Last updated on July 4th, 2025
Decimals are usually multiplied when grouping items. We multiply the numbers as if they are whole numbers and then place the decimal point in the product at the correct position based on the decimal places in the original numbers. We will now learn more about multiplication of decimals in the following topic.
Decimals are a way of representing numbers that are not whole. We separate the numbers by using a dot (.) called the decimal point. The numbers to the left of the decimal point represent whole numbers. Each digit to the right of the decimal point represents a fractional value such as tenths (1/10), hundredths (1/100), thousandths (1/1000), and so on.
Multiplying decimals follows the same steps as multiplying whole numbers, with additional attention to placing the decimal point. The key difference is that the decimal point in the answer must be placed based on the number of decimal places in both multiplier and multiplicand. In our daily life, we often come across situations where multiplication of decimals takes place. For instance, when converting currencies, we often multiply decimal values.
To multiply decimals with whole numbers, we follow the following steps:
Step 1: The first step is to ignore the decimal point and multiply as we would normally do.
Step 2: After multiplying the numbers, count the number of decimal places in the original decimal number. The final answer should have the same number of decimal places.
Step 3: Place the decimal point accordingly in the final result.
When we multiply decimals by a power of 10 (10, 100, or 1000), we should count the number of zeros in the number and shift the decimal point towards the right. The number of shifts in the decimal point should be equal to the number of zeros in the power of 10.
To multiply two decimal numbers, we have to follow the steps mentioned below:
Step 1: Ignore the decimals and multiply the numbers as you would normally.
Step 2: Once multiplication is done, count the decimal places in both multiplier and multiplicand. Now, the answer will have as many decimal places as the total number of decimal places in both the multiplicand and the multiplier.
Step 3: Place the decimal point accordingly in the final answer.
In real-life, decimals are used and multiplied for various purposes. Let us take a look at them here:
Students tend to make mistakes while understanding the concept of multiplying decimals. Let us see some common mistakes and how to avoid them, in multiplying decimals:
Multiply 0.2 by 0.3.
0.06
Ignore the decimals:
0.2 becomes 2 and 0.3 becomes 3
Multiply the whole numbers:
2 x 3 = 6
Count the decimal places:
0.2 has 1 decimal place and 0.3 has 1 decimal place, so total = 2
Place the decimal in the product:
Insert the decimal point 2 places from the right in 6 to get 0.06.
Multiply 1.2 by 3.4.
4.08
Ignore the decimals:
1.2 becomes 12 and 3.4 becomes 34.
Multiply the whole numbers:
12 x 34 = 408
Count the decimal places:
1.2 has 1 decimal and 3.4 has 1 decimal; total = 2.
Place the decimal:
Adjust 408 to 4.08
Multiply 0.25 by 0.4
0.1
Remove decimals:
0.25 becomes 25 and 0.4 becomes 4.
Multiply:
25 x 4 = 100
Count decimal places:
0.25 has 2 decimals and 0.4 has 1 decimal; total = 3.
Place the decimal:
100 becomes 0.100, which simplifies to 0.1.
Multiply 2.5 by 0.2.
0.5
Remove decimals:
2.5 becomes 25 and 0.2 becomes 2.
Multiply:
25 x 2 = 50
Total decimal places:
2.5 has 1 decimal and 0.2 has 1 decimal; total = 2.
Place the decimal:
Adjust 50 to 0.50, which is 0.5.
Multiply 1.05 and 2.0
2.1
Remove decimals:
1.05 becomes 105 and 2.0 becomes 20.
Multiply:
105 x 20 = 2100
Count decimal places:
1.05 has 2 decimals; 2.0 has 1 decimal; total = 3.
Place the decimal:
2100 becomes 2.100, which is 2.1
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.