Multiplying a decimal by a whole number means adding the decimal value to itself a certain number of times. It’s just like multiplying whole numbers, but you must keep track of where the decimal point belongs in the answer.
Multiplying a decimal by a whole number works the same as multiplying whole numbers—just place the decimal correctly in your answer.
Follow these steps to multiply decimals by whole numbers correctly:
Multiplying does not change the number of decimal places in the factor; it only affects the position of the decimal in the result.
Let’s look at several examples to see how the decimal moves when you multiply by different whole numbers.
Example 1:
Example 2:
Example 3:
Check your answers by estimating. For example, 0.72 × 5 is close to 1 × 5 = 5, so 3.6 makes sense.
When multiplying a decimal by a multi-digit whole number, use the same steps you would for whole-number multiplication. Ignore the decimal at first, multiply as usual, then place the decimal point in the product based on the number of decimal places in the decimal factor.
Example 1:
Here, 4.2 × 12 = 50.4 because 42 × 12 = 504, and we place the decimal one position from the right.
Example 2:
Multiply as 365 × 24 = 8760, then move the decimal two places to the left to get 87.60.
Example 3:
Think: 48 × 36 = 1728, and since 0.48 has two decimal places, the product is 17.28.
Line up the digits carefully and keep track of your decimal places at the end. Estimating before multiplying helps you see if your answer is reasonable. For example, 0.5 × 36 should be close to 18, so 17.28 makes sense.
When multiplying a decimal by 10, 100, 1,000, or any power of ten, move the decimal point to the right for each zero in the multiplier.
Example 1:
Example 2:
Example 3:
Each zero in the whole number moves the decimal one place to the right. Multiplying by 10 moves it once, by 100 moves it twice, and so on.
Always estimate to see if your answer makes sense. If you multiply a small decimal by a small whole number, the result should be smaller than 10.
Estimate before multiplying to avoid mistakes. 2.5 is close to 3, and 3 × 4 = 12, so 10.0 is a reasonable answer.