Comparing and Ordering Decimals
Comparing decimals means finding which decimal number is greater, smaller, or whether they are equal. Ordering decimals means arranging them in ascending (smallest to largest) or descending (largest to smallest) order.
This skill is used constantly in daily life. When you compare prices at two shops, check which athlete ran faster, or see which city had higher rainfall, you are comparing decimals. A common mistake is thinking that 0.15 is larger than 0.9 because 15 > 9. But 0.9 = 0.90, and 90 hundredths > 15 hundredths. The correct method avoids this trap.
In Class 5, you will learn a systematic method to compare decimals by equalising decimal places and checking each position from left to right. You will also arrange multiple decimals in ascending and descending order.
What is Comparing and Ordering Decimals - Class 5 Maths (Decimals)?
Comparing decimals involves checking each place value starting from the leftmost digit and moving right until a difference is found.
Step-by-step method:
1. Make the number of decimal places equal (add trailing zeros).
2. Compare the whole-number parts first.
3. If equal, compare tenths, then hundredths, then thousandths.
The first position (from the left) where the digits differ determines which number is greater.
Comparing and Ordering Decimals Formula
Rules for comparing decimals:
- Equalise decimal places by adding trailing zeros. Example: 0.5 becomes 0.500; 0.35 becomes 0.350. This does NOT change the value.
- Compare the whole-number part. The number with the larger whole part is greater. If whole parts differ, you are done.
- If whole parts are equal, compare the tenths digit.
- If tenths are equal, compare hundredths.
- If hundredths are equal, compare thousandths.
- Continue until you find a difference or confirm they are equal.
Ordering definitions:
- Ascending order: Smallest to largest (uses the < symbol). Example: 2.3 < 2.5 < 2.8
- Descending order: Largest to smallest (uses the > symbol). Example: 2.8 > 2.5 > 2.3
Types and Properties
Types of decimal comparison problems:
- Same whole-number part: Compare the decimal digits. Example: 5.47 vs 5.39 → tenths: 4 > 3, so 5.47 > 5.39.
- Different whole-number parts: Example: 12.8 vs 9.95 → 12 > 9, so 12.8 > 9.95. No need to check decimal places.
- Different number of decimal places: Add trailing zeros to equalise. Example: 3.5 vs 3.48 → 3.50 vs 3.48 → compare hundredths: 50 > 48, so 3.5 > 3.48.
- Tricky comparisons: 0.9 vs 0.09. Equalise: 0.90 vs 0.09. Tenths: 9 > 0, so 0.9 > 0.09. Many students get this wrong!
- Ordering 3 or more decimals: Compare each pair, or convert all to the same number of decimal places and compare the numbers formed after removing the decimal.
Solved Examples
Example 1: Example 1: Same Whole Part, Different Tenths
Problem: Compare 7.45 and 7.38. Write using > or <.
Solution:
Step 1: Whole parts are both 7. Equal.
Step 2: Compare tenths: 4 vs 3. Since 4 > 3, we have 7.45 > 7.38.
No need to check hundredths because the tenths digit already decided the answer.
Answer: 7.45 > 7.38
Example 2: Example 2: Different Number of Decimal Places
Problem: Compare 4.6 and 4.58.
Solution:
Step 1: Equalise decimal places: 4.60 and 4.58 (both now have 2 decimal places).
Step 2: Whole parts are both 4. Equal.
Step 3: Compare tenths: 6 vs 5. Since 6 > 5, we have 4.60 > 4.58.
Alternatively: Think of it as 460 hundredths vs 458 hundredths. 460 > 458.
Answer: 4.6 > 4.58
Example 3: Example 3: Different Whole-Number Parts
Problem: Compare 15.3 and 9.87.
Solution:
Step 1: Compare whole parts: 15 vs 9. Since 15 > 9, we know 15.3 > 9.87.
When the whole parts are different, you don't need to look at the decimal part at all.
Answer: 15.3 > 9.87
Example 4: Example 4: Ascending Order (4 decimals)
Problem: Arrange in ascending order: 2.05, 2.5, 2.005, 2.50.
Solution:
Step 1: Equalise to 3 decimal places: 2.050, 2.500, 2.005, 2.500
Step 2: Ignore the decimal point and compare: 2050, 2500, 2005, 2500
Step 3: Order: 2005 < 2050 < 2500 = 2500
Note: 2.5 and 2.50 are equivalent decimals (equal values).
Answer: 2.005 < 2.05 < 2.5 = 2.50
Example 5: Example 5: Descending Order
Problem: Arrange in descending order: 0.8, 0.08, 0.88, 0.808.
Solution:
Step 1: Equalise to 3 decimal places: 0.800, 0.080, 0.880, 0.808
Step 2: Compare as whole numbers (ignoring "0."): 800, 080, 880, 808
Step 3: Descending: 880 > 808 > 800 > 080
Answer: 0.88 > 0.808 > 0.8 > 0.08
Example 6: Example 6: Word Problem (Shopping)
Problem: Ria finds mangoes at Rs.85.50 per kg at Shop A and Rs.85.05 per kg at Shop B. Which shop is cheaper?
Solution:
Step 1: Both prices have the same whole part (85).
Step 2: Compare tenths: 5 vs 0. Since 5 > 0, Rs.85.50 > Rs.85.05.
Savings: By buying from Shop B, Ria saves 85.50 − 85.05 = Rs.0.45 per kg.
Answer: Shop B (Rs.85.05) is cheaper.
Example 7: Example 7: Word Problem (Race Timing)
Problem: In a 100m race, Arjun finished in 14.32 seconds, Dev in 14.3 seconds, and Kavi in 14.325 seconds. Rank them from first to last.
Solution:
Step 1: Equalise to 3 places: 14.320, 14.300, 14.325
Step 2: In a race, the smallest time wins. Compare: 300 < 320 < 325.
Step 3: Ranking (fastest to slowest): Dev (14.300) → Arjun (14.320) → Kavi (14.325)
Answer: 1st: Dev (14.3 s), 2nd: Arjun (14.32 s), 3rd: Kavi (14.325 s).
Example 8: Example 8: Word Problem (Weight Comparison)
Problem: Three packets weigh 1.5 kg, 1.055 kg, and 1.49 kg. Arrange from heaviest to lightest.
Solution:
Step 1: Equalise to 3 places: 1.500, 1.055, 1.490
Step 2: Compare: 500 > 490 > 055
Heaviest to lightest: 1.500 > 1.490 > 1.055
Answer: 1.5 kg > 1.49 kg > 1.055 kg
Example 9: Example 9: Finding a Decimal Between Two Others
Problem: Write three decimals between 3.4 and 3.5.
Solution:
Step 1: 3.4 = 3.40 and 3.5 = 3.50. Any decimal between 3.40 and 3.50 works.
Step 2: Examples with 2 decimal places: 3.41, 3.42, 3.43, 3.44, 3.45, 3.46, 3.47, 3.48, 3.49.
Step 3: Three answers: 3.42, 3.45, 3.48.
Key concept: Between any two decimals, there are infinitely many other decimals. You can always add more decimal places.
Answer: Three decimals between 3.4 and 3.5: 3.42, 3.45, 3.48
Example 10: Example 10: Comparing a Decimal and a Fraction
Problem: Which is greater: 0.75 or 7/10?
Solution:
Step 1: Convert 7/10 to a decimal: 7 ÷ 10 = 0.70
Step 2: Now compare 0.75 and 0.70. Both have 2 decimal places.
Step 3: Tenths are equal (both 7). Compare hundredths: 5 > 0.
Answer: 0.75 > 7/10 (or equivalently, 0.75 > 0.7)
Real-World Applications
Where do we compare and order decimals in real life?
- Shopping: Comparing prices at different shops to find the best deal. Rs.42.50 vs Rs.42.05 — the difference of Rs.0.45 matters when buying in bulk.
- Sports: Ranking athletes by timing (sprints, swimming) or distance (long jump, javelin). Smaller time = faster; larger distance = better.
- Science: Comparing measurements like temperature (36.5°C vs 37.2°C), rainfall (5.4 mm vs 5.38 mm), or chemical concentrations.
- Banking: Comparing interest rates (6.5% vs 6.25% per year) to choose the best savings account.
- Cooking: Measuring ingredients precisely when a recipe says 0.75 kg of flour and you have 0.7 kg — you need 0.05 kg more.
Key Points to Remember
- Always equalise the number of decimal places by adding trailing zeros before comparing.
- Compare from left to right: whole part → tenths → hundredths → thousandths.
- If the whole parts are different, the decimal with the larger whole part is greater. Stop there.
- Trailing zeros do not change the value: 3.5 = 3.50 = 3.500.
- Ascending order means smallest first. Descending order means largest first.
- Between any two decimals, there are infinitely many other decimals.
- To compare a fraction and a decimal, convert both to the same form first.
- Common trap: 0.9 > 0.85 even though 9 < 85. Always equalise first: 0.90 vs 0.85 → 90 > 85.
Practice Problems
- Compare 6.72 and 6.7. Write using > or <.
- Compare 0.009 and 0.09. Which is greater?
- Arrange in ascending order: 5.1, 5.01, 5.101, 5.011.
- Arrange in descending order: 0.45, 0.405, 0.5, 0.045.
- Priya ran 100m in 16.08 seconds and Aditi ran it in 16.8 seconds. Who was faster? By how many seconds?
- Write three decimals between 2.3 and 2.4.
- Which is greater: 3/5 or 0.55? Show your working by converting to the same form.
- A shopkeeper sells rice at Rs.42.50 per kg and wheat at Rs.42.05 per kg. Which grain costs more? What is the price difference?
Frequently Asked Questions
Q1. How do I compare two decimals?
Equalise the number of decimal places by adding trailing zeros. Then compare digit by digit from left to right: whole part first, then tenths, hundredths, thousandths. Stop at the first position where the digits differ.
Q2. Does adding a zero at the end change a decimal's value?
No. Trailing zeros after the last non-zero decimal digit do not change the value. 4.5 = 4.50 = 4.500. However, 4.05 is NOT the same as 4.5 — the zero in 4.05 is a placeholder in the tenths place.
Q3. Is 0.5 greater than 0.50?
They are equal. Both represent five-tenths or one-half. 0.5 = 0.50 = 0.500. Trailing zeros do not change the value.
Q4. Which is larger: 0.9 or 0.09?
0.9 is much larger. 0.9 = 9 tenths = 90 hundredths. 0.09 = 9 hundredths. So 0.9 is 10 times larger than 0.09. This is a very common mistake — always equalise decimal places first.
Q5. How do I compare a fraction with a decimal?
Convert both to the same form. Either convert the fraction to a decimal (divide numerator by denominator), or convert the decimal to a fraction. Then compare using the standard method.
Q6. What is ascending order for decimals?
Ascending order means arranging from smallest to largest. Use the less-than symbol: 0.05 < 0.5 < 0.55 < 5.0. Think of it as climbing up a staircase.
Q7. Can two different-looking decimals be equal?
Yes. Decimals like 2.30 and 2.3 look different but have the same value (both are two and three-tenths). These are called equivalent decimals. Also, 2.300 = 2.30 = 2.3.
Q8. How many decimals exist between 1.1 and 1.2?
Infinitely many. Examples include 1.11, 1.12, 1.15, 1.111, 1.199, and so on. Between any two decimals, you can always find another decimal by adding more decimal places.
Q9. Is this topic in the NCERT Class 5 syllabus?
Yes. Comparing and ordering decimals is part of the NCERT/CBSE Class 5 Maths curriculum under the Decimals chapter. It is frequently tested in school exams and is essential for decimal operations.
Related Topics
- Decimals (Grade 5)
- Addition of Decimals
- Subtraction of Decimals
- Multiplication of Decimals
- Division of Decimals
- Converting Fractions to Decimals (Grade 5)
- Converting Decimals to Fractions
- Decimal Word Problems (Grade 5)
- Decimal Place Value (Grade 5)
- Rounding Decimals
- Multiplying Decimals by 10, 100 and 1000
- Dividing Decimals by 10, 100 and 1000
