Comparing Decimals (Grade 4)
Comparing decimals means finding out which decimal number is greater, smaller, or if two decimals are equal. This skill is used in daily life when comparing prices, measurements, and scores.
The key rule: compare place by place, starting from the leftmost (largest) place value. The first place where the digits differ tells you which number is greater.
What is Comparing Decimals - Class 4 Maths (Decimals)?
Steps to Compare Decimals:
- Make the decimal places equal by adding trailing zeros if needed (0.5 = 0.50).
- Compare the whole number parts first. The one with the larger whole part is greater.
- If whole parts are equal, compare the tenths digits.
- If tenths are also equal, compare the hundredths digits.
- Continue until you find a difference.
Compare left to right: Whole → Tenths → Hundredths
Solved Examples
Example 1: Example 1: Compare Whole Parts Different
Problem: Compare 3.7 and 5.2.
Solution:
Step 1: Whole parts: 3 and 5. Since 3 < 5.
Answer: 3.7 < 5.2
Example 2: Example 2: Same Whole Part, Compare Tenths
Problem: Compare 4.3 and 4.7.
Solution:
Step 1: Whole parts: both are 4 (equal).
Step 2: Tenths: 3 and 7. Since 3 < 7.
Answer: 4.3 < 4.7
Example 3: Example 3: Compare Hundredths
Problem: Compare 6.45 and 6.42.
Solution:
Step 1: Whole parts: both 6 (equal).
Step 2: Tenths: both 4 (equal).
Step 3: Hundredths: 5 and 2. Since 5 > 2.
Answer: 6.45 > 6.42
Example 4: Example 4: Compare with Different Number of Decimal Places
Problem: Compare 0.5 and 0.38.
Solution:
Step 1: Make decimal places equal: 0.5 = 0.50.
Step 2: Compare 0.50 and 0.38.
Step 3: Whole parts: both 0. Tenths: 5 and 3. Since 5 > 3.
Answer: 0.5 > 0.38
Example 5: Example 5: Compare Equal Decimals
Problem: Compare 2.30 and 2.3.
Solution:
Step 1: 2.30 = 2.3 (trailing zero does not change value).
Answer: 2.30 = 2.3
Example 6: Example 6: Order Three Decimals
Problem: Arrange in ascending order: 3.5, 3.15, 3.51.
Solution:
Step 1: Make all two decimal places: 3.50, 3.15, 3.51.
Step 2: All have whole part 3. Compare tenths: 5, 1, 5.
Step 3: 3.15 is smallest (tenths = 1). Among 3.50 and 3.51, compare hundredths: 0 < 1.
Answer: 3.15 < 3.50 < 3.51
Example 7: Example 7: Word Problem
Problem: Aman scored 8.5 in a competition and Priya scored 8.45. Who scored higher?
Solution:
Step 1: Make equal: 8.50 and 8.45.
Step 2: Whole parts: both 8. Tenths: 5 and 4. Since 5 > 4.
Answer: Aman scored higher (8.5 > 8.45).
Example 8: Example 8: Word Problem (Money)
Problem: Pencil A costs ₹5.75 and Pencil B costs ₹5.80. Which is cheaper?
Solution:
Step 1: Whole parts: both 5. Tenths: 7 and 8. Since 7 < 8.
Answer: Pencil A (₹5.75) is cheaper.
Example 9: Example 9: Arrange in Descending Order
Problem: Arrange in descending order: 1.2, 1.09, 1.25, 1.19.
Solution:
Step 1: Make all two decimal places: 1.20, 1.09, 1.25, 1.19.
Step 2: All have whole part 1. Compare tenths: 2, 0, 2, 1.
Step 3: 1.25 and 1.20 have tenths = 2; hundredths: 5 > 0, so 1.25 > 1.20.
Step 4: 1.19 has tenths = 1, 1.09 has tenths = 0.
Answer: 1.25 > 1.20 > 1.19 > 1.09
Key Points to Remember
- Compare decimals place by place, starting from the left (whole number → tenths → hundredths).
- Add trailing zeros to make the number of decimal places equal before comparing.
- The first place where digits differ determines which number is greater.
- Trailing zeros do not change a decimal's value: 0.5 = 0.50 = 0.500.
- On a number line, the decimal farther to the right is greater.
- These skills are used in comparing prices, measurements, and scores.
Practice Problems
- Compare 7.6 and 7.4. Which is greater?
- Compare 0.9 and 0.85.
- Arrange in ascending order: 2.3, 2.09, 2.35.
- Which is cheaper: a pen for Rs.12.50 or a pen for Rs.12.05?
- Compare 5.1 and 5.10. Are they equal?
- Arrange in descending order: 0.7, 0.72, 0.07, 0.77.
- Kavi ran 100 m in 14.35 seconds and Arjun ran it in 14.3 seconds. Who was faster?
Frequently Asked Questions
Q1. How do you compare two decimal numbers?
Start by comparing the whole number parts. If they are equal, compare the tenths. If still equal, compare the hundredths. The first place where the digits differ tells you which number is greater.
Q2. Do you need the same number of decimal places to compare?
It helps to add trailing zeros to make the decimal places equal. For example, compare 0.5 and 0.35 by writing 0.50 and 0.35. Then compare normally.
Q3. Is 0.5 greater than 0.50?
No, they are equal. Adding a zero after the last decimal digit does not change the value. 0.5 = 0.50.
Q4. Is 0.9 greater than 0.85?
Yes. Write as 0.90 and 0.85. Tenths: 9 > 8. So 0.9 > 0.85.
Q5. How do you arrange decimals in ascending order?
Compare all the decimals and write them from smallest to largest. Make decimal places equal first, then compare place by place.
Q6. Can comparing decimals help with money?
Yes. When comparing prices like Rs.15.75 and Rs.15.60, you can see that 15.60 < 15.75, so the second item is cheaper.
Q7. What is the common mistake in comparing decimals?
A common mistake is thinking that more digits means a bigger number. For example, students may think 0.35 > 0.5 because 35 > 5, but 0.50 > 0.35.
Q8. How does a number line help compare decimals?
On a number line, the number farther to the right is always greater. Plotting decimals visually shows their relative size.
Q9. Is comparing decimals in the NCERT Class 4 syllabus?
Yes. Comparing and ordering decimals is an important part of the Decimals chapter in Class 4 NCERT Maths. Students learn to compare decimals using place value and number lines.
