Ordering Large Numbers (Grade 4)
Ordering numbers means arranging a group of numbers in a particular sequence — either from smallest to largest (ascending order) or from largest to smallest (descending order).
In Class 4, you learn to order 4-digit and 5-digit numbers. This skill is used in everyday life when ranking scores, sorting prices, or organizing data.
What is Ordering Large Numbers - Class 4 Maths (Large Numbers)?
Ascending order: Arranging numbers from the smallest to the largest.
1,200 < 2,500 < 3,400 < 7,800
Descending order: Arranging numbers from the largest to the smallest.
7,800 > 3,400 > 2,500 > 1,200
Steps to order numbers:
- First, separate numbers by their digit count (5-digit numbers are greater than 4-digit).
- Within the same digit count, compare from the leftmost digit.
- Arrange based on the comparison.
Solved Examples
Example 1: Example 1: Ascending order of 4-digit numbers
Problem: Arrange in ascending order: 5,432; 3,210; 7,654; 2,891.
Solution:
Step 1: All are 4-digit numbers. Compare the thousands digits: 5, 3, 7, 2.
Step 2: Order thousands digits: 2 < 3 < 5 < 7
Answer: 2,891 < 3,210 < 5,432 < 7,654
Example 2: Example 2: Descending order of 4-digit numbers
Problem: Arrange in descending order: 4,589; 4,598; 4,895; 4,859.
Solution:
Step 1: All have Th = 4. Compare hundreds: 5, 5, 8, 8.
Step 2: Numbers with H = 8 are larger: 4,895 and 4,859.
Step 3: 4,895 vs 4,859: T = 9 > 5, so 4,895 > 4,859.
Step 4: Numbers with H = 5: 4,598 vs 4,589: T = 9 > 8, so 4,598 > 4,589.
Answer: 4,895 > 4,859 > 4,598 > 4,589
Example 3: Example 3: Mixed 4-digit and 5-digit numbers
Problem: Arrange in ascending order: 9,876; 12,345; 8,765; 10,000.
Solution:
Step 1: Separate by digit count: 4-digit (9,876; 8,765) and 5-digit (12,345; 10,000).
Step 2: All 4-digit numbers < all 5-digit numbers.
Step 3: Among 4-digit: 8,765 < 9,876.
Step 4: Among 5-digit: 10,000 < 12,345.
Answer: 8,765 < 9,876 < 10,000 < 12,345
Example 4: Example 4: Word problem - heights of mountains
Problem: Heights of four peaks: Nanda Devi = 7,816 m, Kangchenjunga = 8,586 m, K2 = 8,611 m, Lhotse = 8,516 m. Arrange in ascending order of height.
Solution:
Step 1: 7,816 is the only one with Th = 7, so it is smallest.
Step 2: Remaining: 8,586; 8,611; 8,516. All have Th = 8.
Step 3: Hundreds: 5, 6, 5. Compare 8,586 vs 8,516: T = 8 > 1, so 8,586 > 8,516.
Step 4: Order: 8,516 < 8,586 < 8,611.
Answer: 7,816 < 8,516 < 8,586 < 8,611 (Nanda Devi < Lhotse < Kangchenjunga < K2)
Example 5: Example 5: Descending order of 5-digit numbers
Problem: Arrange in descending order: 45,321; 54,123; 45,231; 54,213.
Solution:
Step 1: TTh digits: 4, 5, 4, 5. Numbers starting with 5 are larger.
Step 2: 54,213 vs 54,123: Th = 2 > 1, so 54,213 > 54,123.
Step 3: 45,321 vs 45,231: Th = 3 > 2, so 45,321 > 45,231.
Answer: 54,213 > 54,123 > 45,321 > 45,231
Example 6: Example 6: Word problem - prices
Problem: Rahul compared TV prices: ₹32,499; ₹29,999; ₹32,599; ₹31,450. Arrange from cheapest to costliest.
Solution:
Step 1: TTh: 3, 2, 3, 3. The one with TTh = 2 is smallest: ₹29,999.
Step 2: Among TTh = 3: Th = 2, 2, 1. So ₹31,450 comes next.
Step 3: ₹32,499 vs ₹32,599: H = 4 < 5, so ₹32,499 < ₹32,599.
Answer: ₹29,999 < ₹31,450 < ₹32,499 < ₹32,599
Example 7: Example 7: Finding position in order
Problem: In ascending order, what position is 6,789 among: 4,567; 6,789; 5,678; 7,890; 3,456?
Solution:
Step 1: Ascending order: 3,456 < 4,567 < 5,678 < 6,789 < 7,890.
Step 2: Count position of 6,789: it is the 4th number.
Answer: 6,789 is in the 4th position.
Example 8: Example 8: Ordering with same digits
Problem: Arrange in ascending order: 1,234; 4,321; 2,143; 3,412.
Solution:
Step 1: All use digits 1, 2, 3, 4 but in different order.
Step 2: Compare Th digits: 1, 4, 2, 3.
Step 3: Order: 1 < 2 < 3 < 4.
Answer: 1,234 < 2,143 < 3,412 < 4,321
Example 9: Example 9: Word problem - populations
Problem: Populations of four towns: Anand = 15,300; Baroda = 42,800; Surat = 38,500; Rajkot = 27,600. Arrange in descending order.
Solution:
Step 1: Compare TTh: 1, 4, 3, 2.
Step 2: Descending: 4 > 3 > 2 > 1.
Answer: 42,800 > 38,500 > 27,600 > 15,300 (Baroda > Surat > Rajkot > Anand)
Example 10: Example 10: Ordering with repeated digits
Problem: Arrange in ascending order: 5,055; 5,505; 5,550; 5,005.
Solution:
Step 1: All have Th = 5. Compare H: 0, 5, 5, 0.
Step 2: H = 0 group: 5,055 vs 5,005. T: 5 > 0, so 5,005 < 5,055.
Step 3: H = 5 group: 5,505 vs 5,550. T: 0 < 5, so 5,505 < 5,550.
Answer: 5,005 < 5,055 < 5,505 < 5,550
Key Points to Remember
- Ascending order = smallest to largest. Descending order = largest to smallest.
- Numbers with more digits are always greater.
- For numbers with the same digit count, compare from the leftmost digit.
- When several numbers have the same leading digit, move to the next place to break the tie.
- Use < for ascending order and > for descending order between consecutive numbers.
- In real life, ordering helps rank scores, sort prices, and organize data.
Practice Problems
- Arrange in ascending order: 7,890; 7,098; 7,908; 7,809.
- Arrange in descending order: 25,430; 24,530; 25,340; 24,350.
- Arrange from cheapest to costliest: ₹6,750; ₹6,570; ₹6,057; ₹6,705.
- Priya scored 8,435 in a game, Aman scored 8,543, and Kavi scored 8,345. Rank them from highest to lowest.
- Arrange in ascending order: 3,456; 34,560; 345; 34,065.
- Five towns have populations: 18,200; 21,500; 18,020; 21,050; 19,900. Arrange in descending order.
Frequently Asked Questions
Q1. What is ascending order?
Ascending order means arranging numbers from the smallest to the largest. For example: 2,000 < 3,500 < 5,100 < 8,400.
Q2. What is descending order?
Descending order means arranging numbers from the largest to the smallest. For example: 8,400 > 5,100 > 3,500 > 2,000.
Q3. How do you order a mix of 4-digit and 5-digit numbers?
All 4-digit numbers come before 5-digit numbers in ascending order because any 5-digit number (starting from 10,000) is greater than any 4-digit number (up to 9,999).
Q4. What if two numbers have the same first digit?
Move to the next digit (hundreds place for 4-digit numbers) and compare. Keep moving right until you find a digit that is different.
Q5. Can you order numbers using place value?
Yes. Place value comparison is the standard method. Compare the highest place first (leftmost digit), then move right. This is the same method used for comparing pairs of numbers.
Q6. Where do we use ordering in real life?
Ordering numbers is used to rank cricket scores, sort prices from cheapest to costliest, arrange heights or distances, and organize data in tables and charts.
Q7. What is the difference between comparing and ordering?
Comparing involves two numbers (which is greater or smaller). Ordering involves three or more numbers arranged in ascending or descending sequence.
Q8. Is ordering large numbers in the NCERT Class 4 syllabus?
Yes. NCERT Class 4 Maths covers ascending and descending order of 4-digit and 5-digit numbers in the chapter on large numbers.
Related Topics
- Comparing Large Numbers (Grade 4)
- 4-Digit Numbers
- Place Value of 4-Digit Numbers
- Expanded Form of 4-Digit Numbers
- 5-Digit Numbers
- Place Value of 5-Digit Numbers
- 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
