Place Value of 5-Digit Numbers
In a 5-digit number, there are five places. The new place introduced is the Ten Thousands (TTh) place, which has a value of 10,000.
Understanding place value of 5-digit numbers is essential for reading large numbers, performing operations, and solving real-life problems involving distances, populations, and large amounts of money.
What is Place Value of 5-Digit Numbers - Class 4 Maths (Large Numbers)?
The place value chart for a 5-digit number has five columns:
| Place | Ten Thousands (TTh) | Thousands (Th) | Hundreds (H) | Tens (T) | Ones (O) |
|---|---|---|---|---|---|
| Value | 10,000 | 1,000 | 100 | 10 | 1 |
Relationships between places:
- 1 Ten Thousand = 10 Thousands = 100 Hundreds = 1,000 Tens = 10,000 Ones
- Each place is 10 times the place to its right
- Each place is one-tenth of the place to its left
Place Value of 5-Digit Numbers Formula
Place Value = Face Value x Position Value
Position values: TTh = 10,000 | Th = 1,000 | H = 100 | T = 10 | O = 1
Solved Examples
Example 1: Example 1: Place value of each digit
Problem: Write the place value of each digit in 73,528.
Solution:
| Digit | Place | Place Value |
|---|---|---|
| 7 | Ten Thousands | 70,000 |
| 3 | Thousands | 3,000 |
| 5 | Hundreds | 500 |
| 2 | Tens | 20 |
| 8 | Ones | 8 |
Answer: Place values are 70,000; 3,000; 500; 20; 8.
Example 2: Example 2: Place value with zeros
Problem: Find the place value of each digit in 40,073.
Solution:
- 4 in ten thousands = 40,000
- 0 in thousands = 0
- 0 in hundreds = 0
- 7 in tens = 70
- 3 in ones = 3
Answer: Place values are 40,000; 0; 0; 70; 3. The zeros are placeholders.
Example 3: Example 3: Comparing place values of repeated digits
Problem: In 55,505, the digit 5 appears four times. Find all four place values.
Solution:
| Position | TTh | Th | H | T | O |
|---|---|---|---|---|---|
| Digit | 5 | 5 | 5 | 0 | 5 |
- TTh: 5 x 10,000 = 50,000
- Th: 5 x 1,000 = 5,000
- H: 5 x 100 = 500
- O: 5 x 1 = 5
Answer: The four place values of 5 are 50,000; 5,000; 500; and 5.
Example 4: Example 4: Building a number from place values
Problem: Form the number with these place values: 20,000 + 6,000 + 300 + 0 + 4.
Solution:
20,000 + 6,000 + 300 + 0 + 4 = 26,304
Answer: The number is 26,304.
Example 5: Example 5: Finding a digit from its place value
Problem: In a 5-digit number, a digit has a place value of 80,000. What is the digit and in which place?
Solution:
Step 1: 80,000 = ? x 10,000
Step 2: ? = 80,000 / 10,000 = 8
Answer: The digit is 8 in the ten thousands place.
Example 6: Example 6: Word problem - school fees
Problem: Priya's annual school fees are ₹42,750. What is the place value of 2 in this amount?
Solution:
Step 1: In 42,750 — 4 is in TTh, 2 is in Th.
Step 2: Place value = 2 x 1,000 = 2,000
Answer: The place value of 2 is ₹2,000.
Example 7: Example 7: Difference of place values
Problem: Find the difference between the place values of the two 3s in 33,456.
Solution:
Step 1: First 3 is in ten thousands: 3 x 10,000 = 30,000
Step 2: Second 3 is in thousands: 3 x 1,000 = 3,000
Step 3: Difference = 30,000 - 3,000 = 27,000
Answer: The difference is 27,000.
Example 8: Example 8: Word problem - distance
Problem: The distance from Mumbai to Kolkata is about 19,654 km by road. What is the place value of 9?
Solution:
Step 1: In 19,654 — 1 is in TTh, 9 is in Th.
Step 2: Place value = 9 x 1,000 = 9,000
Answer: The place value of 9 is 9,000 km.
Example 9: Example 9: Ratio of place values
Problem: The ten thousands place is how many times the tens place?
Solution:
Step 1: Ten thousands = 10,000; Tens = 10
Step 2: 10,000 / 10 = 1,000
Answer: The ten thousands place is 1,000 times the tens place.
Example 10: Example 10: Mystery number
Problem: A 5-digit number has: TTh place value = 60,000, Th = 0, H = 800, T = 50, O = 2. What is the number?
Solution:
60,000 + 0 + 800 + 50 + 2 = 60,852
Answer: The number is 60,852.
Key Points to Remember
- A 5-digit number has 5 places: Ten Thousands, Thousands, Hundreds, Tens, Ones.
- The ten thousands place is the new place (value = 10,000).
- Each place is 10 times the place to its right.
- The place value of 0 is always 0, but 0 is essential as a placeholder.
- Same digit in different places has different values (e.g., 5 in TTh = 50,000 vs 5 in O = 5).
- Sum of all place values = the number itself.
- Ten thousands is 10,000 times the ones place.
Practice Problems
- Write the place value of each digit in 85,204.
- What is the place value of 6 in 16,439?
- Find the place value of each 4 in 44,400.
- Form the number: 50,000 + 0 + 700 + 30 + 9.
- A digit has place value 90,000. What digit is it and in which place?
- Find the difference between the place values of the two 7s in 77,123.
- Kavi's father earns ₹68,500 per month. What is the place value of 8 in this amount?
- True or false: In 20,345, the place value of 0 is zero but it cannot be removed.
Frequently Asked Questions
Q1. What is the ten thousands place?
It is the fifth place from the right (or leftmost place in a 5-digit number). Its value is 10,000. For example, in 82,463, the digit 8 has a place value of 80,000.
Q2. How is place value in 5-digit numbers different from 4-digit numbers?
5-digit numbers have one extra place: the ten thousands (TTh) place, worth 10,000. The other four places (Th, H, T, O) work the same way as in 4-digit numbers.
Q3. What happens when 0 is in the ten thousands place?
A number cannot have 0 in the ten thousands place. That would make it a 4-digit (or smaller) number, not a 5-digit number. The TTh digit must be 1-9.
Q4. How many times is the ten thousands place compared to the ones place?
10,000 times. Ten Thousands = 10,000 and Ones = 1, so 10,000 / 1 = 10,000.
Q5. Can the same digit have different place values in the same number?
Yes. In 66,606, the digit 6 appears four times with place values 60,000 (TTh), 6,000 (Th), 600 (H), and 6 (O).
Q6. How do you use place value to compare 5-digit numbers?
Compare the digits from left to right starting with the ten thousands place. The number with a larger digit in the leftmost differing place is greater.
Q7. Why is place value of 5-digit numbers important?
It is needed for reading and writing large numbers, performing addition and subtraction of large numbers, rounding, estimation, and understanding real-world quantities like distances and prices.
Q8. Is this topic in the NCERT Class 4 syllabus?
Yes. NCERT Class 4 Maths (Math Magic) introduces 5-digit numbers and their place values as part of the large numbers chapter.
Related Topics
- 5-Digit Numbers
- Place Value of 4-Digit Numbers
- 4-Digit Numbers
- Expanded Form of 4-Digit Numbers
- Comparing Large Numbers (Grade 4)
- Ordering Large Numbers (Grade 4)
- Rounding Numbers (Grade 4)
- Estimation (Grade 4)
- Roman Numerals (I to C)
- Numbers up to 1,00,000
- Predecessor and Successor (Grade 4)
- Number Names for Large Numbers
