Division by 10 and 100
Division by 10 and 100 is the reverse of multiplying by 10 and 100. Instead of adding zeros, you remove zeros from the end of a number. This is a quick shortcut that helps in calculations, unit conversions, and estimations.
For example, if 100 pencils cost ₹500, you can find the cost of 1 pencil by dividing: ₹500 ÷ 100 = ₹5.
What is Division by 10 and 100 - Class 4 Maths (Division)?
When you divide a number ending in zeros by 10 or 100, you remove one or two zeros from the end.
Number ÷ 10 → Remove 1 zero from the end
Number ÷ 100 → Remove 2 zeros from the end
Why does this work? Dividing by 10 shifts every digit one place to the right, which removes the trailing zero. Dividing by 100 shifts digits two places to the right.
What if the number does not end in enough zeros? You get a remainder or a decimal. For example, 53 ÷ 10 = 5 remainder 3.
Solved Examples
Example 1: Example 1: Dividing by 10
Problem: Find 470 ÷ 10.
Solution:
Step 1: Remove 1 zero from the end of 470.
470 ÷ 10 = 47
Answer: 47
Example 2: Example 2: Dividing by 100
Problem: Find 6,300 ÷ 100.
Solution:
Step 1: Remove 2 zeros from the end of 6,300.
6,300 ÷ 100 = 63
Answer: 63
Example 3: Example 3: Dividing a Large Number by 10
Problem: Find 58,000 ÷ 10.
Solution:
Remove 1 zero: 58,000 ÷ 10 = 5,800
Answer: 5,800
Example 4: Example 4: Division with Remainder
Problem: Find 345 ÷ 10.
Solution:
Step 1: 345 does not end in 0, so we perform the division.
345 ÷ 10 = 34 remainder 5
Answer: Quotient = 34, Remainder = 5
Example 5: Example 5: Word Problem — Equal Sharing
Problem: Kavi has ₹8,000. He divides the money equally among 100 children. How much does each child get?
Solution:
Step 1: 8,000 ÷ 100 = 80
Answer: Each child gets ₹80.
Example 6: Example 6: Unit Conversion — cm to m
Problem: A rope is 500 cm long. Convert to metres. (100 cm = 1 m)
Solution:
Step 1: Divide by 100: 500 ÷ 100 = 5
Answer: The rope is 5 metres long.
Example 7: Example 7: Dividing Round Thousands by 100
Problem: Find 45,000 ÷ 100.
Solution:
Remove 2 zeros: 45,000 ÷ 100 = 450
Answer: 450
Example 8: Example 8: Fill in the Blank
Problem: _____ ÷ 10 = 230.
Solution:
Step 1: If dividing by 10 gives 230, then the original number is 230 x 10 = 2,300.
Answer: 2,300
Example 9: Example 9: Word Problem — Packing
Problem: A factory produces 7,200 biscuits. If 10 biscuits are packed in each box, how many boxes are needed?
Solution:
7,200 ÷ 10 = 720
Answer: 720 boxes are needed.
Example 10: Example 10: Connecting Multiplication and Division
Problem: If 47 x 100 = 4,700, find 4,700 ÷ 100.
Solution:
Division is the reverse of multiplication.
4,700 ÷ 100 = 47
Answer: 47
Key Points to Remember
- Dividing by 10 removes 1 zero from the end of the number.
- Dividing by 100 removes 2 zeros from the end.
- If the number does not end in enough zeros, there will be a remainder.
- Division by 10 and 100 is the reverse of multiplication by 10 and 100.
- This shortcut is useful in unit conversions (cm to m, paise to rupees).
- To check: Quotient x Divisor + Remainder = Dividend.
Practice Problems
- Find 3,600 ÷ 10.
- Find 9,000 ÷ 100.
- Find 725 ÷ 10 and state the quotient and remainder.
- A farmer harvested 5,400 mangoes. He packs 100 mangoes in each crate. How many crates does he need?
- Convert 2,300 cm to metres.
- Fill in the blank: _____ ÷ 100 = 56.
- If 82 x 10 = 820, what is 820 ÷ 10?
Frequently Asked Questions
Q1. How do you divide a number by 10?
If the number ends in 0, remove one zero from the end. For example, 560 ÷ 10 = 56. If it does not end in 0, divide normally — you will get a remainder.
Q2. What happens if you divide a number by 100 and it does not end in two zeros?
You will get a remainder. For example, 450 ÷ 100 = 4 remainder 50. The quotient is 4 and the remainder is 50.
Q3. Is dividing by 10 the same as removing the last digit?
When the number ends in 0, removing the zero gives the correct answer. When it does not end in 0, the last digit becomes the remainder, and the remaining digits form the quotient.
Q4. How is dividing by 10 related to multiplying by 10?
They are inverse operations. If 25 x 10 = 250, then 250 ÷ 10 = 25. Multiplication adds zeros; division removes them.
Q5. Where is division by 10 and 100 used in real life?
It is used in converting units (cm to m, paise to rupees, grams to kg), splitting amounts equally, calculating averages, and understanding place value shifts.
Q6. Can you divide by 1000 the same way?
Yes. Dividing by 1000 removes 3 trailing zeros. For example, 45,000 ÷ 1000 = 45. This is covered in detail at higher levels.
Q7. What is 0 ÷ 10?
0 divided by any non-zero number is 0. So 0 ÷ 10 = 0.
Q8. Is this topic covered in the NCERT Class 4 textbook?
Yes, division by 10 and 100 is part of the CBSE/NCERT Class 4 Maths curriculum under the division chapter. It builds on the concept of multiplying by 10 and 100.
