Before ordering a list of decimals, rewrite them all with the same number of decimal places, padding shorter numbers with trailing zeros so every number has the same length. This lets you compare them digit by digit, column by column, without the different lengths causing mistakes.
Example 1 — Order 0.3, 0.32, 0.309, 0.31 from smallest to largest
Step 1
Find the maximum number of decimal places: 3 (from 0.309)
Step 2
Pad all to 3 d.p.: 0.300, 0.320, 0.309, 0.310
Step 3
Tenths column: all have 3 — move to hundredths
Step 4
Hundredths column: 0, 2, 0, 1 — so 0.300 and 0.309 are smaller; 0.320 is currently largest
Step 5
Compare 0.300 vs 0.309: thousandths 0 vs 9 → 0.300 < 0.309
Step 6
Order: 0.3, 0.309, 0.31, 0.32
Example 2 — Are 38.5 and 38.50 the same value?
Step 1
38.5 padded to 2 d.p. = 38.50 — trailing zeros don't change the value
Step 2
YES — 38.5 = 38.50
⚠ Watch out: Trailing zeros (after the decimal point, after the last non-zero digit) are fine to add for comparison. But do NOT add zeros to the left of a decimal without a placeholder: \(0.3 \neq 3.0\).
✓ Quick Check 1 — Padding and ordering with equal decimal places
Question 1 of 10
Ordering Decimals on a Number Line
A number line is a powerful visual tool. Numbers increase from LEFT to RIGHT. Plotting decimals on a number line confirms their order without any column comparisons.
Example 3 — Plot 0.2, 0.7, 0.45, 0.05 on a number line and write in order
Step 1
Draw a number line from 0 to 1 with tick marks every 0.1
Step 2
Mark each point: 0.05 (close to 0), 0.2 (just past first tick), 0.45 (nearly halfway), 0.7 (past halfway)
Step 3
Reading left to right: 0.05, 0.2, 0.45, 0.7
Example 4 — Is 0.35 closer to 0.3 or 0.4?
Step 1
0.35 is exactly halfway between 0.30 and 0.40
Step 2
Distance to 0.3: \(0.35 - 0.30 = 0.05\). Distance to 0.4: \(0.40 - 0.35 = 0.05\)
Step 3
0.35 is equidistant from both — it is the midpoint
Tip: When comparing decimals close together (like 0.309 vs 0.310), try zooming in on the number line between 0.30 and 0.32 so you can see the difference clearly.
✓ Quick Check 2 — Number line and plotting
Question 1 of 10
Mixed Numbers and Real-Life Ordering
In real life, you often need to order a mix of whole numbers and decimals, or decimals where the whole number parts differ. Always compare the whole number part first, then the decimal part.
Example 5 — Order prices £1.99, £2.10, £1.90, £2.09 cheapest to most expensive
Step 1
Compare whole number part: items with £1 are cheaper than £2 items
Step 2
£1.90 vs £1.99: tenths 9 = 9, hundredths 0 vs 9 → £1.90 < £1.99
Step 3
£2.09 vs £2.10: tenths 0 vs 1 → £2.09 < £2.10
Step 4
Order: £1.90, £1.99, £2.09, £2.10
Example 6 — Rank 100m times 10.42s, 10.24s, 10.4s, 10.04s fastest to slowest
Step 1
Pad to 2 d.p.: 10.42, 10.24, 10.40, 10.04
Step 2
Whole numbers all 10 — compare tenths: 4, 2, 4, 0
Step 3
10.04 (tenths = 0) is the fastest (smallest time)
Step 4
Then 10.24 (tenths = 2), then 10.40 and 10.42 (both tenths = 4)
Step 5
Compare 10.40 vs 10.42: hundredths 0 vs 2 → 10.40 < 10.42
Type your answers and click Check All. For ordered lists, write with commas (e.g. 0.1, 0.2, 0.3).
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Question
Answer
Result
1
Order from smallest: 0.5, 0.05, 0.55
2
Are 3.40 and 3.4 the same? (yes or no)
3
Order from largest (note 1.9 = 1.90): 1.9, 1.09, 1.90, 1.099
4
Which is smallest: 0.304, 0.34, 0.3, 0.043?
5
Order prices cheapest first: £4.50, £4.05, £4.55, £4.99
6
What is the midpoint between 0.3 and 0.5?
7
Order largest first: 2.1, 21, 0.21, 0.021
8
True or false: 0.309 > 0.31
9
Order from smallest: 0.6, 0.16, 0.61
10
True or false: 0.5 = 0.500
⚠ Things to Watch Out For
Not padding with zeros: Before ordering 0.3, 0.32, 0.309 — pad them: 0.300, 0.320, 0.309. Now compare digit by digit.
Longer decimal = larger value: FALSE. 0.3 is larger than 0.25 even though 0.25 has more digits. Always compare by place value, not length.
Ignoring the whole number part: When ordering 1.9, 2.1, 1.85 — always compare whole numbers first. 1.9 and 1.85 are both less than 2.1 regardless of decimal parts.
0.10 vs 0.1: These are equal. Trailing zeros after the last non-zero decimal digit don't change the value.
Mixing up ascending and descending: Ascending = smallest first (going UP). Descending = largest first (going DOWN). Read the question carefully.