Multiplication of Decimals
Multiplication of decimals builds on what you know about whole-number multiplication. The key difference is handling the decimal point in the answer. In Class 5, you will learn to multiply a decimal by a whole number, multiply a decimal by 10, 100, or 1000, and multiply a decimal by another decimal.
This skill is essential for calculating the total cost of multiple items, converting units, and solving measurement problems.
What is Multiplication of Decimals - Class 5 Maths (Decimals)?
Multiplying decimals means finding the product of two numbers where at least one is a decimal.
Rule: Multiply as if both numbers are whole numbers. Then count the total decimal places in both factors and place the decimal point that many places from the right in the product.
Multiplication of Decimals Formula
Steps to multiply decimals:
- Ignore the decimal points. Multiply the numbers as whole numbers.
- Count the total number of decimal places in both factors.
- In the product, place the decimal point so that it has the same total number of decimal places.
Multiplying by powers of 10:
Decimal x 10 → Move decimal 1 place right
Decimal x 100 → Move decimal 2 places right
Decimal x 1000 → Move decimal 3 places right
Types and Properties
Types of decimal multiplication:
- Decimal x Whole number: e.g., 3.5 x 4 = 14.0 (1 decimal place in factors, 1 in answer)
- Decimal x 10, 100, 1000: e.g., 4.56 x 100 = 456 (shift decimal 2 places right)
- Decimal x Decimal: e.g., 0.3 x 0.7 = 0.21 (1 + 1 = 2 decimal places)
- Word problems: Total cost, total weight, area calculations, etc.
Solved Examples
Example 1: Example 1: Decimal x Whole Number
Problem: Multiply 4.25 x 6.
Solution:
Step 1: Multiply as whole numbers: 425 x 6 = 2550
Step 2: 4.25 has 2 decimal places. Place decimal 2 places from right: 25.50
Answer: 4.25 x 6 = 25.50 (or 25.5)
Example 2: Example 2: Decimal x 10
Problem: Multiply 3.72 x 10.
Solution:
Step 1: Move the decimal point 1 place to the right.
Step 2: 3.72 → 37.2
Answer: 3.72 x 10 = 37.2
Example 3: Example 3: Decimal x 100
Problem: Multiply 0.456 x 100.
Solution:
Step 1: Move the decimal point 2 places to the right.
Step 2: 0.456 → 45.6
Answer: 0.456 x 100 = 45.6
Example 4: Example 4: Decimal x 1000
Problem: Multiply 2.5 x 1000.
Solution:
Step 1: Move the decimal point 3 places to the right.
Step 2: 2.5 → 2500 (add two zeros)
Answer: 2.5 x 1000 = 2500
Example 5: Example 5: Decimal x Decimal
Problem: Multiply 0.6 x 0.8.
Solution:
Step 1: Multiply as whole numbers: 6 x 8 = 48
Step 2: Total decimal places: 1 + 1 = 2. Place decimal: 0.48
Answer: 0.6 x 0.8 = 0.48
Example 6: Example 6: Two-decimal-place x Two-decimal-place
Problem: Multiply 1.25 x 0.04.
Solution:
Step 1: Multiply as whole numbers: 125 x 4 = 500
Step 2: Total decimal places: 2 + 2 = 4. Place decimal: 0.0500 = 0.05
Answer: 1.25 x 0.04 = 0.05
Example 7: Example 7: Word Problem (Total Cost)
Problem: One kg of apples costs Rs.85.50. Aditi buys 3 kg. How much does she pay?
Solution:
Step 1: Total cost = 85.50 x 3
Step 2: 8550 x 3 = 25650. Decimal places = 2.
Step 3: Answer = 256.50
Answer: Aditi pays Rs.256.50.
Example 8: Example 8: Word Problem (Distance)
Problem: An auto-rickshaw travels 0.75 km per minute. How far does it travel in 8 minutes?
Solution:
Step 1: Distance = 0.75 x 8
Step 2: 75 x 8 = 600. Decimal places = 2.
Step 3: Answer = 6.00 = 6
Answer: The auto-rickshaw travels 6 km.
Example 9: Example 9: Word Problem (Area)
Problem: A rectangular garden measures 5.5 m by 3.2 m. Find its area.
Solution:
Step 1: Area = 5.5 x 3.2
Step 2: 55 x 32 = 1760. Total decimal places = 1 + 1 = 2.
Step 3: Answer = 17.60 = 17.6
Answer: Area = 17.6 sq. m
Example 10: Example 10: Word Problem (Weight)
Problem: Each packet of biscuits weighs 0.125 kg. Rahul buys 8 packets. What is the total weight?
Solution:
Step 1: Total weight = 0.125 x 8
Step 2: 125 x 8 = 1000. Decimal places = 3.
Step 3: Answer = 1.000 = 1
Answer: Total weight = 1 kg.
Real-World Applications
Real-life uses of decimal multiplication:
- Shopping: Calculating total cost when buying multiple items at a decimal price.
- Measurement: Finding area of rectangles with decimal dimensions.
- Unit conversion: Multiplying by 10, 100, or 1000 to convert between cm, m, and km, or between g and kg.
- Speed and distance: Distance = speed x time, where speed is often a decimal.
- Recipes: Scaling up ingredient quantities (e.g., 2.5 times a recipe).
Key Points to Remember
- Multiply the numbers as whole numbers (ignoring the decimal point).
- Count total decimal places in both factors. Place that many decimal places in the product.
- Multiplying by 10: shift decimal 1 place right. By 100: 2 places. By 1000: 3 places.
- When multiplying two decimals less than 1, the product is smaller than either number.
- When multiplying a decimal by a whole number greater than 1, the product is larger.
- Trailing zeros can be dropped: 25.50 = 25.5, but 25.05 ≠ 25.5.
- Estimate first to check if your answer is reasonable (e.g., 4.25 x 6 ≈ 4 x 6 = 24).
Practice Problems
- Multiply 3.6 x 7.
- Multiply 0.45 x 100.
- Multiply 2.08 x 5.
- Multiply 0.3 x 0.9.
- Multiply 1.5 x 2.4.
- Ria buys 4 notebooks at Rs.32.50 each. What is the total cost?
- A tile measures 0.25 m by 0.25 m. What is its area in square metres?
- Dev runs 1.35 km every day. How far does he run in 10 days?
Frequently Asked Questions
Q1. How do I multiply decimals?
Multiply the numbers as if they were whole numbers. Then count the total number of decimal places in both factors and place the decimal point that many places from the right in the product.
Q2. What is the shortcut for multiplying by 10, 100, or 1000?
Move the decimal point to the right: 1 place for x10, 2 places for x100, 3 places for x1000. For example, 3.45 x 100 = 345.
Q3. Why does 0.5 x 0.5 = 0.25 and not 0.10?
When you multiply 5 x 5 = 25, and the total decimal places are 1 + 1 = 2, so the answer is 0.25. The product of two decimals less than 1 is always smaller than either factor.
Q4. Can multiplying decimals give a whole number answer?
Yes. For example, 0.125 x 8 = 1.000 = 1. Also, 2.5 x 4 = 10.0 = 10. This happens when the decimal part cancels out exactly.
Q5. How many decimal places will the answer have?
The product has decimal places equal to the sum of decimal places in both factors. If one factor has 2 decimal places and the other has 1, the product has 3 decimal places.
Q6. Do I need to align decimal points when multiplying?
No. Decimal point alignment is needed only for addition and subtraction. In multiplication, you multiply as whole numbers and count decimal places at the end.
Q7. How do I check my answer?
Estimate by rounding each factor to the nearest whole number. If 4.25 x 6 gives 25.5, check: 4 x 6 = 24. Since 25.5 is close to 24, the answer is likely correct.
Q8. What if the product needs more decimal places than digits?
Add zeros to the left. For example, 0.02 x 0.3: 2 x 3 = 6, but you need 3 decimal places, so the answer is 0.006.
Q9. Is this topic in the NCERT Class 5 syllabus?
Yes. Multiplication of decimals is part of the NCERT/CBSE Class 5 Maths curriculum under the Decimals chapter. Students learn to multiply by whole numbers, by 10/100/1000, and by other decimals.
Related Topics
- Division of Decimals
- Addition of Decimals
- Decimals (Grade 5)
- Comparing and Ordering Decimals
- Subtraction of Decimals
- Converting Fractions to Decimals (Grade 5)
- Converting Decimals to Fractions
- Decimal Word Problems (Grade 5)
- Decimal Place Value (Grade 5)
- Rounding Decimals
- Multiplying Decimals by 10, 100 and 1000
- Dividing Decimals by 10, 100 and 1000
