Ordering Decimals – Smallest to Largest
Ordering decimals means arranging a list of decimal numbers from smallest to largest (ascending) or from largest to smallest (descending). The skill builds directly on comparing decimals.
The Method
- Add trailing zeros so all numbers have the same number of decimal places.
- Ignore the decimal point and compare the resulting whole numbers.
- Arrange in the required order, then remove the added zeros.
Ascending Order (Smallest to Largest)
Order: 0.4, 0.04, 0.44, 0.404
Add zeros: 0.400, 0.040, 0.440, 0.404.
Compare: 040 < 400 < 404 < 440.
Order: 0.04, 0.4, 0.404, 0.44.
Order: 3.5, 3.05, 3.55, 3.505
Add zeros: 3.500, 3.050, 3.550, 3.505.
Compare: 050 < 500 < 505 < 550.
Order: 3.05, 3.5, 3.505, 3.55.
Descending Order (Largest to Smallest)
Order: 1.2, 0.9, 1.02, 0.99
Add zeros: 1.20, 0.90, 1.02, 0.99.
Compare: 120 > 102 > 099 > 090.
Order: 1.2, 1.02, 0.99, 0.9.
Mixed Whole Numbers and Decimals
Order: 2, 1.9, 2.1, 1.99
Write 2 as 2.00 and 1.9 as 1.90. Compare: 190 < 199 < 200 < 210.
Ascending order: 1.9, 1.99, 2, 2.1.
Real-Life Context
| Scenario | Numbers to Order | Why It Matters |
|---|---|---|
| Race finishing times (s) | 10.42, 10.39, 10.5, 10.04 | Lowest time wins; ascending order gives race positions |
| Prices (£) | 2.99, 2.9, 3.00, 2.09 | Finding the cheapest item |
| Temperatures (°C) | -0.5, 0.2, -0.05, 0.25 | Warmest to coldest or vice versa |
Key Takeaways
- Add trailing zeros before ordering so all numbers have equal decimal places.
- Compare from the largest place value column inward.
- Ascending = smallest first; descending = largest first.
- Always remove the added zeros in your final answer.
Practice Questions
- Write in ascending order: 0.7, 0.07, 0.77, 0.707.
- Write in descending order: 5.1, 5.01, 5.11, 5.101.
- Five athletes ran 400 m in: 49.8 s, 49.08 s, 50.1 s, 49.80 s, 48.99 s. Rank them from fastest to slowest.
- A shop sells four pens at £0.99, £1.09, £0.9, and £1.00. List them cheapest to most expensive.
- Order from smallest: 0, 0.001, 0.01, 0.1, 1.