Place Value of Large Numbers
Place value tells us the value of each digit based on its position in a number. In Class 5, you extend your understanding of place value from 5-digit numbers to 6-digit and 7-digit numbers -- going up to the ten-lakhs place.
Every digit in a large number has a specific place. The same digit can have completely different values depending on where it sits. For instance, the digit 4 in 4,00,000 is worth four lakh, but in 40 it is worth only forty. This is the power of place value -- it gives meaning to every digit based on its position.
Place value is the foundation of our entire number system. Without it, we could not add, subtract, multiply, or divide. Every arithmetic operation depends on knowing what each digit is worth. In this lesson, you will learn to find the place value and face value of any digit, write numbers in expanded form, and construct numbers from their place values.
Understanding place value also helps you compare and order numbers, round numbers, and estimate answers -- all of which are key Class 5 skills.
What is Place Value of Large Numbers - Class 5 Maths (Large Numbers)?
The place value of a digit is the product of the digit and its positional value. The face value of a digit is the digit itself, regardless of its position.
Example: In the number 3,72,456:
- The digit 3 has a face value of 3 and a place value of 3,00,000 (since it is in the lakhs place).
- The digit 7 has a face value of 7 and a place value of 70,000 (since it is in the ten-thousands place).
- The digit 0, if present, always has a place value of 0, but serves as an essential placeholder.
The Indian place value chart for numbers up to ten lakhs:
| Place Name | Ten Lakhs (TL) | Lakhs (L) | Ten Thousands (T.Th) | Thousands (Th) | Hundreds (H) | Tens (T) | Ones (O) |
|---|---|---|---|---|---|---|---|
| Position Value | 10,00,000 | 1,00,000 | 10,000 | 1,000 | 100 | 10 | 1 |
Each place is 10 times the place to its right. This means:
- Moving one place to the left multiplies the value by 10.
- Moving one place to the right divides the value by 10.
Place Value of Large Numbers Formula
Place Value of a Digit = Face Value x Position Value
Each place = 10 x (place to its right)
Conversely:
Face Value of a Digit = Place Value / Position Value
Types and Properties
Complete place value relationships:
| Place | Value | Relation to Previous | In Words |
|---|---|---|---|
| Ones | 1 | -- | One |
| Tens | 10 | 10 x 1 | Ten |
| Hundreds | 100 | 10 x 10 | One Hundred |
| Thousands | 1,000 | 10 x 100 | One Thousand |
| Ten Thousands | 10,000 | 10 x 1,000 | Ten Thousand |
| Lakhs | 1,00,000 | 10 x 10,000 | One Lakh |
| Ten Lakhs | 10,00,000 | 10 x 1,00,000 | Ten Lakh |
Three forms of writing a number:
- Standard form: The usual way -- 5,32,478
- Expanded form: Sum of place values -- 5,00,000 + 30,000 + 2,000 + 400 + 70 + 8
- Number name: In words -- Five lakh thirty-two thousand four hundred and seventy-eight
The role of zero as a placeholder:
Zero has a face value of 0 and a place value of 0 in any position. However, it is critically important as a placeholder. Without the zero in 3,05,000, the number would collapse to 35,000 -- a completely different value. Never skip zeros when writing a number in standard form.
Solved Examples
Example 1: Example 1: Place Value Chart for a 6-Digit Number
Problem: Write 6,83,215 in a place value chart and state the place and period of each digit.
Solution:
| L | T.Th | Th | H | T | O |
|---|---|---|---|---|---|
| 6 | 8 | 3 | 2 | 1 | 5 |
Step 1: The digit 6 is in the Lakhs place (Lakhs period).
Step 2: The digit 8 is in the Ten Thousands place (Thousands period).
Step 3: The digit 3 is in the Thousands place (Thousands period).
Step 4: The digits 2, 1, 5 are in the Hundreds, Tens, and Ones places respectively (Ones period).
Answer: In 6,83,215 -- 6 is in lakhs, 8 in ten thousands, 3 in thousands, 2 in hundreds, 1 in tens, and 5 in ones.
Example 2: Example 2: Place Value vs Face Value (Complete Table)
Problem: Find the place value and face value of each digit in 4,09,361.
Solution:
| Digit | Place | Face Value | Place Value | Calculation |
|---|---|---|---|---|
| 4 | Lakhs | 4 | 4,00,000 | 4 x 1,00,000 |
| 0 | Ten Thousands | 0 | 0 | 0 x 10,000 |
| 9 | Thousands | 9 | 9,000 | 9 x 1,000 |
| 3 | Hundreds | 3 | 300 | 3 x 100 |
| 6 | Tens | 6 | 60 | 6 x 10 |
| 1 | Ones | 1 | 1 | 1 x 1 |
Key observations:
- The place value of 0 is always 0, regardless of its position. But the 0 is essential -- without it, the number becomes 49,361 (a 5-digit number), not 4,09,361 (a 6-digit number).
- The face value of any digit is always the digit itself and never changes.
Answer: The table above shows all place values and face values.
Example 3: Example 3: Expanded Form with Detailed Steps
Problem: Write 7,25,048 in expanded form.
Solution:
Step 1: Identify each digit and its position:
- 7 is in the Lakhs place: 7 x 1,00,000 = 7,00,000
- 2 is in the Ten Thousands place: 2 x 10,000 = 20,000
- 5 is in the Thousands place: 5 x 1,000 = 5,000
- 0 is in the Hundreds place: 0 x 100 = 0 (skip in expanded form)
- 4 is in the Tens place: 4 x 10 = 40
- 8 is in the Ones place: 8 x 1 = 8
Step 2: Write as a sum, omitting the zero term:
7,25,048 = 7,00,000 + 20,000 + 5,000 + 40 + 8
Verification: 7,00,000 + 20,000 = 7,20,000. Then + 5,000 = 7,25,000. Then + 40 = 7,25,040. Then + 8 = 7,25,048. Correct.
Answer: 7,25,048 = 7,00,000 + 20,000 + 5,000 + 40 + 8
Example 4: Example 4: Standard Form from Expanded Form
Problem: Write in standard form: 3,00,000 + 60,000 + 200 + 7
Solution:
Step 1: Identify which place each value fills:
- 3,00,000 → Lakhs digit = 3
- 60,000 → Ten Thousands digit = 6
- (No Thousands value) → Thousands digit = 0
- 200 → Hundreds digit = 2
- (No Tens value) → Tens digit = 0
- 7 → Ones digit = 7
Step 2: Fill the place value chart:
| L | T.Th | Th | H | T | O |
|---|---|---|---|---|---|
| 3 | 6 | 0 | 2 | 0 | 7 |
Step 3: The number is 3,60,207.
Answer: 3,60,207
Example 5: Example 5: Same Digit in Every Place
Problem: In the number 5,55,555, find the place value of each 5 and their total.
Solution:
| Position | Digit | Place Value |
|---|---|---|
| Lakhs | 5 | 5,00,000 |
| Ten Thousands | 5 | 50,000 |
| Thousands | 5 | 5,000 |
| Hundreds | 5 | 500 |
| Tens | 5 | 50 |
| Ones | 5 | 5 |
Total of all place values: 5,00,000 + 50,000 + 5,000 + 500 + 50 + 5 = 5,55,555
Key insight: The same digit 5 has six different place values, and each is exactly 10 times the one to its right. This perfectly demonstrates how the place value system works.
Answer: The place values are 5,00,000; 50,000; 5,000; 500; 50; and 5. Their sum is 5,55,555.
Example 6: Example 6: Finding a Digit from its Place Value
Problem: In a 6-digit number, a digit has a place value of 70,000. Which place is it in, and what is the digit?
Solution:
Step 1: Use the formula: Place Value = Face Value x Position Value.
Step 2: 70,000 = ? x 10,000. So the position value is 10,000, which is the ten-thousands place.
Step 3: Face Value = 70,000 / 10,000 = 7.
Answer: The digit is 7, and it is in the ten-thousands place.
Example 7: Example 7: Word Problem on Place Value
Problem: Ria's father bought a car for ₹6,45,000. What is the place value of the digit 4 in the price? Also find the place value of 6 and the difference between them.
Solution:
Step 1: In 6,45,000:
- Digit 4 is in the ten-thousands place. Place value = 4 x 10,000 = ₹40,000.
- Digit 6 is in the lakhs place. Place value = 6 x 1,00,000 = ₹6,00,000.
Step 2: Difference = ₹6,00,000 - ₹40,000 = ₹5,60,000.
Answer: Place value of 4 = ₹40,000. Place value of 6 = ₹6,00,000. Difference = ₹5,60,000.
Example 8: Example 8: Sum and Difference of Place Values
Problem: In the number 3,72,346, find the sum of the place values of the two 3s.
Solution:
Step 1: Find both 3s and their positions:
- First 3 (leftmost): in the lakhs place → place value = 3 x 1,00,000 = 3,00,000
- Second 3: in the hundreds place → place value = 3 x 100 = 300
Step 2: Sum = 3,00,000 + 300 = 3,00,300
Step 3: Difference = 3,00,000 - 300 = 2,99,700
Answer: Sum of place values = 3,00,300. The two 3s have vastly different values because of their positions.
Example 9: Example 9: 7-Digit Number Place Value
Problem: Write 15,43,200 in a place value chart and find the place value of every digit.
Solution:
| T.L | L | T.Th | Th | H | T | O |
|---|---|---|---|---|---|---|
| 1 | 5 | 4 | 3 | 2 | 0 | 0 |
Place values:
- 1 x 10,00,000 = 10,00,000 (ten lakh)
- 5 x 1,00,000 = 5,00,000 (five lakh)
- 4 x 10,000 = 40,000
- 3 x 1,000 = 3,000
- 2 x 100 = 200
- 0 x 10 = 0
- 0 x 1 = 0
Answer: The place value of 1 is 10,00,000 (ten lakh). Expanded form: 10,00,000 + 5,00,000 + 40,000 + 3,000 + 200 = 15,43,200.
Example 10: Example 10: Building a Number from Place Values
Problem: Form a 6-digit number where: lakhs digit = 2, ten-thousands digit = 0, thousands digit = 9, hundreds digit = 5, tens digit = 3, ones digit = 7.
Solution:
Step 1: Place each digit in the chart:
| L | T.Th | Th | H | T | O |
|---|---|---|---|---|---|
| 2 | 0 | 9 | 5 | 3 | 7 |
Step 2: Read the number: 2,09,537
Step 3: In words: Two lakh nine thousand five hundred and thirty-seven.
Step 4: Verify expanded form: 2,00,000 + 9,000 + 500 + 30 + 7 = 2,09,537. Correct.
Answer: The number is 2,09,537.
Real-World Applications
Understanding place value of large numbers is used throughout mathematics and daily life:
- Banking: Reading account balances like ₹8,45,230 requires knowing what each digit represents.
- Geography: Understanding population figures such as 12,50,000 people in a district.
- Shopping: Comparing prices of expensive items like flats (₹65,00,000 vs ₹72,00,000) -- the lakhs digit matters most.
- Arithmetic: Addition with carrying, subtraction with borrowing, and long multiplication all depend on place value.
- Rounding and estimation: You need to know which digit to look at when rounding to the nearest thousand or lakh.
- Comparing and ordering: Place value tells you to compare from the leftmost (highest-value) place first.
Key Points to Remember
- Place value = digit x positional value. Face value = the digit itself.
- Each place is 10 times the place to its right (and 1/10 of the place to its left).
- The places from right to left: Ones, Tens, Hundreds, Thousands, Ten Thousands, Lakhs, Ten Lakhs.
- The place value of 0 is always 0, but 0 is essential as a placeholder -- removing it changes the number entirely.
- Expanded form = sum of the place values of all digits in the number.
- Two identical digits in different places have different place values. In 3,00,300, the first 3 = 3,00,000 and the second 3 = 300.
- Place value is the foundation for all arithmetic operations and for comparing, ordering, and rounding numbers.
- You can find a digit's face value from its place value by dividing the place value by the positional value.
Practice Problems
- Write 9,04,376 in a place value chart and identify the place of each digit.
- Find the place value and face value of every digit in 5,60,812.
- Write the expanded form of 8,03,540.
- Write in standard form: 6,00,000 + 40,000 + 5,000 + 900 + 20 + 3.
- In 7,77,777, what is the difference between the place value of the 7 in the lakhs place and the 7 in the tens place?
- Dev's school raised ₹2,36,450 for flood relief. What is the place value of the digit 3 in this amount?
- Form the largest 6-digit number using digits 4, 0, 8, 1, 5, 3 (each once). Write its expanded form.
- A digit in the number 4,_2,108 has a place value of 50,000. Find the missing digit and the complete number.
Frequently Asked Questions
Q1. What is the difference between place value and face value?
Face value is the digit itself and never changes -- the face value of 4 is always 4 no matter where it appears. Place value is the digit multiplied by its positional value. In 3,45,000, the face value of 4 is 4, but its place value is 40,000 because it occupies the ten-thousands place.
Q2. What is the place value of 0 in any number?
The place value of 0 is always 0, regardless of its position. However, 0 serves as a crucial placeholder. Without it, the number 3,05,000 (six digits) would become 35,000 (five digits) -- a completely different number. Never drop zeros from a number.
Q3. How many places are there in a 6-digit number?
A 6-digit number has six places: Ones, Tens, Hundreds, Thousands, Ten Thousands, and Lakhs. Each successive place from right to left is worth 10 times more than the previous one.
Q4. What is the expanded form of a number?
Expanded form expresses a number as the sum of the place values of each digit. For example, 5,23,004 in expanded form is 5,00,000 + 20,000 + 3,000 + 4. Zeros are typically omitted since they add 0 to the sum.
Q5. How do I find which digit is in a given place?
Count positions from the right: ones (1st), tens (2nd), hundreds (3rd), thousands (4th), ten-thousands (5th), lakhs (6th), ten-lakhs (7th). The digit at the position you counted to is the answer.
Q6. Why is place value important for Class 5 students?
Place value is the basis of the entire number system. It enables you to read and write numbers, perform addition with carrying, subtraction with borrowing, long multiplication, and long division. It is also essential for comparing, ordering, rounding, and estimating -- all core Class 5 skills.
Q7. Can two digits in a number have the same place value?
No. Even if two digits in a number are identical, they occupy different positions, so their place values are always different. In 3,00,300, the first 3 (lakhs place) has a place value of 3,00,000 and the second 3 (hundreds place) has a place value of only 300.
Q8. What comes after the ten-lakhs place?
After the ten-lakhs place comes the crores place (1,00,00,000 = one crore = 10 million). The crores place is usually introduced in Class 6 or Class 7 of the CBSE curriculum.
Q9. How is place value different in the Indian and international systems?
The positional logic is identical -- each place is 10 times the one to its right. The difference is in grouping: the Indian system uses Lakhs and Crores (groups of 2 after the first 3), while the International system uses Millions and Billions (groups of 3). So 10,00,000 is called 'ten lakh' in India and '1 million' internationally.
Q10. Is place value covered in the NCERT Class 5 syllabus?
Yes. Place value of large numbers (up to lakhs and ten lakhs) is a foundational topic in the NCERT Class 5 Maths curriculum. It appears in the chapters on large numbers and is prerequisite knowledge for all arithmetic operations taught in Class 5.
Related Topics
- 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
- Expanded Form of Large Numbers
- Predecessor and Successor (Grade 5)
