Rewrite as Whole Numbers
Temporarily remove the decimal points while keeping every digit in the same order.
Free Interactive Math Tool
Decimal Multiplication Practice
Complete partial products, multiply as if the factors were whole numbers, count the decimal places, and place the decimal in the final product.
Learn the Decimal Multiplication Algorithm
Learn why decimal points are temporarily ignored, how partial products work, and how the factors determine the decimal placement in the product.
Read the Decimal Multiplication GuideHow It Works
Multiply First, Then Place the Decimal
Unlike decimal addition and subtraction, the decimal points do not need to line up. Multiply the digits as whole numbers, then use the total number of decimal places in the factors to place the decimal in the product.
Find Partial Products
Multiply by each digit of the bottom factor and shift each new row one place to the left.
Add the Decimal Places
Count the decimal places in both original factors and add those two counts together.
Place and Check the Decimal
Starting at the product’s right edge, move left by the combined number of decimal places.
Interactive Practice
Multiply the Decimals
Correct
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Problems
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Streak
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Decimal × Decimal
Medium MultiplicationMultiply 3.24 × 1.6.
3.24
1.6
First multiply 324 × 16 as whole numbers.
Whole-number multiplication board for 324 times 16.
| First factor | 3 | 2 | 4 | |||||
|---|---|---|---|---|---|---|---|---|
| × | 1 | 6 | ||||||
| First partial product | ||||||||
| Second partial product | ||||||||
| Whole-number product |
Multiply 324 by 6 for the first row. Then multiply 324 by 1 ten for the second row and include the place-value zero.
Whole-Number Work
Complete the partial products and product.
Enter one digit in each outlined box. Work from the rightmost digit toward the left and include each row’s place-value shift.
Decimal Placement
Count the decimal places and place the decimal.
Add the decimal-place counts from the original factors. Then select the position where the decimal belongs in the product.
2
1
decimal places
5
1
8
4
Select one of the decimal-point positions shown between the product digits.
Correct!
You completed the partial products and placed the decimal correctly.
Problem
3.24 × 1.6
Whole Product
5,184
Decimal Places
3
Final Answer
5.184
Multiply 324 × 16 to get 5,184. The factors have three decimal places altogether, so the final product is 5.184.
Helpful Strategies
Keep the Multiplication Organized
Most decimal multiplication errors come from incomplete partial products or incorrect decimal placement.
Ignore Decimals Temporarily
Preserve the digit order, but carry out the standard algorithm using whole-number factors first.
Shift Every New Row
A multiplier digit in the tens place creates a partial product that begins one place farther left.
Count Both Factors
The product’s decimal-place count equals the sum of the decimal-place counts in the two factors.
Estimate the Size
Round the factors and compare the estimated product with your exact answer to catch decimal errors.
Important Distinction
Decimal Multiplication Uses a Different Rule
Align the Decimal Points
Matching place values must occupy the same vertical columns before adding or subtracting.
4.50 + 0.37 = 4.87
Count the Decimal Places
Multiply the digits first, then place the decimal according to both factors’ combined decimal places.
3.24 × 1.6 = 5.184
Real-World Applications
Where Decimal Multiplication Appears
Shopping
Multiply a price by a quantity or calculate a discount, tax, or markup represented by a decimal.
Measurement
Find areas, scaled dimensions, and converted measurements that include decimal values.
Rates and Distance
Multiply a decimal rate by time, distance, mass, or another measured quantity.
Science and Data
Scale experimental values, probabilities, and data recorded with decimal precision.
Practice Another Decimal Product
Generate another problem to practice partial products, place-value shifts, decimal-place counting, and estimation.