Ordering Decimals (Grade 4)
Ordering decimals means arranging decimal numbers from the smallest to the largest (ascending order) or from the largest to the smallest (descending order).
In Class 4, you will learn to compare and order decimals up to two decimal places (hundredths). This skill is used in measuring lengths, comparing prices, and reading sports scores.
What is Ordering Decimals - Class 4 Maths (Decimals)?
To order decimals, you compare them digit by digit from left to right, just like whole numbers — but you must pay special attention to the decimal point.
Steps to compare decimals:
- Step 1: Compare the whole number part first. The larger whole number means the larger decimal.
- Step 2: If the whole number parts are equal, compare the tenths digit.
- Step 3: If the tenths are also equal, compare the hundredths digit.
Tip: Make all numbers have the same number of decimal places by adding zeros
Solved Examples
Example 1: Example 1: Comparing two decimals
Problem: Which is greater — 3.7 or 3.5?
Solution:
Step 1: Whole number part: both are 3 (equal).
Step 2: Tenths: 7 > 5.
Answer: 3.7 > 3.5
Example 2: Example 2: Comparing with different decimal places
Problem: Which is greater — 4.8 or 4.56?
Solution:
Step 1: Make decimal places equal: 4.80 and 4.56.
Step 2: Whole parts equal (4). Tenths: 8 > 5.
Answer: 4.8 > 4.56 (or 4.80 > 4.56).
Example 3: Example 3: Ascending order
Problem: Arrange in ascending order: 2.45, 2.09, 2.4, 2.51
Solution:
Step 1: Make all have 2 decimal places: 2.45, 2.09, 2.40, 2.51
Step 2: Whole parts all 2. Compare tenths: 0, 4, 4, 5.
Step 3: 2.09 is smallest. For 2.45 and 2.40: hundredths 5 > 0, so 2.40 < 2.45. Then 2.51.
Answer: 2.09 < 2.4 < 2.45 < 2.51
Example 4: Example 4: Descending order
Problem: Arrange in descending order: 7.3, 7.08, 7.35, 7.1
Solution:
Step 1: Equalise: 7.30, 7.08, 7.35, 7.10
Step 2: Tenths: 3, 0, 3, 1. Group: {7.30, 7.35} and {7.08, 7.10}.
Step 3: 7.35 > 7.30 (hundredths 5>0). 7.10 > 7.08.
Answer: 7.35 > 7.3 > 7.1 > 7.08
Example 5: Example 5: Heights of students
Problem: Heights: Aman — 1.32 m, Priya — 1.28 m, Dev — 1.3 m, Meera — 1.35 m. Arrange from shortest to tallest.
Solution:
Step 1: Equalise: 1.32, 1.28, 1.30, 1.35
Step 2: Compare tenths (all 2 or 3): 1.28, 1.30, 1.32, 1.35
Answer: Shortest to tallest: Priya (1.28) < Dev (1.3) < Aman (1.32) < Meera (1.35)
Example 6: Example 6: Comparing money
Problem: Which costs more — ₹15.50 or ₹15.05?
Solution:
Step 1: Whole parts equal (15). Tenths: 5 > 0.
Answer: ₹15.50 > ₹15.05. The difference is ₹0.45.
Example 7: Example 7: Ordering race times
Problem: Race times (seconds): Arjun — 12.4, Kavi — 12.08, Rahul — 12.15, Dev — 12.3. Who won (least time)?
Solution:
Step 1: Equalise: 12.40, 12.08, 12.15, 12.30
Step 2: Order: 12.08, 12.15, 12.30, 12.40
Answer: Kavi won with the least time (12.08 seconds). Order: Kavi < Rahul < Dev < Arjun.
Example 8: Example 8: Tricky comparison — 0.5 vs 0.50 vs 0.500
Problem: Are 0.5, 0.50, and 0.500 different values?
Solution:
Step 1: 0.5 = 5 tenths = 0.50 = 0.500
Step 2: Adding zeros after the last decimal digit does not change the value.
Answer: They are all equal. 0.5 = 0.50 = 0.500.
Example 9: Example 9: Between two decimals
Problem: Find a decimal number between 3.4 and 3.5.
Solution:
Step 1: Write as 3.40 and 3.50.
Step 2: Numbers between: 3.41, 3.42, 3.43, ..., 3.49.
Answer: One possible answer: 3.45 (the midpoint). Any value from 3.41 to 3.49 works.
Example 10: Example 10: Ordering five decimals
Problem: Order from smallest to largest: 0.7, 0.07, 0.77, 7.0, 0.17
Solution:
Step 1: Equalise: 0.70, 0.07, 0.77, 7.00, 0.17
Step 2: 7.00 has largest whole part. Remaining all have 0.
Step 3: Compare tenths: 0.07(0), 0.17(1), 0.70(7), 0.77(7).
Step 4: 0.70 vs 0.77: hundredths 0 < 7.
Answer: 0.07 < 0.17 < 0.7 < 0.77 < 7.0
Key Points to Remember
- To compare decimals, first compare the whole number part, then tenths, then hundredths.
- Make all numbers have the same number of decimal places by adding trailing zeros.
- Adding zeros after the last decimal digit does not change the value: 0.5 = 0.50.
- Ascending order: smallest to largest. Descending order: largest to smallest.
- A common mistake is thinking 0.18 > 0.9 because 18 > 9. Compare place by place: 0.18 has 1 tenth, while 0.9 has 9 tenths, so 0.9 > 0.18.
- There are infinitely many decimals between any two decimal numbers.
Practice Problems
- Which is greater — 5.6 or 5.06? Explain.
- Arrange in ascending order: 1.5, 1.05, 1.55, 1.50
- Arrange in descending order: 8.9, 8.09, 8.91, 8.19
- Heights: Aditi — 1.42 m, Neha — 1.4 m, Ria — 1.24 m. Order from tallest to shortest.
- Find 3 decimal numbers between 6.1 and 6.2.
- Is 0.3 greater than 0.29? Explain using place value.
- Order these prices from cheapest to most expensive: ₹10.50, ₹10.05, ₹10.55, ₹10.15
Frequently Asked Questions
Q1. How do you compare two decimal numbers?
Compare digit by digit from left to right. First compare the whole number parts. If equal, compare tenths. If still equal, compare hundredths. The first difference determines which is larger.
Q2. Why should you add zeros to make decimal places equal?
Adding trailing zeros (like writing 3.5 as 3.50) makes it easier to compare digit by digit. It does not change the value of the number.
Q3. Is 0.9 greater than 0.85?
Yes. Write 0.9 as 0.90. Compare tenths: 9 > 8. So 0.90 > 0.85.
Q4. What is ascending order?
Ascending order means arranging numbers from smallest to largest. For example, 1.2, 1.5, 1.8 is in ascending order.
Q5. What is descending order?
Descending order means arranging numbers from largest to smallest. For example, 5.9, 5.6, 5.1 is in descending order.
Q6. Can there be decimals between 2.3 and 2.4?
Yes, infinitely many. Examples: 2.31, 2.35, 2.39. You can always find more by using more decimal places, like 2.315 or 2.372.
Q7. Is 0.5 the same as 0.50?
Yes. Adding a zero after the last decimal digit does not change the value. 0.5, 0.50, and 0.500 are all equal to five-tenths.
Q8. Why do students confuse 0.18 with being larger than 0.9?
Because 18 > 9 as whole numbers. But in decimals, you must compare place by place: 0.18 has 1 tenth, while 0.9 has 9 tenths. Since 1 < 9, 0.18 < 0.9.
