Division of Decimals
Division of decimals means splitting a decimal number into equal parts. Just like dividing whole numbers, we can divide decimals by whole numbers and by other decimals.
In Class 5, you will learn how to divide decimal numbers step by step using long division. This skill is used in everyday life — from sharing money equally to measuring lengths, weights, and capacities.
For example, if ₹45.50 is shared equally among 5 friends, each friend gets ₹45.50 ÷ 5 = ₹9.10. If a 2.4 kg bag of rice is packed into smaller bags of 0.3 kg each, we divide 2.4 ÷ 0.3 = 8 bags.
Decimal division builds on your knowledge of whole number division and decimal place value. Before starting, make sure you are comfortable with long division and understand what tenths and hundredths mean.
What is Division of Decimals - Class 5 Maths (Decimals)?
Division of decimals is the process of dividing a number that has a decimal point by another number. The result (quotient) may also be a decimal.
There are four main cases of decimal division:
- Dividing a decimal by a whole number — e.g., 8.4 ÷ 2 = 4.2
- Dividing a whole number by a decimal — e.g., 15 ÷ 0.5 = 30
- Dividing a decimal by another decimal — e.g., 6.3 ÷ 0.3 = 21
- Dividing a decimal by 10, 100, or 1000 — e.g., 45.3 ÷ 10 = 4.53
The most important rule to remember: place the decimal point in the quotient directly above the decimal point in the dividend when performing long division.
Division of Decimals Formula
To divide by a decimal, multiply both dividend and divisor by 10 (or 100) to make the divisor a whole number, then divide as usual.
Method 1: Dividing a decimal by a whole number (Long Division)
- Set up the long division as you would for whole numbers.
- Divide digit by digit from left to right.
- When you reach the decimal point in the dividend, place a decimal point in the quotient at the exact same position.
- Continue dividing the remaining digits after the decimal.
- If there is a remainder, add zeros after the last decimal digit and keep dividing.
Method 2: Dividing by a decimal (Convert to Whole Number)
- Count the number of decimal places in the divisor.
- Multiply both the dividend and divisor by 10 (for 1 decimal place) or 100 (for 2 decimal places). This removes the decimal from the divisor.
- Now divide as you would with a whole number divisor.
- The quotient is your answer — no further adjustment needed.
Method 3: Dividing by 10, 100, or 1000 (Shortcut)
- Dividing by 10 → move the decimal point 1 place to the left.
- Dividing by 100 → move the decimal point 2 places to the left.
- Dividing by 1000 → move the decimal point 3 places to the left.
This shortcut works because dividing by powers of 10 simply shifts the decimal point.
Types and Properties
Type 1: Dividing a decimal by a whole number
This is the simplest type. Set up long division normally and place the decimal point in the quotient above the decimal point in the dividend.
Example: 9.6 ÷ 4
- Divide 9 by 4 → quotient 2, remainder 1
- Place decimal point in quotient → 2.
- Bring down 6 → 16 ÷ 4 = 4
- Answer: 2.4
Type 2: Dividing a whole number by a decimal
Convert the problem so the divisor is a whole number by multiplying both numbers.
Example: 15 ÷ 0.5
- Multiply both by 10 → 150 ÷ 5 = 30
Type 3: Dividing a decimal by a decimal
Multiply both numbers by 10 or 100 to make the divisor a whole number.
Example: 2.46 ÷ 0.6
- Multiply both by 10 → 24.6 ÷ 6 = 4.1
Type 4: Dividing by 10, 100, or 1000
Simply shift the decimal point to the left.
- 45.3 ÷ 10 = 4.53 (shift 1 place left)
- 45.3 ÷ 100 = 0.453 (shift 2 places left)
- 45.3 ÷ 1000 = 0.0453 (shift 3 places left)
Type 5: Division where quotient is less than 1
When the dividend is smaller than the divisor, the quotient is a decimal less than 1.
Example: 0.6 ÷ 3 = 0.2
Example: 2 ÷ 5 = 0.4
Solved Examples
Example 1: Dividing a Decimal by a Whole Number
Problem: Divide 12.6 by 3.
Solution:
Step 1: Set up long division. Divide 12 by 3 = 4.
Step 2: Place the decimal point in the quotient directly above the decimal point in 12.6. Quotient so far: 4.
Step 3: Bring down 6. Divide 6 by 3 = 2.
Step 4: Quotient = 4.2
Verification: 4.2 × 3 = 12.6 ✓
Answer: 12.6 ÷ 3 = 4.2
Example 2: Sharing Money Equally
Problem: Aman has ₹56.80. He shares it equally among 4 friends. How much does each friend get?
Solution:
Step 1: We need to calculate 56.80 ÷ 4.
Step 2: 56 ÷ 4 = 14. Write 14 in the quotient.
Step 3: Place decimal point in the quotient → 14.
Step 4: Bring down 8. 8 ÷ 4 = 2 → quotient becomes 14.2
Step 5: Bring down 0. 0 ÷ 4 = 0 → quotient becomes 14.20
Verification: 14.20 × 4 = 56.80 ✓
Answer: Each friend gets ₹14.20.
Example 3: Division with Remainder Carry-Over
Problem: Divide 7.5 by 6.
Solution:
Step 1: 7 ÷ 6 = 1, remainder 1. Write 1 in quotient.
Step 2: Place decimal point in quotient → 1.
Step 3: Bring down 5 → we have 15. 15 ÷ 6 = 2, remainder 3. Quotient so far: 1.2
Step 4: There is a remainder 3. Add a zero to the dividend: 30 ÷ 6 = 5. Quotient: 1.25
Verification: 1.25 × 6 = 7.50 = 7.5 ✓
Answer: 7.5 ÷ 6 = 1.25
Example 4: Dividing a Decimal by a Decimal
Problem: Divide 4.8 by 0.6.
Solution:
Step 1: The divisor 0.6 has 1 decimal place. To remove the decimal, multiply both numbers by 10.
Step 2: 4.8 × 10 = 48 and 0.6 × 10 = 6
Step 3: Now divide: 48 ÷ 6 = 8
Why this works: Multiplying both numbers by the same value does not change the quotient. 4.8 ÷ 0.6 = 48 ÷ 6 = 8.
Verification: 8 × 0.6 = 4.8 ✓
Answer: 4.8 ÷ 0.6 = 8
Example 5: Dividing by 10 — Shortcut
Problem: Divide 83.5 by 10.
Solution:
Step 1: To divide by 10, shift the decimal point one place to the left.
Step 2: 83.5 → 8.35
Think of it this way: 83.5 has 8 tens, 3 ones, 5 tenths. Dividing by 10 makes it 8 ones, 3 tenths, 5 hundredths = 8.35.
Answer: 83.5 ÷ 10 = 8.35
Example 6: Dividing by 100
Problem: Divide 246.8 by 100.
Solution:
Step 1: To divide by 100, shift the decimal point two places to the left.
Step 2: 246.8 → 2.468
Place value explanation: The 2 (hundreds) becomes 2 ones, the 4 (tens) becomes 4 tenths, the 6 (ones) becomes 6 hundredths, and the 8 (tenths) becomes 8 thousandths.
Answer: 246.8 ÷ 100 = 2.468
Example 7: Word Problem — Ribbon Cutting
Problem: Priya has a ribbon of length 15.75 m. She cuts it into 5 equal pieces. What is the length of each piece?
Solution:
Step 1: Calculate 15.75 ÷ 5.
Step 2: 15 ÷ 5 = 3. Write 3.
Step 3: Place the decimal point → 3.
Step 4: 7 ÷ 5 = 1, remainder 2. Write 1 → 3.1
Step 5: Bring down 5 → 25 ÷ 5 = 5. Write 5 → 3.15
Verification: 3.15 × 5 = 15.75 ✓
Answer: Each piece is 3.15 m long.
Example 8: Dividing by a Decimal — Two Decimal Places
Problem: Divide 3.24 by 0.04.
Solution:
Step 1: The divisor 0.04 has 2 decimal places. Multiply both by 100.
Step 2: 3.24 × 100 = 324 and 0.04 × 100 = 4
Step 3: Divide: 324 ÷ 4 = 81
Think about it: How many groups of 0.04 fit into 3.24? The answer is 81 groups.
Verification: 81 × 0.04 = 3.24 ✓
Answer: 3.24 ÷ 0.04 = 81
Example 9: Word Problem — Weight Distribution
Problem: Rahul bought 2.4 kg of sweets for a festival. He packed them into small boxes of 0.3 kg each. How many boxes did he fill?
Solution:
Step 1: We need to find how many groups of 0.3 fit in 2.4. Calculate 2.4 ÷ 0.3.
Step 2: Multiply both by 10 to remove the decimal: 24 ÷ 3 = 8
Think about it: 0.3 + 0.3 + 0.3 + 0.3 + 0.3 + 0.3 + 0.3 + 0.3 = 2.4 (adding 0.3 eight times).
Verification: 8 × 0.3 = 2.4 ✓
Answer: Rahul filled 8 boxes.
Example 10: Multi-step — Cost Per Notebook
Problem: Kavi spent ₹124.50 on 6 notebooks. What is the cost of one notebook?
Solution:
Step 1: Calculate 124.50 ÷ 6.
Step 2: 12 ÷ 6 = 2. Write 2.
Step 3: Bring down 4. 4 ÷ 6 = 0, remainder 4. Write 0 → 20.
Step 4: Place decimal point → 20.
Step 5: Bring down 5 → 45 ÷ 6 = 7, remainder 3. Write 7 → 20.7
Step 6: Bring down 0 → 30 ÷ 6 = 5. Write 5 → 20.75
Verification: 20.75 × 6 = 124.50 ✓
Answer: Each notebook costs ₹20.75.
Real-World Applications
Where do we use division of decimals in real life?
- Sharing money: Dividing ₹85.50 equally among 3 people. Each person gets ₹85.50 ÷ 3 = ₹28.50.
- Shopping: Finding the cost per item. If 4 pens cost ₹62.00, each pen costs ₹62.00 ÷ 4 = ₹15.50.
- Measurement: Cutting a rope of 12.6 m into equal pieces of 1.8 m each → 12.6 ÷ 1.8 = 7 pieces.
- Cooking: Dividing 2.5 litres of milk equally into 5 glasses → each glass gets 0.5 litres.
- Speed and distance: If a car travels 156.8 km in 4 hours, its speed = 156.8 ÷ 4 = 39.2 km/h.
- Average calculation: Finding the average of decimal values involves adding them and then dividing.
- Unit conversion: Converting grams to kilograms involves dividing by 1000 (e.g., 750 g ÷ 1000 = 0.75 kg).
Key Points to Remember
- When dividing a decimal by a whole number, place the decimal point in the quotient directly above the decimal point in the dividend.
- When dividing by a decimal, multiply both dividend and divisor by 10 (or 100) to make the divisor a whole number first, then divide normally.
- Dividing by 10 moves the decimal point one place to the left.
- Dividing by 100 moves the decimal point two places to the left.
- Dividing by 1000 moves the decimal point three places to the left.
- Always check your answer by multiplying: quotient × divisor should equal the dividend.
- If the dividend is smaller than the divisor, the quotient will be less than 1 (e.g., 0.6 ÷ 3 = 0.2).
- You can add zeros after the decimal point in the dividend to continue dividing when there is a remainder.
- Dividing by 0.1 is the same as multiplying by 10. Dividing by 0.01 is the same as multiplying by 100.
Practice Problems
- Divide 18.6 by 3.
- Ria has ₹72.40. She divides it equally among 4 friends. How much does each friend get?
- Divide 9.36 by 0.4.
- A rope of 25.5 m is cut into 5 equal pieces. What is the length of each piece?
- Calculate: 456.3 ÷ 100.
- Dev bought 3.6 kg of rice. He puts it into bags of 0.9 kg each. How many bags does he need?
- Divide 0.48 by 8.
- Aditi scored a total of 42.5 marks in 5 tests. What is her average score per test?
Frequently Asked Questions
Q1. How do you divide a decimal by a whole number?
Set up long division as usual. When you reach the decimal point in the dividend, place a decimal point in the quotient at the same position and continue dividing. For example, 8.4 ÷ 2: divide 8 by 2 = 4, place decimal, 4 ÷ 2 = 2, so the answer is 4.2.
Q2. How do you divide a decimal by another decimal?
Multiply both the dividend and divisor by 10 (or 100) so the divisor becomes a whole number. Then divide normally. For example, 6.3 ÷ 0.9: multiply both by 10 to get 63 ÷ 9 = 7. The answer is 7.
Q3. What happens when you divide a decimal by 10?
The decimal point moves one place to the left. For example, 45.6 ÷ 10 = 4.56. Similarly, dividing by 100 moves it two places left (45.6 ÷ 100 = 0.456), and dividing by 1000 moves it three places left.
Q4. Can the quotient of two decimals be a whole number?
Yes. When a decimal divides evenly into another decimal, the quotient can be a whole number. For example, 4.8 ÷ 0.6 = 8. This happens when the dividend is an exact multiple of the divisor.
Q5. What if the dividend is smaller than the divisor?
The quotient will be less than 1. For example, 0.6 ÷ 3 = 0.2. You place a 0 before the decimal point in the quotient and continue dividing.
Q6. How do you check your answer in decimal division?
Multiply the quotient by the divisor. The result should equal the dividend. For example, if 12.6 ÷ 3 = 4.2, check: 4.2 × 3 = 12.6. Since it matches, the answer is correct.
Q7. Why do we add zeros after the decimal point sometimes?
When the division is not complete and there is a remainder, we add zeros after the last digit of the decimal to continue dividing. For example, in 7.5 ÷ 6, after getting 1.2 with remainder 3, we add a zero to make 30 ÷ 6 = 5, giving the final answer 1.25.
Q8. Is dividing by 0.1 the same as multiplying by 10?
Yes. Dividing by 0.1 is equivalent to multiplying by 10. For example, 5.3 ÷ 0.1 = 53, which is the same as 5.3 × 10 = 53. Similarly, dividing by 0.01 equals multiplying by 100.
Q9. What is the difference between dividing by 10 and multiplying by 10 for decimals?
Dividing by 10 moves the decimal point one place to the left, making the number smaller (34.5 ÷ 10 = 3.45). Multiplying by 10 moves it one place to the right, making the number larger (34.5 × 10 = 345). They are opposite operations.
Related Topics
- Multiplication of Decimals
- Subtraction of Decimals
- Decimals (Grade 5)
- Comparing and Ordering Decimals
- Addition 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
