Multiply as Whole Numbers
Remove the decimal points temporarily and multiply the remaining digits using the standard whole-number algorithm.
3.24 × 1.6 becomes 324 × 16
Free Math Guide
Decimal Multiplication Explained
Learn how to multiply decimals as whole numbers, organize partial products, count decimal places, place the decimal point, and check whether the answer is reasonable.
Decimal multiplication uses the same digit-by-digit process as whole-number multiplication. The decimal points are set aside during the multiplication, but they are not forgotten. After finding the whole-number product, the total number of decimal places in the two factors determines where the decimal belongs in the final answer.
Multiply First, Then Place the Decimal
The multiplication and decimal placement are two separate parts of the same problem. Keeping them separate makes the standard algorithm easier to follow.
Restore the Decimal Point
Add the decimal-place counts from the original factors. Move left that many places from the right side of the whole-number product.
2 places + 1 place = 3 places
Why This Works
Removing a decimal point multiplies a factor by a power of ten. Counting the combined decimal places reverses those powers of ten in the final product.
Build the Product With Partial Products
After rewriting the factors as whole numbers, multiply by each digit of the bottom factor from right to left. Every new row represents a different place value.
Example: Multiply 324 × 16
- Multiply 324 by 6 ones: 324 × 6 = 1,944.
- Multiply 324 by 1 ten: 324 × 10 = 3,240.
- Add the partial products: 1,944 + 3,240 = 5,184.
Whole-number work
324
×16
1,944
+3,240
5,184
Do Not Forget the Place-Value Shift
The 1 in 16 means one ten, not one one. The second partial product must therefore shift one place left, which can be shown with a zero in the ones place.
Add the Decimal Places in Both Factors
Count every digit to the right of the decimal point in the first factor. Do the same for the second factor, then add the two counts.
| Problem | First Factor | Second Factor | Total Places | Final Product |
|---|---|---|---|---|
| 3.24 × 1.6 | 2 places | 1 place | 3 places | 5.184 |
| 4.08 × 0.3 | 2 places | 1 place | 3 places | 1.224 |
| 2.35 × 6 | 2 places | 0 places | 2 places | 14.10 |
| 0.7 × 0.04 | 1 place | 2 places | 3 places | 0.028 |
Count From the Right Edge
In 5,184, moving three places left from the right edge places the decimal after the 5: 5.184.
Add Leading Zeros When the Product Needs More Places
Sometimes the whole-number product does not contain enough digits for the required decimal-place count. Add zeros to the left before placing the decimal.
Example
0.7 × 0.04 → 7 × 4 = 28 → 0.028
Count Three Places
The factors contain one plus two decimal places, so the product needs three decimal places.
Use a Placeholder Zero
Write 28 as 028, then move three places left from the right edge to obtain 0.028.
Multiplying two positive numbers less than one must produce an answer smaller than either factor.
Worked Decimal Multiplication Examples
Decimal × Decimal
Multiply 3.24 × 1.6.
- Multiply 324 × 16 = 5,184.
- Count 2 + 1 = 3 decimal places.
- Move three places left in 5,184.
3.24 × 1.6 = 5.184
Product Less Than One
Multiply 0.7 × 0.04.
- Multiply 7 × 4 = 28.
- Count 1 + 2 = 3 decimal places.
- Add a leading zero and place the decimal.
0.7 × 0.04 = 0.028
Find a Total Cost
Six notebooks cost $2.35 each. Find the total.
- Multiply 235 × 6 = 1,410.
- The price has two decimal places.
- Write the monetary answer with two digits after the decimal.
The total cost is $14.10.
A Zero Inside a Factor
Multiply 4.08 × 0.3.
- Keep the zero when rewriting 4.08 as 408.
- Multiply 408 × 3 = 1,224.
- Count three decimal places altogether.
4.08 × 0.3 = 1.224
Multiply by a Whole Number
Multiply 12.5 × 4.
- Multiply 125 × 4 = 500.
- There is one decimal place altogether.
- Write 50.0, which is equal to 50.
12.5 × 4 = 50
Two-Digit Decimal Factor
Multiply 6.02 × 1.4.
- Multiply 602 × 14 = 8,428.
- Count 2 + 1 = 3 decimal places.
- Move three places left from the right edge.
6.02 × 1.4 = 8.428
Estimate the Product Before or After Calculating
A quick estimate helps detect misplaced decimal points. Round the factors to friendly numbers, multiply, and compare the estimate with the exact result.
Estimate 3.24 × 1.6
Use 3 × 2 = 6. The exact answer 5.184 is close to 6, so its size is reasonable.
Estimate 6.02 × 1.4
Use 6 × 1.5 = 9. The exact answer 8.428 is near 9.
Multiply by less than 1
Multiplying a positive number by a positive factor below 1 makes the result smaller.
Multiply by more than 1
Multiplying a positive number by a factor greater than 1 makes the result larger.
Estimation checks the size of the answer; decimal-place counting determines its exact placement.
Common Decimal Multiplication Mistakes
Aligning Decimal Points Before Multiplying
Decimal points must line up for addition and subtraction, but not for multiplication. Align the factors on the right as whole numbers.
Counting Decimal Places in Only One Factor
The product uses the combined decimal-place count from both factors.
Counting Digits Instead of Decimal Places
Count only the digits to the right of each decimal point, not every digit in each factor.
Forgetting the Partial-Product Shift
When multiplying by a tens digit, shift that partial product one place left. Shift two places for a hundreds digit.
Dropping Zeros Inside a Factor
In 4.08, the zero preserves the tenths place. Removing it changes the number and the whole-number multiplication.
Forgetting a Leading Zero
If the product needs more decimal places than it has digits, add zeros to the left before placing the decimal.
Skipping the Estimate
A correct-looking whole-number product can still have a misplaced decimal. An estimate makes that error easier to notice.
How to Multiply Decimals Step by Step
1. Estimate
Round the factors and predict the approximate size of the product.
2. Remove the decimals temporarily
Rewrite each factor using the same digits in the same order, but without the decimal points.
3. Find the partial products
Multiply by each digit of the bottom factor from right to left and include each place-value shift.
4. Add the partial products
Combine the shifted rows to obtain the whole-number product.
5. Place the decimal
Add the decimal-place counts in the original factors and move left that many places in the product.
6. Check the result
Compare the exact answer with the estimate and verify whether multiplication should make the original amount larger or smaller.
Practice Decimal Multiplication
Complete randomized partial products one digit at a time, find the whole-number product, count the decimal places, and choose the correct decimal-point position with immediate feedback and targeted hints.
Open the Decimal Multiplication ToolRelated Math Resources
Interactive Decimal Multiplication
Practice partial products and decimal placement with randomized problems and immediate feedback.
Decimal Addition and Subtraction Guide
Learn to align place values, use placeholder zeros, carry, borrow, and check decimal sums and differences.
Decimal Place Value Guide
Review how each position to the right of a decimal point represents tenths, hundredths, thousandths, and beyond.
Math Resources
Browse additional guides, worksheets, lessons, and interactive learning tools.
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