Multiplying and Dividing Decimals

Example 1: Multiplying Decimals 0 decimal places 2  0.51 2 decimal places 1.02 0 + 2 = 2 decimal places. B. (0.4)(3.75) 3.75 2 decimal places  0.4 1 decimal place 1.500 2 + 1 = 3 decimal places or 1.5

Check It Out! Multiply. A. 3.1(0.28) 3.1 1 decimal place  0.28 2 decimal places 0.868 1 + 2 = 3 decimal places B. (0.4)(2.53) 0.4 1 decimal place X 2.53 2 decimal places 1.012 1 + 2 = 3 decimal places

You will travel about 10.75 miles. Word Problem Multiplying Decimals RAFTING You travel downstream in a raft at a rate of 4.3 miles per hour. How far will you travel in 2.5 hours? To find how far you travel in the rafting problem above, substitute the given values into the distance formula: distance rate time. = • d rt = = 2.5 • 4.3 1 decimal place 215  + = 10.75 860 2 decimal places ANSWER You will travel about 10.75 miles.

WP Cont… Multiplying Decimals CHECK A number’s leading digit is its leftmost nonzero digit. To check for reasonableness, round each factor to its leading digit and multiply. 2.5 • 4.3 3 4 12 =

More Practice  Find the product. Check that the answer is reasonable. 2.1 • 7.39 1. ANSWER 15.519 5.07 • 19.62 2. ANSWER 99.4734 0.04 • 1.13 3. ANSWER 0.0452 8 • 0.85 4. ANSWER 6.8

When dividing a decimal by a decimal, multiply both numbers by a power of 10 so you can divide by a whole number. To decide which power of 10 to multiply by, look at the denominator. The number of decimal places represents the number of zeros after the 1 in the power of 10. 1.32 0.4 1.32 0.4 10 13.2 4 = = 1 decimal place 1 zero

To find some quotients, you may need to use zeros as placeholders. Strategy Using Zeros as Placeholders To find some quotients, you may need to use zeros as placeholders. Placeholder in Dividend Placeholder in Quotient 6 ÷ 1.2 0.0126 ÷ 1.8 6.0 1.2 0.0126 1.8 126 0.007 0.126 18 60 5 12

Example 2: Dividing Decimals Find 0.384 ÷ 0.24. Estimate the reasonableness of your answer. 0.24 )0.384 0.24 has two decimal places so multiple both numbers by 100 to make the divisor an integer. 1 .6 24 )38.4 Then divide as a whole number. - 24 0.384 ÷ 0.24 = 1.6 Estimate: 40 ÷ 20 = 2 14 4 – 144 The answer is reasonable.

Find 0.65 ÷ 0.25. Estimate the reasonableness of your answer. Check It Out! Find 0.65 ÷ 0.25. Estimate the reasonableness of your answer. 0.25 )0.65 0.25 has two decimal places so multiple both numbers by 100 to make the divisor an integer. 2 .6 25 )65.0 Then divide as a whole number. - 50 15 –150 n 0 The answer is reasonable. 0.65 ÷ 0.25 = 2.6 Estimate: 60 ÷ 20 = 3

Example 3: Evaluating Expressions with Rational Numbers Evaluate the expression for the given value of the variable. 5.25 for n = 0.15 n 5.25 n 0.15 = Substitute 0.15 for n. 0.15 has two decimal places, so multiply both numbers by 100 to make the divisor an integer. 0.15 )5.25 35 15 )525 When n = 0.15, = 35. 5.25 n - 525

3.60 for n = 0.12 n 3.60 = Substitute 0.12 for n. n 0.12 Check It Out! Evaluate the expression for the given value of the variable. 3.60 for n = 0.12 n 3.60 n 0.12 = Substitute 0.12 for n. 0.12 has two decimal places, so multiply both numbers by 100 to make the divisor an integer. 0.12 )3.60 30 12 )360 When n = 0.12, = 30. 3.60 n - 360

More Practice  Find the quotient. Check that the answer is reasonable. 5. 0.04 ÷ 1.6 ANSWER 40 6. 0.79 ÷ 0.632 ANSWER 0.8 7. 0.65 ÷ 13 ANSWER 20 8. 4.5 ÷ 4.365 ANSWER 0.97 9. 0.3744 ÷ 1.56 ANSWER 0.24 10. 2.7 ÷ 0.0108 ANSWER 0.004

Lesson Quiz Find the product or quotient. Check that the answer is reasonable. 1.5 –  ) ( 2.3 1. ANSWER 3.45 2. 9.6 –  0.64 ANSWER 6.144 – 5.35 – ) ( 2.5 3. ÷ ANSWER 2.14 ÷ – 3.9 5.2 4. b. 2.1 ANSWER 0.75 –