Step-by-Step Method to Multiply Decimals with Practice Questions
Multiplying by decimals is an important arithmetic skill that is tested in every major school exam and is also essential in daily life for dealing with money, measurements, and data. Mastering the concept of Multiply By Decimals helps students confidently solve word problems, science questions, and practical situations. This guide explains decimal multiplication in clear steps, with examples and practice for students of all levels.
Understanding Multiply By Decimals
To multiply by decimals means to find the product when at least one of the factors is a number with a decimal point. Decimals are special numbers that represent parts of a whole and use place values like tenths, hundredths, and thousandths. Common examples include calculating amounts in money (like ₹8.75 × 3), measurements (such as 0.4 m × 6), or working with scientific data.
Understanding decimal multiplication prevents confusion in calculations and is important for building strong arithmetic and problem-solving skills.
Decimal Multiplication: Step-by-Step Guide
When multiplying by decimals, the most important rule is to multiply as you would with whole numbers, then correctly place the decimal point in your answer. Here are the steps:
- Ignore the decimal points and multiply the numbers as if they are whole numbers.
- Count the total number of decimal places in both original numbers.
- Place the decimal point in your answer so the product has the same number of decimal places as calculated in step 2.
This method works whether you are multiplying two decimals, or a decimal by a whole number.
Summary Table of Decimal Places
| Operation | How Many Decimal Places? |
|---|---|
| Decimal × Decimal | Sum of decimal places in both numbers |
| Decimal × Whole Number | Same as the decimal number |
| Decimal × 10, 100, 1000... | Move the decimal right (matches the zeros in multiplier) |
Worked Examples of Multiplying Decimals
Example 1: Multiplying a Decimal by a Whole Number
- Problem: 0.8 × 7
- Ignore the decimal. Multiply 8 × 7 = 56.
- There is 1 decimal place in 0.8, so answer is 5.6.
Example 2: Multiplying Two Decimals
- Problem: 0.25 × 0.4
- Ignore decimals and multiply 25 × 4 = 100.
- Total decimal places: 0.25 (2) + 0.4 (1) = 3. So answer is 0.100.
- Simplify: trailing zeros can be dropped, so 0.25 × 0.4 = 0.1
Example 3: Multiplying by 10, 100, 1000
| Operation | Result | Explanation |
|---|---|---|
| 2.31 × 10 | 23.1 | Move decimal one place right |
| 0.53 × 100 | 53 | Move decimal two places right |
Practice Problems
- 1.3 × 6 = ?
- 0.25 × 0.9 = ?
- 7.45 × 100 = ?
- 0.14 × 0.5 = ?
- 3.06 × 8 = ?
Common Mistakes to Avoid
- Forgetting to count total decimal places from both numbers before placing the decimal in your answer.
- Multiplying as decimals, but putting the decimal point at random.
- Dropping or adding zeros incorrectly in the final answer (always match the decimal places counted).
- Thinking decimal multiplication uses different digit rules than whole numbers—it does not.
- When multiplying by 10, 100, etc., students sometimes move the decimal the wrong direction (always right).
Real-World Applications
Multiplying decimals is vital in real life:
- Shopping: Finding the total cost when items are priced in rupees and paise (decimals).
- Measurements: Calculating materials needed when measurements are in decimals (e.g., metres, litres).
- Science: Data and lab results often require multiplying decimals.
- Finance: Calculating interest, tax, or commission involves decimals.
At Vedantu, we help students master decimal multiplication through easy-to-follow explanations, live tutoring, and practice worksheets so you’re ready for school exams and everyday challenges.
Want to learn more about decimals? Check out our pages on Decimal Number System, Addition and Subtraction of Decimals, or Place Value for thorough understanding.
To summarize, Multiply By Decimals involves multiplying the numbers and then placing the decimal point by counting the total decimal places in both factors. With regular practice and attention to steps, you can solve decimal multiplication easily and avoid common mistakes. This skill is crucial for student success in both exams and practical life.
FAQs on How to Multiply by Decimals (Concept & Examples)
1. How do you multiply a number by a decimal?
To multiply a number by a decimal, ignore the decimal points initially, then multiply the numbers as if they were whole numbers. Afterward, count the total number of decimal places in both numbers and place the decimal point in your answer so that it has the same total number of decimal places. For example, 2.4 × 0.3 = 0.72 (1 decimal place + 1 decimal place = 2 decimal places).
2. How do you find where to put the decimal point when multiplying decimals?
Count the total number of digits to the right of the decimal point in both numbers you are multiplying. Then, in your answer, place the decimal point so that the number of digits to its right is equal to this total. For instance, in 0.15 × 0.2, there are three total decimal places (2 + 1), so the answer 30 becomes 0.030.
3. How do you multiply decimals by powers of 10 (10, 100, 1000)?
Multiplying decimals by powers of 10 is straightforward. Simply move the decimal point to the right by the number of zeros in the power of 10. For example: 3.26 × 10 = 32.6 (one zero, one place right), 3.26 × 100 = 326 (two zeros, two places right), and 3.26 × 1000 = 3260 (three zeros, three places right).
4. What is 0.5 multiplied by 10?
0.5 multiplied by 10 equals 5. When multiplying by 10, move the decimal point one place to the right.
5. Can I use a calculator for decimal multiplication?
Yes, using a calculator is a great way to check your answers when multiplying decimals. However, it's crucial to understand the method of decimal multiplication to solve problems efficiently and accurately and avoid common mistakes.
6. How do you multiply 0.1 and 0.01 by a decimal?
Multiply 0.1 and 0.01 by a decimal using the standard method: ignore the decimal points, perform the multiplication as whole numbers, then count the total number of decimal places in all numbers involved. Place the decimal point in your final answer according to the total count of decimal places. For example: 0.1 x 0.2 = 0.02 and 0.01 x 0.5 = 0.005.
7. How do you multiply equations with decimals?
To multiply equations with decimals, follow the order of operations (BODMAS/PEMDAS) and apply the rules of decimal multiplication to each calculation. Remember to handle the decimal points carefully and maintain proper place value throughout the process.
8. How to multiply a decimal by a whole number?
Multiply the decimal number by the whole number as you would with whole numbers, ignoring the decimal point. Count the number of decimal places in the decimal number, then place the decimal point in the result so that it has the same number of decimal places. For example: 0.75 x 4 = 3.00
9. How does multiplying by a number less than 1 affect the product?
Multiplying by a number less than 1 (a decimal) always results in a product that is smaller than the original number. This is because you are essentially finding a fraction of the original number. For example, 0.5 x 10 = 5, which is half of 10.
10. Why do place value errors often occur in decimal multiplication?
Place value errors often arise from miscounting the total number of decimal places in the factors, leading to the incorrect placement of the decimal point in the product. Careful attention to counting the total number of decimal places and aligning digits before and after multiplying is crucial in avoiding such errors.
