Compare Decimals Notes & Questions | Class 5 Mathematics | Drishti OS

Compare Decimals

What you'll learn

To order and compare decimals using place value — not just counting digits.
To compare decimals in money (which item costs more?) and measurement contexts.
To use number-line reasoning and padding zeros for fair comparison.
To apply NCERT Math-Magic 5, Chapter 10 strategies for ranking lengths and prices.

Key concepts

Level 1 — Compare from left to right

Verbal: Compare digits in the highest place first; if equal, move to the next place to the right.

Symbolic: To compare 0.6 and 0.59 → tenths: 6 vs 5 → 0.6 > 0.59.

Pair	Comparison steps	Result
3.4 vs 3.38	Ones equal; tenths 4 > 3	3.4 > 3.38
0.8 vs 0.80	Pad: 0.80 = 0.8	Equal
2.05 vs 2.5	Tenths: 0 < 5	2.05 < 2.5

NCERT link: Math-Magic 5, Ch 10 — comparing heights (1.45 m vs 1.5 m) and race timings.

Level 2 — Ordering lists and number line

Verbal: On a number line, further right means greater.

Symbolic: Order 0.7, 0.07, 0.707 from smallest: 0.07 < 0.7 < 0.707.

Real-life: Juice A = ₹18.50, Juice B = ₹18.05, Juice C = ₹19.00 → cheapest to costliest: B, A, C.

Symbol	Meaning	Memory hook
>	Greater than	Open mouth toward larger number
<	Less than	Point toward smaller number
=	Equal	Same place values throughout

Worked example

Arrange in ascending order: 2.5, 2.05, 2.50, 2.15

Step 1 — Pad mentally: 2.50, 2.05, 2.50, 2.15
Step 2 — Compare ones (all 2), then tenths: 0, 1, 5, 5
Step 3 — Order: 2.05 < 2.15 < 2.5 = 2.50
Answer: 2.05, 2.15, 2.5 (or 2.50)

Which is cheaper: ₹45.7 or ₹45.65?

Step 1 — Compare: 45.70 vs 45.65
Step 2 — Tenths: 7 > 6 → 45.7 > 45.65
Answer: ₹45.65 is cheaper by ₹0.05 (5 paise)

Common mistakes

Mistake	Why it happens	Fix
0.9 < 0.45 because 9 < 45	Comparing digits without place	0.9 = 0.90 > 0.45
Longer decimal always bigger	Digit-count trap	Compare place by place from the left
2.5 ≠ 2.50	Thinking trailing zero changes value	Equal — pad zeros for comparison
Wrong order in ascending/descending	Mixing directions	Ascending = small → large; check the question word

Quick check

Insert <, >, or =: 0.6 ___ 0.59; 3.08 ___ 3.8.
Order: 1.2, 1.02, 1.22, 1.002 (smallest first).
Two ribbons: 2.45 m and 2.5 m — which is longer?
Stretch: A shop lists prices ₹99.9, ₹99.09, ₹99.99. Rank from cheapest to costliest.

Revision tip: Draw a 0 to 1 number line, mark tenths, and place three decimals you find in today's newspaper (fuel price, gold rate, etc.).

Open the Practice tab for graded questions on Compare Decimals.

Compare Decimals