3 4 Multiplying Decimals 2010 Pearson Prentice Hall

§ 3. 4 Multiplying Decimals © 2010 Pearson Prentice Hall. All rights reserved

Multiplying Decimals The multiplication of decimals is related to the multiplication of fractions. one decimal place two decimal places three decimal places Multiplying Decimals 1. 2. 3. Multiply the numbers just as you would multiply whole numbers. Find the sum of the decimal places in the two factors. Place the decimal point in the product so that the product has the same number of decimal places as the sum in step 2. You may need to write zeros to the left of the number found in step 1. Tobey & Slater, Basic College Mathematics, 6 e 2

Multiplying Decimals Example: Multiply 0. 17 0. 4. 2 decimal places 1 decimal place 0. 068 3 decimal places in product (2 + 1 = 3) Tobey & Slater, Basic College Mathematics, 6 e 3

Multiplying Decimals Example: Multiply 0. 043 0. 012. 3 decimal places 2 decimal places 86 43 0. 00 516 5 decimal places in product (3 + 2 = 5) Note the we need to insert two zeros before the 516. Tobey & Slater, Basic College Mathematics, 6 e 4

Multiplying by a Power of 10 Observe the following pattern. one zero Decimal point moved one place to the right. 0. 025 101 = 0. 025 10 = 0. 25 two zeros Decimal point moved two places to the right. 0. 025 102 = 0. 025 100 = 2. 5 three zeros Decimal point moved three places to the right. 0. 025 103 = 0. 025 1000 = 25 Tobey & Slater, Basic College Mathematics, 6 e 5

Multiplying by a Power of 10 Multiplication of a Decimal by a Power of 10 To multiply a decimal by a power of 10, move the decimal point to the right the same number of places as the number of zeros in the power of 10. Example: Multiply 4. 59 10, 000 = 4, 590, 000 four zeros Decimal point moved four places to the right. Tobey & Slater, Basic College Mathematics, 6 e 6