Decimal Multiplication Practice
A product can look almost right while its decimal point is in the wrong place. Use these generated questions to practise both parts of multiplication: calculating the digits and deciding their value. Begin with a decimal times a whole number, then try two decimal factors, numbers below one, and powers of ten. Choose each product to receive instant feedback. The working shows the decimal place count so you can check the method as well as the result.
Start decimal multiplication practiceHow to multiply decimals
Treat the digits in each factor as a whole number for the first calculation. To multiply 2.4 by 3, work out 24 × 3 = 72. You have temporarily made the first factor ten times larger, so the product is also ten times larger than the answer you need. Dividing 72 by ten gives 7.2. This scaling explains why the decimal point must be restored.
With two decimal factors, count the places in both. A factor with one decimal place has been scaled by ten; a factor with two has been scaled by one hundred. Together those changes scale the product by one thousand. Therefore 3.6 × 1.25 can be calculated as 36 × 125, followed by placing three digits after the decimal point.
Count from the right end of the whole number product. If there are too few digits, insert zeros on the left until the fractional places are filled. For 0.04 × 0.2, calculate 4 × 2 = 8. The factors have three decimal places altogether, so the answer is 0.008. The zeros are necessary because the eight represents thousandths.
Multiplication does not always make a number bigger. A positive factor below one takes only part of the other quantity. Half of 0.6 is 0.3, so 0.5 × 0.6 is smaller than either factor. Estimating the size of the result before calculating helps catch a misplaced decimal point, especially when both factors are less than one.
For multiplication by 10, 100, or 1000, each digit moves into a place with a greater value. Multiplying by one hundred makes every digit worth one hundred times as much. Thus 0.37 × 100 = 37. When a finished product ends in fractional zeros, they may be removed: 4.500 and 4.5 are the same number. Keep any zeros needed to hold a place inside the result.
Worked examples
1. 2.4 × 3
- Calculate 24 × 3 = 72.
- The factors contain one decimal place altogether.
7.2
2. 3.6 × 1.25
- Calculate 36 × 125 = 4500.
- There are 1 + 2 = 3 decimal places in the factors.
- Write 4.500, then remove the trailing zeros.
4.5
Common mistake: guessing where the decimal belongs
Do not copy the decimal position from just one factor. Count the fractional places in both factors and use their total when writing the product.
Questions about decimal multiplication
- How do you know where to put the decimal when multiplying?
- Count all decimal places in both factors. The unsimplified product must have that many fractional places, adding leading zeros if necessary.
- Can a decimal product be smaller than both factors?
- Yes. When both positive factors are below one, their product is smaller than either. For example, 0.2 × 0.3 = 0.06.
- What happens when multiplying decimals by 10, 100, or 1000?
- The digits move one, two, or three places towards larger place values. For example, 1.25 × 100 = 125.