L E S S O N 2 3 . Multiplying Decimals 0.7 You can use graph paper to model decimal multiplication. Here is a model of the product of 0.7 and 0.3. 0.3 1 Because 21 of the 100 squares are shaded, 0.7  0.3 = 0.21. 1

L E S S O N 2 3 . Multiplying Decimals 0.7 You can use graph paper to model decimal multiplication. Here is a model of the product of 0.7 and 0.3. 0.3 1 Because 21 of the 100 squares are shaded, 0.7  0.3 = 0.21. 1 NOTE BOOK Multiplying Decimals Multiply decimals as you would whole numbers. Then place the decimal point in the product. The number of decimal places in the product is equal to the sum of the number of decimal places in the factors. Words Numbers 0.7  0.3 = 0.21

2 3 . 1 Multiplying Decimals  Multiplying Decimals 5.82 –––––– 0.41 L E S S O N 2 3 . EXAMPLE 1 Multiplying Decimals 5.82 2 decimal places ––––––  0.41 ––– + 2 decimal places 5 8 2 2 3 2 8 ––––––– 2.3 8 6 2 4 decimal places 4 3 1 2

Multiplying Decimals L E S S O N 2 3 . Checking Reasonableness To check that the product in Example 1 is reasonable, round each factor to the place value of the leading digit, then multiply. The leading digit of a number is the first nonzero digit. 5.82 6 Round to the nearest whole number. 0.41 0.4 Round to the nearest tenth. Because 6  0.4 = 2.4, the product of the previous example is reasonable.

2 3 . 2 Multiplying Decimals  Multiplying Decimals 6.45 –––––– 18 ––– L E S S O N 2 3 . EXAMPLE 2 Multiplying Decimals 6.45 2 decimal places ––––––  18 0 decimal places ––– + 5160 645 –––––– 116.10 2 decimal places After you place the decimal point, you can drop any zeros at the end of an answer. ANSWER 6.45  18 = 116.1 CHECK Because 6  20 = 120, the product is reasonable.

2 3 . 2 Multiplying Decimals   Multiplying Decimals 6.45 1.273 18 L E S S O N 2 3 . EXAMPLE 2 Multiplying Decimals 6.45 2 decimal places 1.273 3 decimal places 18 ––––––  0 decimal places ––– + –––––––  0.06 2 decimal places ––– + 5160 0.0 7638 5 decimal places 645 –––––– 116.10 2 decimal places Write a zero before the 7 as a placeholder so that the number has 5 decimal places. After you place the decimal point, you can drop any zeros at the end of an answer. ANSWER 6.45  18 = 116.1 ANSWER 1.273  0.06 = 0.07638 CHECK CHECK Because 6  20 = 120, the product is reasonable. Because 1  0.06 = 0.06, the product is reasonable.

2 3 . 3 Multiplying Decimals Multiplying Decimals to Find Area L E S S O N 2 3 . EXAMPLE 3 Multiplying Decimals to Find Area Central Park Central Park is a rectangular park about 2.5 miles long and about 0.5 mile wide. What is the area of Central Park? SOLUTION A = l w Write formula for area of a rectangle. = l w 2.5 (0.5) Substitute 2.5 for l and 0.5 for w. = 1.25 Multiply. ANSWER The area of Central Park is about 1.25 square miles.