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Chapter 5 Decimals 5-6 Multiplying Decimals | The procedures for multiplying decimal fractions is almost the same as multiplying whole numbers. The only difference is that we have to deal with the decimal points in the decimal-fraction versions—but not until the final step. | 
Review the names of the parts of a multiplication operation.
| | Procedure | | Step 1: Write the decimal values in vertical form, aligning the right-hand digits in the factors. 
Note: Align the right-hand digits, and not the decimal points as in decimal addition and subtraction. | Step 2: Perform the multiplication operation without paying any attention to the decimal points. 
| Step 3: Count the total number of digits to the right of the decimal points in the factors. Count that many places to the left in the product, and place the decimal point there. 
| Example 3.2 x 6 = ? | The Problem | | 3.2 x 6 = ? | Step 1: Write the decimal values in vertical form, aligning the right-hand digits in the factors. | 3.2
x 6 | | Step 2: Perform the multiplication operation without paying any attention to the decimal points. | 3.2
x 6
192 | Note: This is essentially 32 x 6. | Step 3: Count the total number of digits to the right of the decimal points in the factors. Count that many places to the left in the product, and place the decimal point there. | 3.2
x 6
19.2 | Note: There is just one decimal place in the two factors. | | The Solution | | 3.2 x 6 = 19.2 | Example 4.21 x 5 = ? | The Problem | | 4.21 x 5 = ? | Step 1: Write the decimal values in vertical form, aligning the right-hand digits in the factors. | 4.21
x 5 | | Step 2: Perform the multiplication operation without paying any attention to the decimal points. | 4.21
x 5
2105 | Note: This is essentially 421 x 5. | Step 3: Count the total number of digits to the right of the decimal points in the factors. Count that many places to the left in the product, and place the decimal point there. | 4.21
x 5
21.05 | Note: There are two decimal places in the factors. | | The Solution | | 4.21 x 5 = 21.05 | Example 6.58 x 3.2 = ? | The Problem | | 6.58 x 3.2 = ? | Step 1: Write the decimal values in vertical form, aligning the right-hand digits in the factors. | 6.58
x 3.2 | | Step 2: Perform the multiplication operation without paying any attention to the decimal points. | 6.58
x 3.2
21056 | Note: This is essentially 658 x 32 | Step 3: Count the total number of digits to the right of the decimal points in the factors. Count that many places to the left in the product, and place the decimal point there. | 6.58
x 3.2
21.056 | Note: There is a total of three decimal places in the factors (.58 and .2) | | The Solution | | 6.58 x 3.2 = 21.056 | Examples and Exercises Use these interactive examples and exercises to strengthen your understanding and build your skills: | |
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