Ordering 3-Digit Numbers
Ordering numbers means arranging them in a specific order. Numbers can be arranged in ascending order (smallest to largest) or descending order (largest to smallest).
To order 3-digit numbers, we compare them using the same method — start from the hundreds digit, then tens, then ones — and place them in the correct sequence.
What is Ordering 3-Digit Numbers - Class 3 Maths (Numbers up to 1000)?
Ascending order: Arranging numbers from the smallest to the largest. Example: 215, 318, 427.
Descending order: Arranging numbers from the largest to the smallest. Example: 427, 318, 215.
Steps to order 3-digit numbers:
- Compare the hundreds digits of all the numbers.
- Numbers with a smaller hundreds digit come first in ascending order.
- If hundreds digits are the same, compare tens digits.
- If tens digits are also the same, compare ones digits.
Solved Examples
Example 1: Ascending Order — Different Hundreds
Question: Arrange in ascending order: 583, 271, 649.
Think:
- Compare hundreds: 5, 2, 6
- Smallest hundreds digit is 2 → 271 comes first
- Next is 5 → 583
- Largest is 6 → 649
Answer: 271, 583, 649
Example 2: Descending Order — Different Hundreds
Question: Arrange in descending order: 312, 785, 460.
Think:
- Compare hundreds: 3, 7, 4
- Largest is 7 → 785 comes first
- Next is 4 → 460
- Smallest is 3 → 312
Answer: 785, 460, 312
Example 3: Same Hundreds — Compare Tens
Question: Arrange in ascending order: 534, 578, 512.
Think:
- All have hundreds digit 5
- Compare tens: 3, 7, 1
- Smallest tens is 1 → 512
- Next is 3 → 534
- Largest is 7 → 578
Answer: 512, 534, 578
Example 4: Same Hundreds and Tens — Compare Ones
Question: Arrange in descending order: 647, 641, 649.
Think:
- Hundreds: all are 6. Tens: all are 4.
- Compare ones: 7, 1, 9
- Largest ones is 9 → 649
- Next is 7 → 647
- Smallest is 1 → 641
Answer: 649, 647, 641
Example 5: Ordering Five Numbers
Question: Arrange in ascending order: 850, 308, 512, 850, 199.
Think:
- Compare hundreds: 8, 3, 5, 8, 1
- Smallest = 1 → 199
- Next = 3 → 308
- Next = 5 → 512
- Two numbers start with 8: both are 850 (equal)
Answer: 199, 308, 512, 850, 850
Example 6: Word Problem — Heights of Students
Question: Ria is 134 cm tall, Aman is 128 cm, Priya is 141 cm, and Kavi is 130 cm. Arrange their heights in ascending order.
Think:
- All have hundreds digit 1
- Compare tens: 3, 2, 4, 3
- Smallest tens = 2 → 128 (Aman)
- Tens = 3: compare ones: 134 vs 130 → 130, 134
- Largest tens = 4 → 141 (Priya)
Answer: 128, 130, 134, 141 (Aman, Kavi, Ria, Priya)
Example 7: Word Problem — Cricket Runs
Question: In three matches, India scored 287, 315, and 264 runs. Arrange the scores from highest to lowest.
Think:
- Hundreds: 2, 3, 2
- Highest hundreds = 3 → 315
- Two numbers have hundreds 2: 287 vs 264
- Tens: 8 > 6 → 287 > 264
Answer: 315, 287, 264
Example 8: Finding the Smallest and Largest
Question: From the numbers 406, 640, 460, and 604, find the smallest and largest.
Think:
- Hundreds: 4, 6, 4, 6
- Numbers with hundreds 4: 406, 460 → compare tens: 0 vs 6 → 406 < 460
- Numbers with hundreds 6: 640, 604 → compare tens: 4 vs 0 → 604 < 640
- Smallest = 406, Largest = 640
Answer: Smallest = 406, Largest = 640.
Example 9: Word Problem — Price Comparison
Question: Aditi sees four school bags priced at ₹375, ₹349, ₹399, and ₹350. Arrange the prices from cheapest to most expensive.
Think:
- All have hundreds digit 3
- Tens: 7, 4, 9, 5
- Order of tens: 4, 5, 7, 9
- 349, 350, 375, 399
Answer: ₹349, ₹350, ₹375, ₹399
Real-World Applications
Where do we order numbers in daily life?
- Test results: After an exam, marks are arranged from highest to lowest to find the topper. If marks are 456, 489, 478, 432, the descending order is 489, 478, 456, 432.
- Prices: When shopping online, you can sort items by price — cheapest first (ascending) or most expensive first (descending).
- Cricket scoreboard: Teams are ranked by runs scored, from highest to lowest.
- Population: Villages can be arranged by population to identify the largest and smallest communities.
- Dictionary: Words are arranged in alphabetical order, which is a type of ordering.
Ordering helps us organise information. Whether ranking students, sorting products, or comparing scores, the ability to arrange numbers in order is a valuable life skill.
Key Points to Remember
- Ascending order = smallest to largest.
- Descending order = largest to smallest.
- Compare hundreds first, then tens, then ones.
- If two numbers are equal, they occupy the same position in the order.
- A number with a greater hundreds digit is always larger, regardless of the tens and ones digits.
- Ordering is used in daily life for ranking prices, marks, heights, and scores.
Practice Problems
- Arrange in ascending order: 725, 572, 257.
- Arrange in descending order: 409, 490, 940, 904.
- Dev scored 456, 489, and 465 in three tests. Arrange from highest to lowest.
- Which is the second smallest number: 333, 313, 331, 303?
- Arrange in ascending order: 800, 808, 880, 888.
- Neha, Arjun, and Meera saved ₹510, ₹501, and ₹515. Who saved the most?
- Arrange 200, 100, 500, 300, 400 in descending order.
Frequently Asked Questions
Q1. What is ascending order?
Ascending order means arranging numbers from the smallest to the largest. For example, 102, 210, 312 is in ascending order.
Q2. What is descending order?
Descending order means arranging numbers from the largest to the smallest. For example, 500, 400, 300 is in descending order.
Q3. How do you order numbers that start with the same digit?
If the hundreds digits are the same, compare the tens digits. If those are also the same, compare the ones digits. The smaller digit comes first in ascending order.
Q4. Can you order more than three numbers at once?
Yes. The same rules apply. Compare the hundreds digits of all numbers first, group those that are equal, then compare tens and ones within each group.
Q5. What is the difference between comparing and ordering?
Comparing looks at two numbers to decide which is greater. Ordering arranges three or more numbers in a specific sequence (ascending or descending).
Q6. How is ordering numbers useful?
Ordering is used to rank items by size, price, distance, or score. For example, arranging test marks from highest to lowest helps find the topper.
Q7. What if two numbers in a list are equal?
Equal numbers sit next to each other in the ordered list. For example, ascending order of 450, 300, 450 is 300, 450, 450.
Q8. Does ordering work the same for 2-digit and 3-digit numbers?
Yes, the comparison rules are the same. Just remember that any 3-digit number is always greater than any 2-digit number.
