104 LearnersLast updated on July 4th, 2025
Multiplying Decimals
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.
What are Decimals?
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.
How to Multiply Decimals?
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.
Multiplying Decimals with Whole Numbers
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.
Multiplying Decimals by 10, 100, and 1000
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.
Multiplying Two Decimal Numbers
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.
Real-life Applications of Multiplying Decimals
In real-life, decimals are used and multiplied for various purposes. Let us take a look at them here:
- Shopping and Discounts
Decimals are often multiplied when calculating discounts on goods and services. This helps us to calculate final prices and make informed shopping decisions.
- Currency Exchange
Multiplication of decimals is used when converting one currency to another currency. This is especially useful for travelers exploring different countries.
- Cooking and Baking
Recipes require decimal quantities when adjusting servings. This is one application of decimals that is truly used in everyday life.
Common mistakes and How to Avoid Them in Multiplying Decimals
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:
Mistake 1
Incorrectly Placing the Decimal Point
Students must remember to ignore the decimal points while multiplying, then count the total decimal places in both numbers and place the decimal in the final product accordingly.
Mistake 2
Forgetting to Count the Decimal Places
Students must multiply as if there are no decimals, then place the decimal according to the total decimal places in both factors.
Mistake 3
Incorrectly Aligning the Numbers
Students must ignore decimal points when setting up the multiplication. Multiply as whole numbers, then correctly place the decimal in the final product.
Mistake 4
Forgetting to Add Zeroes When Needed
Students must always ensure the correct number of decimal places by adding leading zeros if necessary.
Mistake 5
Treating Decimal Multiplication Like Addition or Subtraction
Students must ignore the decimal points when multiplying and place the decimal at the end by counting decimal places.
Solved Examples on Multiplying Decimals
Problem 1
Multiply 0.2 by 0.3.
0.06
Explanation
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.
Problem 2
Multiply 1.2 by 3.4.
4.08
Explanation
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
Problem 3
Multiply 0.25 by 0.4
0.1
Explanation
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.
Problem 4
Multiply 2.5 by 0.2.
0.5
Explanation
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.
Problem 5
Multiply 1.05 and 2.0
2.1
Explanation
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
FAQs on Multiplying Decimals
1.What does it mean to multiply decimals?
2.How do I multiply decimals?
3.Why do we ignore the decimal point initially?
4.Can I multiply decimals without a calculator?
5.Why does the product seem to have extra zeros?
6.How can children in United States use numbers in everyday life to understand Multiplying Decimals?
7.What are some fun ways kids in United States can practice Multiplying Decimals with numbers?
8.What role do numbers and Multiplying Decimals play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve Multiplying Decimals skills?
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Hiralee Lalitkumar Makwana
About the Author
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.
Fun Fact
: She loves to read number jokes and games.
