Expanded Form of Large Numbers
The expanded form of a number shows the value of each digit based on its place. In Class 5, students work with numbers up to crores. Writing a number in expanded form helps in understanding the contribution of each digit to the total value of the number.
For example, in 3,45,678, the digit 3 does not simply mean 3 — it means 3,00,000 (three lakhs). Expanded form makes this relationship between a digit and its place value explicit and clear.
What is Expanded Form of Large Numbers - Class 5 Maths (Large Numbers)?
The expanded form of a number is an expression that shows each digit multiplied by its place value, with all the products added together.
Standard form: 5,23,461
Expanded form: 5,00,000 + 20,000 + 3,000 + 400 + 60 + 1
This can also be written as:
5 × 1,00,000 + 2 × 10,000 + 3 × 1,000 + 4 × 100 + 6 × 10 + 1 × 1
Key rule: If a digit is 0, its contribution is zero, and it is usually omitted from the expanded form.
Expanded Form of Large Numbers Formula
Expanded Form = (digit × place value) + (digit × place value) + ...
Place values in the Indian system (right to left):
| Place | Value |
|---|---|
| Ones | 1 |
| Tens | 10 |
| Hundreds | 100 |
| Thousands | 1,000 |
| Ten Thousands | 10,000 |
| Lakhs | 1,00,000 |
| Ten Lakhs | 10,00,000 |
| Crores | 1,00,00,000 |
| Ten Crores | 10,00,00,000 |
Solved Examples
Example 1: Example 1: Expanded form of a 5-digit number
Problem: Write the expanded form of 47,835.
Solution:
Step 1: Identify each digit and its place value:
- 4 is in Ten Thousands place → 4 × 10,000 = 40,000
- 7 is in Thousands place → 7 × 1,000 = 7,000
- 8 is in Hundreds place → 8 × 100 = 800
- 3 is in Tens place → 3 × 10 = 30
- 5 is in Ones place → 5 × 1 = 5
Answer: 47,835 = 40,000 + 7,000 + 800 + 30 + 5
Example 2: Example 2: Expanded form of a 6-digit number
Problem: Write the expanded form of 6,03,250.
Solution:
Step 1: Identify each digit:
- 6 × 1,00,000 = 6,00,000
- 0 × 10,000 = 0 (skip)
- 3 × 1,000 = 3,000
- 2 × 100 = 200
- 5 × 10 = 50
- 0 × 1 = 0 (skip)
Answer: 6,03,250 = 6,00,000 + 3,000 + 200 + 50
Example 3: Example 3: Expanded form of a 7-digit number
Problem: Write the expanded form of 35,12,406.
Solution:
- 3 × 10,00,000 = 30,00,000
- 5 × 1,00,000 = 5,00,000
- 1 × 10,000 = 10,000
- 2 × 1,000 = 2,000
- 4 × 100 = 400
- 0 × 10 = 0 (skip)
- 6 × 1 = 6
Answer: 35,12,406 = 30,00,000 + 5,00,000 + 10,000 + 2,000 + 400 + 6
Example 4: Example 4: Expanded form of an 8-digit number
Problem: Write the expanded form of 7,08,60,052.
Solution:
- 7 × 1,00,00,000 = 7,00,00,000
- 0 × 10,00,000 = 0 (skip)
- 8 × 1,00,000 = 8,00,000
- 6 × 10,000 = 60,000
- 0 × 1,000 = 0 (skip)
- 0 × 100 = 0 (skip)
- 5 × 10 = 50
- 2 × 1 = 2
Answer: 7,08,60,052 = 7,00,00,000 + 8,00,000 + 60,000 + 50 + 2
Example 5: Example 5: Converting expanded form to standard form
Problem: Write the standard form: 40,00,000 + 5,00,000 + 30,000 + 2,000 + 100 + 9.
Solution:
Step 1: Add all the values:
40,00,000 + 5,00,000 = 45,00,000
45,00,000 + 30,000 = 45,30,000
45,30,000 + 2,000 = 45,32,000
45,32,000 + 100 = 45,32,100
45,32,100 + 9 = 45,32,109
Answer: 45,32,109
Example 6: Example 6: Expanded form using multiplication notation
Problem: Express 2,15,07,300 in expanded form using multiplication.
Solution:
2,15,07,300 = 2 × 1,00,00,000 + 1 × 10,00,000 + 5 × 1,00,000 + 0 × 10,000 + 7 × 1,000 + 3 × 100 + 0 × 10 + 0 × 1
Removing zero terms:
Answer: 2 × 1,00,00,000 + 1 × 10,00,000 + 5 × 1,00,000 + 7 × 1,000 + 3 × 100
Example 7: Example 7: Word problem — Distance
Problem: The distance between two cities is 12,05,300 metres. Write this distance in expanded form.
Solution:
- 1 × 10,00,000 = 10,00,000
- 2 × 1,00,000 = 2,00,000
- 0 × 10,000 = 0 (skip)
- 5 × 1,000 = 5,000
- 3 × 100 = 300
- 0 × 10 = 0 (skip)
- 0 × 1 = 0 (skip)
Answer: 12,05,300 = 10,00,000 + 2,00,000 + 5,000 + 300 metres
Example 8: Example 8: Finding a digit from expanded form
Problem: In the expanded form 3,00,00,000 + 40,000 + 200 + 7, what digit is in the ten thousands place?
Solution:
Step 1: Write the standard form: 3,00,40,207
Step 2: The ten thousands place is the 5th digit from the right.
Step 3: In 3,00,40,207, the ten thousands digit is 4.
Answer: The digit in the ten thousands place is 4
Example 9: Example 9: Expanded form of a 9-digit number
Problem: Write the expanded form of 62,04,05,010.
Solution:
- 6 × 10,00,00,000 = 60,00,00,000
- 2 × 1,00,00,000 = 2,00,00,000
- 0 × 10,00,000 = 0 (skip)
- 4 × 1,00,000 = 4,00,000
- 0 × 10,000 = 0 (skip)
- 5 × 1,000 = 5,000
- 0 × 100 = 0 (skip)
- 1 × 10 = 10
- 0 × 1 = 0 (skip)
Answer: 62,04,05,010 = 60,00,00,000 + 2,00,00,000 + 4,00,000 + 5,000 + 10
Key Points to Remember
- Expanded form shows each digit multiplied by its place value, with all products added together.
- Digits with value 0 contribute nothing and can be omitted from the expanded form.
- Expanded form can be written as sums (40,000 + 3,000 + 200) or as multiplication expressions (4 × 10,000 + 3 × 1,000 + 2 × 100).
- To convert expanded form back to standard form, add all the place values together.
- The number of terms in the expanded form equals the number of non-zero digits in the number.
- Expanded form helps verify the place value of each digit and is useful for addition and subtraction of large numbers.
Practice Problems
- Write the expanded form of 8,23,15,074.
- Write the expanded form of 50,00,609.
- Convert to standard form: 9,00,00,000 + 3,00,000 + 40,000 + 500 + 8.
- Write the expanded form of 1,00,00,001 (smallest and largest non-zero digits only).
- The population of a city is 14,32,000. Write it in expanded form.
- Which is greater: 6,00,00,000 + 50,000 + 3 or 6,00,50,300? Explain using expanded form.
- Write 70,30,00,500 in expanded form using multiplication notation.
- A number in expanded form is 2 × 10,00,000 + 8 × 1,000 + 4 × 10. Write it in standard form.
Frequently Asked Questions
Q1. What is the expanded form of a number?
The expanded form expresses a number as the sum of each digit multiplied by its place value. For example, 5,432 = 5,000 + 400 + 30 + 2. It shows the actual value each digit contributes to the number.
Q2. How do you handle zeros in expanded form?
Digits that are 0 have a place value of 0 and contribute nothing to the sum. They are usually left out. For example, 3,04,050 = 3,00,000 + 4,000 + 50 (the zero in ten-thousands, hundreds, and ones places are omitted).
Q3. What is the difference between expanded form and standard form?
Standard form is the usual way of writing a number (e.g., 4,56,789). Expanded form breaks the number into the sum of place values (e.g., 4,00,000 + 50,000 + 6,000 + 700 + 80 + 9). Both represent the same number.
Q4. Can expanded form have more than one way of writing?
Yes. You can write it as a sum of values (40,000 + 3,000 + 200) or as multiplication expressions (4 × 10,000 + 3 × 1,000 + 2 × 100). Both are correct forms of expanded notation.
Q5. How does expanded form help in addition?
Expanded form makes addition easier by letting you add place values separately. For example, to add 3,400 + 2,500: (3,000 + 400) + (2,000 + 500) = (3,000 + 2,000) + (400 + 500) = 5,000 + 900 = 5,900.
Q6. How many terms does the expanded form have?
The number of terms equals the number of non-zero digits. For example, 5,03,020 has three non-zero digits (5, 3, 2), so its expanded form has 3 terms: 5,00,000 + 3,000 + 20.
Q7. What is the expanded form of 1,00,00,000?
1,00,00,000 (one crore) in expanded form is simply 1 × 1,00,00,000. Since all other digits are 0, there is only one term.
Q8. Is expanded form taught in the NCERT Class 5 syllabus?
Yes. Expanded form of large numbers (up to crores) is part of the NCERT Class 5 Maths curriculum under the Large Numbers chapter. Students learn to express numbers in both standard and expanded form.
Related Topics
- Place Value of Large Numbers
- Numbers up to Lakhs
- Indian and International Number System (Grade 5)
- Reading and Writing Large Numbers
- Comparing Large Numbers (Grade 5)
- Ordering Large Numbers (Grade 5)
- Rounding Large Numbers
- Estimation (Grade 5)
- Roman Numerals (I to M)
- Numbers up to Crores
- Number Names in Lakhs and Crores
- Predecessor and Successor (Grade 5)
