5-Digit Numbers
A 5-digit number is any number from 10,000 to 99,999. These numbers use five places: Ten Thousands, Thousands, Hundreds, Tens, and Ones.
The smallest 5-digit number is 10,000 (ten thousand) and the largest is 99,999 (ninety-nine thousand nine hundred ninety-nine). There are 90,000 five-digit numbers in all.
In Class 4, students learn to read, write, compare, and order 5-digit numbers. These numbers appear in real life as populations of towns, distances between cities, and prices of appliances.
What is 5-Digit Numbers - Class 4 Maths (Large Numbers)?
A 5-digit number has exactly five digits. The first digit (from the left) is in the ten thousands place and must be 1 to 9.
| Ten Thousands (TTh) | Thousands (Th) | Hundreds (H) | Tens (T) | Ones (O) |
|---|---|---|---|---|
| 10,000 | 1,000 | 100 | 10 | 1 |
Key facts:
- Smallest 5-digit number: 10,000
- Largest 5-digit number: 99,999
- Total 5-digit numbers: 99,999 - 10,000 + 1 = 90,000
- 9,999 + 1 = 10,000 (bridge from 4-digit to 5-digit)
5-Digit Numbers Formula
5-digit number = TTh x 10,000 + Th x 1,000 + H x 100 + T x 10 + O x 1
Types and Properties
Reading 5-digit numbers (Indian system):
In the Indian system, we use commas after the thousands place.
- 23,456 — Twenty-three thousand four hundred fifty-six
- 50,008 — Fifty thousand eight
- 10,700 — Ten thousand seven hundred
- 99,999 — Ninety-nine thousand nine hundred ninety-nine
Expanded form of 5-digit numbers:
For 47,263:
| Digit | Place | Value |
|---|---|---|
| 4 | Ten Thousands | 40,000 |
| 7 | Thousands | 7,000 |
| 2 | Hundreds | 200 |
| 6 | Tens | 60 |
| 3 | Ones | 3 |
47,263 = 40,000 + 7,000 + 200 + 60 + 3
Solved Examples
Example 1: Example 1: Identifying 5-digit numbers
Problem: Which of these are 5-digit numbers: 9,999; 10,000; 85,342; 1,00,000?
Solution:
- 9,999 — 4 digits (not 5-digit)
- 10,000 — 5 digits (5-digit number)
- 85,342 — 5 digits (5-digit number)
- 1,00,000 — 6 digits (not 5-digit)
Answer: 10,000 and 85,342 are 5-digit numbers.
Example 2: Example 2: Writing a number in words
Problem: Write 36,205 in words.
Solution:
Step 1: 36 thousand = thirty-six thousand
Step 2: 2 hundreds = two hundred
Step 3: 0 tens (skip)
Step 4: 5 ones = five
Answer: Thirty-six thousand two hundred five
Example 3: Example 3: Writing numeral from words
Problem: Write the numeral for "Seventy thousand forty-three."
Solution:
Step 1: Seventy thousand = 70,000
Step 2: Forty-three = 43
Step 3: No hundreds mentioned = 0 hundreds
Answer: 70,043
Example 4: Example 4: Place value in a 5-digit number
Problem: Find the place value of each digit in 58,091.
Solution:
| Digit | Place | Place Value |
|---|---|---|
| 5 | Ten Thousands | 50,000 |
| 8 | Thousands | 8,000 |
| 0 | Hundreds | 0 |
| 9 | Tens | 90 |
| 1 | Ones | 1 |
Answer: Place values are 50,000; 8,000; 0; 90; 1.
Example 5: Example 5: Expanded form
Problem: Write 62,408 in expanded form.
Solution:
62,408 = 60,000 + 2,000 + 400 + 0 + 8
Answer: 60,000 + 2,000 + 400 + 8
Example 6: Example 6: Standard form from expanded
Problem: Write the standard form: 30,000 + 5,000 + 60 + 9.
Solution:
Step 1: 30,000 + 5,000 = 35,000
Step 2: No hundreds, so hundreds digit = 0
Step 3: 35,000 + 60 + 9 = 35,069
Answer: 35,069
Example 7: Example 7: Predecessor and successor
Problem: Find the predecessor and successor of 40,000.
Solution:
Step 1: Predecessor = 40,000 - 1 = 39,999
Step 2: Successor = 40,000 + 1 = 40,001
Answer: Predecessor = 39,999 (a 5-digit number), Successor = 40,001
Example 8: Example 8: Forming largest and smallest numbers
Problem: Using digits 6, 0, 3, 9, 2 (each once), form the largest and smallest 5-digit numbers.
Solution:
Largest: Arrange in descending order: 9, 6, 3, 2, 0 = 96,320
Smallest: Ascending order would give 0, 2, 3, 6, 9 but 0 cannot be first. Use next smallest digit first: 20,369
Answer: Largest = 96,320, Smallest = 20,369
Example 9: Example 9: Word problem - population
Problem: The population of Ria's town is 45,872. Aman's town has a population of 38,965. Which town has more people and by how much?
Solution:
Step 1: Compare: 45,872 and 38,965. Ten thousands: 4 > 3
Step 2: So 45,872 > 38,965. Ria's town has more people.
Step 3: Difference = 45,872 - 38,965 = 6,907
Answer: Ria's town has more people by 6,907.
Example 10: Example 10: Word problem - price
Problem: A laptop costs ₹52,490. Write this amount in expanded form and in words.
Solution:
Expanded form: 50,000 + 2,000 + 400 + 90
In words: Fifty-two thousand four hundred ninety
Answer: ₹52,490 = 50,000 + 2,000 + 400 + 90 = Fifty-two thousand four hundred ninety
Key Points to Remember
- A 5-digit number ranges from 10,000 to 99,999.
- The five places are: Ten Thousands, Thousands, Hundreds, Tens, Ones.
- The ten thousands digit is always 1 to 9.
- There are 90,000 five-digit numbers in all.
- 9,999 + 1 = 10,000 (the bridge from 4-digit to 5-digit numbers).
- In the Indian system, commas are placed after the thousands: 45,678.
- When forming the smallest 5-digit number with given digits including 0, place the smallest non-zero digit first.
- The ten thousands place is 10 times the thousands place and 10,000 times the ones place.
Practice Problems
- Write 81,006 in words.
- Write the numeral for "Forty-five thousand three hundred twenty."
- What is the place value of 7 in 73,482?
- Write 60,905 in expanded form.
- Convert to standard form: 90,000 + 4,000 + 200 + 7.
- Find the predecessor and successor of 99,999.
- Using digits 1, 5, 0, 8, 3, form the largest and smallest 5-digit numbers.
- The distance from Delhi to Chennai is 21,640 km by road. What is the place value of 2 in this number?
Frequently Asked Questions
Q1. What is the smallest 5-digit number?
The smallest 5-digit number is 10,000 (ten thousand). It comes right after 9,999, the largest 4-digit number.
Q2. What is the largest 5-digit number?
The largest 5-digit number is 99,999. Adding 1 to it gives 1,00,000 (one lakh), which is a 6-digit number.
Q3. How many 5-digit numbers are there?
There are 90,000 five-digit numbers: from 10,000 to 99,999. That is 99,999 - 10,000 + 1 = 90,000.
Q4. What is the ten thousands place?
It is the leftmost place in a 5-digit number. Its value is 10,000. For example, in 47,356, the digit 4 is in the ten thousands place and has a place value of 40,000.
Q5. How do you read 5-digit numbers in the Indian system?
In the Indian system, read the first two digits as 'X thousand' and the rest normally. 56,234 is read as 'fifty-six thousand two hundred thirty-four.' A comma is placed after the thousands.
Q6. Can a 5-digit number have 0 in the ten thousands place?
No. If the ten thousands place is 0, it would be a 4-digit or smaller number. The ten thousands digit must be 1 to 9.
Q7. What is the difference between Indian and International number systems for 5-digit numbers?
For 5-digit numbers, both systems read the same way. The difference appears at 6 digits and above: Indian system uses lakhs while International uses hundred thousands.
Q8. Are 5-digit numbers covered in NCERT Class 4?
Yes. NCERT Class 4 Maths introduces 5-digit numbers in the chapter on large numbers, covering reading, writing, place value, expanded form, and comparison.
Related Topics
- 4-Digit Numbers
- Place Value of 5-Digit Numbers
- Place Value of 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
