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Mastering Decimal Multiplication: Step-by-Step Guide with Examples

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Learn how to multiply decimals effectively with our comprehensive guide. This resource covers essential techniques, including the correct alignment of numbers, counting decimal places, and placing the decimal in the product. We provide clear examples and practice problems, helping you understand the commutative and associative properties of multiplication. Plus, discover how multiplying by powers of ten affects decimal placement. Perfect for students and anyone looking to strengthen their math skills!

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Mastering Decimal Multiplication: Step-by-Step Guide with Examples

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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

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