Multiplying by 10, 100 and 1000
Multiplying by 10, 100, and 1000 is one of the most useful shortcuts in mathematics. Instead of performing long multiplication, you simply add zeros to the end of the number. This pattern works because our number system is based on powers of 10.
This shortcut is used every day — when converting metres to centimetres, calculating prices in bulk, or working with large quantities.
What is Multiplying by 10, 100 and 1000 - Class 4 Maths (Multiplication)?
When you multiply a whole number by 10, 100, or 1000, you add one, two, or three zeros to the right of the number.
Number x 10 → Add 1 zero
Number x 100 → Add 2 zeros
Number x 1000 → Add 3 zeros
Why does this work? Multiplying by 10 shifts every digit one place to the left. The ones place becomes empty, so we write 0 there. Multiplying by 100 shifts digits two places left, and multiplying by 1000 shifts digits three places left.
Solved Examples
Example 1: Example 1: Multiplying by 10
Problem: Find 36 x 10.
Solution:
Step 1: Write 36 and add 1 zero at the end.
36 x 10 = 360
Answer: 360
Example 2: Example 2: Multiplying by 100
Problem: Find 45 x 100.
Solution:
Step 1: Write 45 and add 2 zeros at the end.
45 x 100 = 4,500
Answer: 4,500
Example 3: Example 3: Multiplying by 1000
Problem: Find 28 x 1000.
Solution:
Step 1: Write 28 and add 3 zeros at the end.
28 x 1000 = 28,000
Answer: 28,000
Example 4: Example 4: Multiplying a 3-digit Number by 10
Problem: Find 254 x 10.
Solution:
254 x 10 = 2,540
Answer: 2,540
Example 5: Example 5: Multiplying a Number Ending in 0
Problem: Find 80 x 100.
Solution:
Step 1: Write 80 and add 2 zeros: 8,000
Answer: 8,000
(Tip: 80 already has one zero. Adding 2 more gives 3 zeros total.)
Example 6: Example 6: Word Problem — Price Calculation
Problem: One notebook costs ₹35. What is the cost of 100 notebooks?
Solution:
Step 1: Cost = 35 x 100
Step 2: Add 2 zeros: 3,500
Answer: 100 notebooks cost ₹3,500.
Example 7: Example 7: Word Problem — Unit Conversion
Problem: A table is 2 metres long. Convert to centimetres. (1 m = 100 cm)
Solution:
Step 1: Length in cm = 2 x 100 = 200 cm
Answer: The table is 200 cm long.
Example 8: Example 8: Word Problem — Weight Conversion
Problem: Ria bought 5 kg of rice. How many grams is that? (1 kg = 1000 g)
Solution:
Step 1: Weight in grams = 5 x 1000 = 5,000 g
Answer: Ria bought 5,000 grams of rice.
Example 9: Example 9: Multiplying Multiples of 10
Problem: Find 30 x 40.
Solution:
Step 1: Multiply the non-zero parts: 3 x 4 = 12
Step 2: Count total trailing zeros: 1 (from 30) + 1 (from 40) = 2 zeros
Step 3: Attach the zeros: 1,200
Answer: 1,200
Example 10: Example 10: Reverse Problem
Problem: 67 x _____ = 67,000. What is the missing number?
Solution:
Step 1: 67,000 has 3 more zeros than 67.
Step 2: So the missing number is 1,000.
Answer: 1,000
Key Points to Remember
- Multiplying by 10 adds 1 zero to the end of the number.
- Multiplying by 100 adds 2 zeros.
- Multiplying by 1000 adds 3 zeros.
- This works because each multiplication by 10 shifts all digits one place to the left.
- When multiplying two numbers that both end in zeros (e.g., 30 x 40), multiply the non-zero parts and then attach all the trailing zeros.
- This shortcut is especially useful in unit conversions (m to cm, kg to g, km to m).
Practice Problems
- Find 73 x 10.
- Find 56 x 100.
- Find 9 x 1000.
- A packet of biscuits costs ₹12. What is the cost of 1000 packets?
- Convert 8 km to metres. (1 km = 1000 m)
- Find 50 x 200.
- Fill in the blank: 45 x _____ = 4,500.
Frequently Asked Questions
Q1. Why do we add zeros when multiplying by 10, 100, or 1000?
Our number system is based on 10. Multiplying by 10 moves every digit one place to the left, leaving the ones place empty (filled with 0). Multiplying by 100 shifts two places, and 1000 shifts three places.
Q2. Does this rule work for all numbers?
Yes, the rule works for all whole numbers. For decimals, the decimal point shifts to the right instead of adding zeros (covered in higher classes).
Q3. How do you multiply 30 x 50?
Multiply the non-zero parts: 3 x 5 = 15. Then count trailing zeros: 1 + 1 = 2 zeros. So 30 x 50 = 1,500.
Q4. What is 0 x 1000?
0 multiplied by any number is always 0. So 0 x 1000 = 0.
Q5. How is multiplying by 10 useful in daily life?
It is used in unit conversions (1 cm = 10 mm, 1 m = 100 cm, 1 kg = 1000 g), calculating prices for bulk items, and understanding place value in the number system.
Q6. What happens when you multiply by 10 twice?
Multiplying by 10 twice is the same as multiplying by 100. For example, 5 x 10 = 50, and 50 x 10 = 500, which equals 5 x 100 = 500.
Q7. How do you find 400 x 1000?
Multiply 4 x 1 = 4, then count all trailing zeros: 2 (from 400) + 3 (from 1000) = 5 zeros. So 400 x 1000 = 4,00,000 (four lakhs).
Q8. Is this topic in the NCERT Class 4 textbook?
Yes, multiplying by 10, 100, and 1000 is covered in the CBSE/NCERT Class 4 syllabus under the multiplication chapter. It connects with place value and unit conversion topics.
