Equal Decimal Places — Padding with Trailing Zeros
You met comparing and ordering decimals briefly in Lesson 1.2 — Comparing and Ordering Numbers. Here we go deeper: before ordering decimals, rewrite them all with the same number of decimal places by adding trailing zeros. A trailing zero after the last significant digit does NOT change the value (\(0.5 = 0.50 = 0.500\)) but makes comparisons column-by-column much easier.
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.