Multiplication by 10 and 100
Multiplying by 10 and 100 follows simple rules that make calculations very fast. When you multiply a number by 10, you add one zero at the end. When you multiply by 100, you add two zeros.
Understanding this rule helps with mental math, place value, and working with larger numbers in Class 3 and beyond.
What is Multiplication by 10 and 100 - Class 3 Maths (Multiplication (Grade 3))?
n × 10 = n followed by one 0
n × 100 = n followed by two 0s
Why does this work? Multiplying by 10 shifts every digit one place to the left. The ones place becomes empty and gets filled with 0.
| Number | × 10 | × 100 |
|---|---|---|
| 3 | 30 | 300 |
| 15 | 150 | 1500 |
| 47 | 470 | 4700 |
| 100 | 1000 | 10000 |
Solved Examples
Example 1: Multiplying a Single Digit by 10
Question: What is 6 × 10?
Think:
- Write 6 and add one zero at the end
- 6 × 10 = 60
Answer: 6 × 10 = 60
Example 2: Multiplying a Single Digit by 100
Question: What is 8 × 100?
Think:
- Write 8 and add two zeros at the end
- 8 × 100 = 800
Answer: 8 × 100 = 800
Example 3: Multiplying a 2-Digit Number by 10
Question: What is 25 × 10?
Think:
- Write 25 and add one zero
- 25 × 10 = 250
Answer: 25 × 10 = 250
Example 4: Multiplying a 2-Digit Number by 100
Question: What is 34 × 100?
Think:
- Write 34 and add two zeros
- 34 × 100 = 3400
Answer: 34 × 100 = 3400
Example 5: Word Problem — Packets of Pencils
Question: A box contains 10 packets. Each packet has 12 pencils. How many pencils are in the box?
Think:
- 10 × 12 = 120
- Write 12 and add one zero
Answer: The box has 120 pencils.
Example 6: Multiplying 10 × 10
Question: What is 10 × 10?
Think:
- 10 × 10 = 100
- Write 10 and add one zero → 100
Answer: 10 × 10 = 100
Example 7: Word Problem — Rupee Notes
Question: Aditi has 7 notes of ₹100 each. How much money does she have?
Think:
- 7 × 100 = 700
Answer: Aditi has ₹700.
Example 8: Using Multiplication by 10 for Larger Products
Question: Find 30 × 4.
Think:
- 30 × 4 = 3 × 10 × 4 = 3 × 4 × 10 = 12 × 10 = 120
Answer: 30 × 4 = 120
Example 9: Multiplying Multiples of 10
Question: What is 40 × 20?
Think:
- 4 × 2 = 8
- Count the zeros: 40 has one 0, 20 has one 0 → total 2 zeros
- 8 followed by 2 zeros = 800
Answer: 40 × 20 = 800
Example 10: Word Problem — School Chairs
Question: A school orders 100 chairs for each of its 5 classrooms. How many chairs were ordered?
Think:
- 5 × 100 = 500
Answer: 500 chairs were ordered.
Real-World Applications
Where is multiplication by 10 and 100 used?
- Currency conversion: 1 ten-rupee note = ₹10. So 7 ten-rupee notes = 7 × 10 = ₹70. Similarly, 5 hundred-rupee notes = 5 × 100 = ₹500.
- Measurement conversion: 1 metre = 100 centimetres. So 3 metres = 3 × 100 = 300 cm.
- Place value: Multiplying by 10 shifts each digit one place to the left. This is the basis of our base-10 number system.
- Mental math: To find 30 × 7, think: 3 × 7 = 21, then add a zero → 210. This is much faster than column multiplication.
- Large quantities: If a packet has 100 seeds, 8 packets = 800 seeds.
- Decades and centuries: 10 years = 1 decade. 100 years = 1 century. These concepts rely on multiplying by 10 and 100.
Multiplying by 10 and 100 is one of the most useful shortcuts in mathematics. It connects place value to arithmetic and makes mental calculations much faster.
Key Points to Remember
- To multiply by 10, add one zero to the end of the number.
- To multiply by 100, add two zeros to the end.
- Multiplying by 10 shifts digits one place to the left in the place value chart.
- For products like 30 × 4: multiply 3 × 4 = 12, then add one zero → 120.
- For products like 40 × 20: multiply 4 × 2 = 8, add two zeros → 800.
- 10 × 10 = 100 and 10 × 100 = 1000.
Practice Problems
- What is 9 × 10?
- What is 5 × 100?
- What is 46 × 10?
- What is 23 × 100?
- Find 50 × 6.
- Ria has 8 bundles of 10 bangles. How many bangles in total?
- What is 20 × 30?
- A school buys 100 books at ₹10 each. What is the total cost?
Frequently Asked Questions
Q1. Why do we add zeros when multiplying by 10 or 100?
Multiplying by 10 moves each digit one place to the left in the place value chart. The ones place becomes empty, which is shown as 0. Multiplying by 100 moves digits two places to the left.
Q2. What is 0 × 10?
0 × 10 = 0. Zero multiplied by any number is always zero.
Q3. What is 10 × 100?
10 × 100 = 1000. You can think of it as: write 10 and add two zeros, giving 1000.
Q4. How do you multiply a number ending in 0 by 10?
Add one more zero. For example, 30 × 10 = 300. The number 30 already has one zero; multiplying by 10 adds another.
Q5. Can this rule be used for multiplying by 1000?
Yes. To multiply by 1000, add three zeros. For example, 5 × 1000 = 5000. This extends the same pattern.
Q6. How is multiplying by 10 useful in daily life?
Counting groups of 10 (₹10 coins, packs of 10), converting tens to ones, and doing mental math all use this rule.
Q7. What happens when you multiply by 10 and then by 10 again?
Multiplying by 10 twice is the same as multiplying by 100. For example, 5 × 10 = 50, then 50 × 10 = 500. This equals 5 × 100 = 500.
Q8. How do you multiply two multiples of 10?
Multiply the non-zero parts, then count total zeros. For 30 × 50: 3 × 5 = 15, two total zeros → 1500.
Related Topics
- Multiplication Tables of 8 and 9
- Multiplication of 2-Digit by 1-Digit
- Multiplication Concept (Grade 3)
- Multiplication Tables of 3 and 4
- Multiplication Tables of 6 and 7
- Multiplication Word Problems (Grade 3)
- Properties of Multiplication
- Multiplying by 0 and 1
- Multiplication Tables (2 to 10)
- Multiplication of 2-Digit Numbers (Grade 3)
