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# Multiplying Decimals

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1. Multiplying Decimals

2. Example: 5.63 x 3.7 1 4 2 5.63 two x 3.7 one 1 1 39 4 1 1 + 16 8 9 0 2 0 . 8 3 1 three

3. To Multiply: • You do not line up the factors by the decimal. • Instead, place the number with more digits on top. • Line up the other number underneath, at the right. • Multiply • Count the number of decimal places (from the right) in each factor. • Use the total number of decimal places in your two factors to place the decimal in your product.

4. Example: 0.53 x 2.618 2.618 has more digits (4) than 0.53 (3), so it goes on top. 3 4 Decimal Places 1 2 2.618 three x 0.53 two 1 7 8 5 4 13 0 9 0 0 + 0 0 0 0 00 . 1 3 8 7 5 4 five

5. Multiplying Decimals  + ––– –––––– 1 EXAMPLE Multiplying Decimals 5.82 2 decimal places 0.41 2 decimal places 582 2328 ––––––– 4 decimal places 2.3862 3 1 2 4

6. Multiplying Decimals  + ––– –––––– After you place the decimal point, you can drop any zeros at the end of an answer. 2 EXAMPLE Multiplying Decimals 6.45 2 decimal places 18 0 decimal places 5160 645 –––––– 116.10 2 decimal places ANSWER 6.45  18 = 116.1

7. Multiplying Decimals   + + ––– ––– –––––– ––––––– 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. 3 EXAMPLE Multiplying Decimals 1.273 3 decimal places 6.45 2 decimal places 0.06 2 decimal places 18 0 decimal places 5160 0.0 7638 5 decimal places 645 –––––– 116.10 2 decimal places

8. Try This: 6.5 x 15.3 3 1 2 1 15.3 one x 6.5 one 1 7 6 5 + 9 1 8 0 . 9 9 4 5 two

9. Multiplication Properties Commutative Property of Multiplication: Factors can be multiplied in any order. Example: 12 x 5 = 5 x 12 Associative Property of Multiplication: Factors can be grouped in any way. Example: (2 x 3) x 5 = 2 x (3 x 5)

10. If a Decimal number is multiplied by 10,100, 1000 etc., the decimal shifts to the right side according to the number of Zeroes. 122.77 Ex) Multiply 12. 277 x 10 = 13227.7 Ex) Multiply 132. 277 x 100 = 425870. Ex) Multiply 42. 587 x 10000 = 0