonable. Find each product. Check by estimating. 1. 0.2 4.6 2. 3.98 7.1 3. 8.54 0.14 4. 0.532 6.4 5. 9.3 5.86 6. 0.37 4.4 Critical Thinking 7. Jackie wants to buy a new CD player. It costs $32.95. She has saved $26 and has a coupon for 30% off the price. Does Jackie have enough money to buy the CD player? 42 Topic 6
Multiplying with Zeros in the Product 6-5 When you multiply decimals, sometimes your product does not have enough places for the decimal point. You will need to insert one or more zeros into your product to serve as placeholders. Gabriella drove 0.3 miles yesterday. Sam drove 0.2 as far as Gabriella. How many miles did Sam drive? A grid can help you visualize the product. The squares that are shaded show 0.3. The squares with a dot show 0.2. The squares that are both shaded and dotted show the product. 0.2 0.3 6 hundredths. To write this decimal correctly, you must add a zero in the tenths place as a placeholder. 6 hundredths 0.06 6-1 6-5 You can also count the number of decimal places in both factors. The total number of decimal places equals the number of decimal places in your product. 0.3 1 decimal place 0.2 1 decimal place 6 Since you need 2 decimal places in your product and you have only one digit in your product, you need to add a zero to the left of the 6 as a placeholder. The product then correctly becomes 0.06. In questions 1 4, find each product. 1. 0.03 2. 4.01 3. 0.16 4. 7.06 0.42 0.02 0.05 0.01 Algebra If 0.4 0.2 0.08, what is the value of n in the following equations? 5. 0.4 n 0.008 6. 0.4 n 0.0008 7. n 0.2 0.00008 48 Topic 6
Problem Solving: Reasonableness 6-6 When solving a word problem, you want to make sure you answer the right question and that your answer is reasonable. Sami earns $5.75 per hour babysitting. She babysat for 6 hours over last weekend. How much money did Sami make? $5.75 6 345.0 Sami made $345.00 over the weekend. Step 1: Did you answer the right question? The problem asked how much money Sami made, so you answered the right question. Step 2: Is the answer reasonable? You can check for reasonableness by estimating. $5.75 6 $6 6 $36 $345.00 is not close to $36, so the answer is not reasonable. Step 3: Go back and find the mistake. The decimal point was placed incorrectly in the product. The correct product is $34.50. This is close to the estimate of $36. 6-6 Sami made $34.50 over the weekend. For questions 1 and 2, look back and check. Tell if the right question was answered and if the answer is reasonable. 1. Abishek sold 13 paintings at the art show. Each painting sold for $25. How much money did Abishek make? Suggested answer: $325 2. Sara s mom gave her $12 to buy 2 tickets to the movie for Sara and her sister. Sara wants to buy popcorn, too. The tickets are $3.50 each and popcorn is $3.00. How much money will Sara have left? Suggested answer: $10. 54 Topic 6