Last updated on July 5th, 2025
One of the basic math skills is multiplying decimals by whole numbers, which is used to solve real-life problems involving money, measurements, and more. In this article, we will learn more about multiplying decimals by whole numbers.
To multiply decimals by a whole number, we follow the steps mentioned below:
Step 1: First, we will multiply the number without considering the decimal points. For example, to multiply 12 × 0.5, we first multiply 12 × 5, ignoring the decimal.
Step 2: Next, count the number of decimal places in the original decimal number.
Here, the product of multiplying 12 × 5 = 60, and the number of decimal places is 1.
Step 3: The number of decimal points in the product should be equal to the number of decimal points in the original decimal number. In other words, the number of decimal points in the products should be equal to the sum of the decimal points in both the multiplicands and the multipliers.
So, 12 × 0.5 = 6.0.
To multiply decimals by a whole number that has two digits, we follow the steps mentioned below:
Step 1: Ignore the Decimal and Multiply as Whole Numbers
Temporarily ignore the decimal in the decimal number. Treat it as a whole number and multiply it by the two-digit whole number.
For example, Multiply 3.42 × 25
Ignore the decimal in 3.42 and treat it as 342.
Multiply 342 × 25 as if they were whole numbers.
Step 2: Multiply by the Ones Digit
Multiply 342 by the one place of the two-digit number (5 in this case).
342 x 5 = 1710
Step 3: Multiply by the Tens Digit
Multiply 342 by the tens place of the two-digit number (2, which represents 20). Remember to add a zero at the end, since you're multiplying by a multiple of ten.
342 x 20 = 6840
Step 4: Add the Two Partial Products
Now, add the results from Step 2 and Step 3.
1710 + 6840 = 8550
Step 5: Count the Decimal Places
Look at the original decimal number (3.42) and count how many decimal places it has (two decimal places).
Step 6: Place the Decimal in the Final Answer
Since 3.42 has two decimal places, place the decimal two places from the right in the final product.
85.50
Thus, 3.42 × 25 = 85.50 or simply 85.5.
To multiply decimals by a whole number that has three digits, we follow the steps mentioned below:
Step 1: Ignore the Decimal and Multiply as Whole Numbers
Remove the decimal from the decimal number and treat it as a whole number. Multiply this number by the three-digit whole number using long multiplication.
For example, Multiply 4.37 × 125
Ignore the decimal and treat 4.37 as 437
Multiply 437 × 125
Step 2: Multiply Using Long Multiplication
Perform long multiplication as usual:
Step 3: Count the Decimal Places
In the original decimal number (4.37), there are two decimal places.
The final product should also have two decimal places.
Step 4: Place the Decimal in the Product
Start from the rightmost digit in 54625 and move two places left to insert the decimal. The final answer is 546.25.
Final Answer: 4.37 × 125 = 546.25
Multiplying decimals by whole numbers is used in various fields. Let us discuss some applications of multiplying decimals by whole numbers:
Students tend to make mistakes while understanding the concept of multiplying decimals by whole numbers. Let us see some common mistakes and how to avoid them, in multiplying decimals by whole numbers:
Multiply 0.5 by 3.
1.5
Ignore the decimal and multiply as whole numbers:
5 × 3 = 15.
Count the decimal places in 0.5 (1 digit).
Place the decimal so that the product has 1 digit after the decimal:
15 becomes 1.5.
Multiply 1.2 by 4.
4.8
Multiply 12 (ignoring the decimal) by 4:
12 × 4 = 48.
Count the decimal places in 1.2 (1 digit).
Place the decimal in 48 to have 1 digit after it:
48 becomes 4.8.
Multiply 0.75 by 8.
6
Ignore the decimal and multiply 75 by 8:
75 × 8 = 600.
Count the decimal places in 0.75 (2 digits).
Adjust the product by placing the decimal point to have 2 digits after it:
600 becomes 6.00, which simplifies to 6.
Multiply 2.5 by 10.
25
Multiply 25 by 10 (ignoring the decimal):
25 × 10 = 250.
Count the decimal places in 2.5 (1 digit).
Since 2.5 has 1 decimal place, place the decimal one digit from the right, 250 becomes 25.0.
Multiply 3.4 by 6.
20.4
Multiply 34 by 6 (ignoring the decimal):
34 × 6 = 204.
Count the decimal places in 3.4 (1 digit).
Place the decimal point in 204 to have 1 digit after it:
204 becomes 20.4.
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
: She loves to read number jokes and games.