PSLE Mathematics Learning Guide · Guide 42
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A longer decimal is not automatically larger. 4.9 is greater than 4.75 even though 4.75 has more digits. The reason is place value: 4.9 = 4.90, and ninety hundredths is greater than seventy-five hundredths.
This guide uses one habit: align the decimal points, compare the highest place first, write trailing zeros when they make the places visible, and stop at the first place where the numbers differ.
Guide 19 develops decimal operations. This page owns the more specific skill of decimal magnitude—deciding which decimal is greater, smaller or equal before arithmetic begins.
The MOE Primary Mathematics syllabus updated October 2025 provides curriculum context. All examples are original eduKate teaching material.
Compare whole-number parts first
Compare 6.42 and 5.987.
The whole-number parts are 6 and 5. Since 6 > 5, 6.42 > 5.987. No decimal-place comparison is needed.
The first place where the values differ already decides the order.
If wholes match, compare tenths
Compare 3.7 and 3.64.
Write 3.7 as 3.70 if helpful. Tenths are 7 and 6. Therefore 3.7 > 3.64.
If tenths match, move to hundredths
Compare 8.53 and 8.57.
Whole parts both 8. Tenths both 5. Hundredths are 3 and 7. Therefore 8.53 < 8.57.
Trailing zeros do not change a decimal’s value
2.5 = 2.50 = 2.500.
The zeros add no new quantity because they occupy places beyond the final non-zero digit.
This makes comparisons easier:
2.5 vs 2.47 becomes 2.50 vs 2.47, so 2.50 is larger.
A zero immediately after the decimal point can matter greatly
0.8 = eight tenths.
0.08 = eight hundredths.
So 0.8 > 0.08.
The zeros are not decorative here. They change the place occupied by the 8.
The same digits can form very different values
4.26, 4.062 and 4.602 use similar digits but place them differently.
Ordering from smallest to largest:
4.062 < 4.26 < 4.602.
Use number-line position as a meaning check
0.4 lies between 0 and 1, four tenths of the way across.
0.35 lies below 0.4 because 0.35 = 35 hundredths while 0.4 = 40 hundredths.
0.405 lies slightly above 0.4 because it adds five thousandths.
Benchmarks can speed comparison
0.49 is less than 0.5.
0.503 is greater than 0.5.
Therefore 0.503 > 0.49 without aligning every digit.
Benchmarks such as 0, 0.5, 1 and whole numbers can make size visible.
Stay within the primary-number boundary
This guide compares non-negative decimals used in Primary Mathematics. Negative decimal ordering belongs to later integer and rational-number work and is not required here.
Order several decimals systematically
Order 2.4, 2.04, 2.44 and 2.404 from smallest to largest.
Write aligned forms:
2.400
2.040
2.440
2.404
Order: 2.04 < 2.4 < 2.404 < 2.44.
Money makes hundredths visible
$4.05 is 4 dollars 5 cents.
$4.50 is 4 dollars 50 cents.
Therefore $4.50 > $4.05.
The final zero in $4.50 is often written to show cents, but the numerical value is the same as 4.5.
Measurement decimals still depend on units
1.2 m and 95 cm cannot be compared by decimal digits alone because the units differ.
Convert 1.2 m = 120 cm. Then 120 cm > 95 cm.
Use Guide 2 when unit alignment is required before comparison.
Main worked workshop: sixteen original decimal comparisons
1.
Compare 5.6 and 5.38.
Answer: 5.6 > 5.38.
2.
Compare 7.08 and 7.8.
Answer: 7.08 < 7.8.
3.
Compare 0.45 and 0.405.
Answer: 0.45 > 0.405.
4.
Compare 3.500 and 3.5.
Answer: equal.
5.
Compare 9.099 and 9.1.
Answer: 9.099 < 9.1.
6.
Order 1.2, 1.02, 1.22.
Answer: 1.02 < 1.2 < 1.22.
7.
Order 0.7, 0.07, 0.707.
Answer: 0.07 < 0.7 < 0.707.
8.
Order 4.04, 4.004, 4.4, 4.044.
Answer: 4.004 < 4.04 < 4.044 < 4.4.
9.
A learner says 0.83 < 0.805 because 83 < 805.
Repair: align as 0.830 and 0.805; 830 thousandths is larger.
10.
A learner says 6.5 < 6.42 because 5 < 42.
Repair: compare tenths first: 5 tenths > 4 tenths.
11.
Which is closer to 1: 0.96 or 0.905?
Answer: 0.96.
12.
Which is larger: 2.999 or 3.0?
Answer: 3.0.
13.
Insert 0.6 into correct position: 0.58, 0.602.
Answer: 0.58 < 0.6 < 0.602.
14.
Compare $3.08 and $3.80.
Answer: $3.80 > $3.08.
15.
Compare 1.05 m and 98 cm.
Answer: 1.05 m = 105 cm, so 1.05 m is larger.
16.
Which is smallest: 5.505, 5.55, 5.055?
Answer: 5.055.
Useful decimal equalities
0.5 = 0.50 = 0.500.
2 = 2.0 = 2.00.
0.25 = 25/100 = 1/4.
These connections can provide independent checks across representations.
Common decimal-ordering errors
Error 1: treat more digits as larger.
Error 2: ignore the decimal point and compare whole digit strings.
Error 3: assume 0.8 < 0.75 because 8 < 75.
Error 4: treat trailing zeros as increasing value.
Error 5: compare measurements without aligning units.
Independent transfer check
- Compare 4.7 and 4.68.
- Compare 0.09 and 0.9.
- Compare 6.040 and 6.04.
- Order 2.03, 2.3, 2.033, 2.003.
- Order 0.49, 0.5, 0.501.
- Explain why 7.2 is larger than 7.19.
- Explain why adding trailing zeros does not change value.
- Explain why 1.2 m and 95 cm must be converted before comparison.
Independent-check answers
1. 4.7 > 4.68.
2. 0.09 < 0.9.
3. equal.
4. 2.003 < 2.03 < 2.033 < 2.3.
5. 0.49 < 0.5 < 0.501.
6. 7.2 = 7.20, and 20 hundredths > 19 hundredths.
7. The added zeros occupy smaller places but add zero quantity.
8. The numerals use different units, so their sizes are not directly comparable until expressed on the same scale.
Parent and tutor guide
Ask the learner to rewrite decimals with aligned place columns rather than saying “ignore the point”. Place value should stay visible.
Use deliberate traps such as 0.8 versus 0.75 and 3.07 versus 3.7. Then ask for a number between two decimals to test number-line understanding.
The learner’s final card
Are the decimal points aligned? Which highest place differs first? Would trailing zeros make the comparison clearer? Are the units already the same? Where would each number sit on a number line?
Continue through Batch 11
Use Guide 41. Continue with Guide 43: Length Problems in Mixed Units and Guide 44: Mass Problems in Kilograms and Grams.
Return to the PSLE Learning Guide Mathematics route.
Sources and boundaries
MOE Primary Mathematics syllabus, updated October 2025; SEAB 2026 PSLE formats.
All examples and solutions are original eduKate teaching material. This guide focuses on cumulative decimal magnitude and ordering relevant to PSLE preparation.