Decimal places count digits from the decimal point, so 0.04 has 2 decimal places regardless of the leading zeros. Significant figures count from the first non-zero digit, so 0.04 has only 1 significant figure. The two rules give different answers for the same number, and mixing them up is one of the most common ways students lose marks in O-Level E-Maths, especially with small decimals.
Most students learn decimal places first, because it feels intuitive: count how many digits sit after the decimal point. Significant figures get introduced later and feel like a variation on the same idea, so students keep applying the decimal-place rule by habit even when a question specifically asks for significant figures (sf). Rounding only applies to a decimal expansion in the first place, which is why every number you round here is a rational number, not an irrational one.
The two rules only agree by coincidence. For a number like 12.6, rounding to 1 decimal place and rounding to 3 significant figures happen to give the same digits. But the moment a number has leading zeros (anything starting 0.0...), the two rules pull apart sharply, and that is exactly where marks get lost.
Decimal places (dp)
Count digits after the decimal point. Leading zeros still count as decimal places.
Significant figures (sf)
Start counting from the first non-zero digit. Leading zeros are never significant.
Zeros between digits
Always significant, for example the 0 in 0.4052 (once counting has started)
Trailing zeros after the point
Significant, for example the 0 in 0.410
The exam default in Singapore O-Level E-Maths is 3 significant figures unless the question tells you otherwise. Two common exceptions: bearings and other angles round to 1 decimal place, and money always rounds to 2 decimal places (the nearest cent). Read the question carefully: "correct to 3 sf" and "correct to 3 dp" are not interchangeable instructions.
Round 0.04052 to (a) 1 sf, (b) 2 sf, (c) 3 sf, (d) 2 dp, (e) 4 dp, and compare.
Solution: significant figures
0.04.0.041.0.0405.Solution: decimal places
0.04.0.0405.The step students get wrong
0.04052 rounded to 2 significant figures is 0.041, not 0.04. Students see "0.04" appear correctly as the 2 dp answer and mistake it for the 2 sf answer too, because both start counting-sounding similar. They are not the same instruction: 2 dp keeps two digits after the point (0.04), while 2 sf keeps the first two non-zero-starting digits (4 and 0), and the digit after those two (a 5, pulled up further by the 2 that follows it) forces a round-up to 0.041.
Calculate (8.45 ÷ 3.7)², giving your answer correct to 3 significant figures. Compare keeping the full calculator value throughout against rounding the division result to 3 sf before squaring.
Correct method: round only at the end
8.45 ÷ 3.7 = 2.283783... (repeating). Keep this full value in the calculator, do not round yet.2.283783...² = 5.215668...5.22.Premature rounding: what goes wrong
8.45 ÷ 3.7 = 2.283783... rounded to 3 sf gives 2.28.2.28² = 5.1984.5.20. This is wrong. The correct answer is 5.22. Rounding the intermediate step threw away exactly the information that decided the third significant figure.Exam habit: use your calculator's Answer (Ans) key, or the memory function, to carry the exact value from one line of working to the next. Only round the number you actually write as your final answer. This matters even more when a question chains several steps together, such as finding an unrounded angle before using it in a further calculation. See checking your calculator is in the right mode for the companion habit of catching a degree-versus-radian slip before it wrecks a whole working.
The three zero rules cover almost every case that appears in E-Maths questions:
This is also the moment to be comfortable converting into standard form: writing 0.04052 as 4.052 × 10⁻² makes the significant figures obvious, because every digit written down in the coefficient is automatically significant. If you are unsure how many sf a small decimal has, converting to standard form first removes the guesswork.
What if the question just says "round your answer" with no instruction?
Use the O-Level default: 3 significant figures, unless the answer is an angle (round to 1 decimal place) or a money amount (round to 2 decimal places, the nearest cent). If earlier parts of the same question gave a specific instruction, that instruction usually carries through the rest of the question too.
Do trailing zeros before the decimal point count as significant, like in 200?
This is genuinely ambiguous without more context, which is why exam questions rarely ask you to state the sf of a whole number like 200 in isolation. If it matters, write it in standard form: 2 × 10² has 1 sf, 2.00 × 10² has 3 sf. Standard form removes the ambiguity completely.
Why does the exam prefer significant figures over decimal places for most answers?
Significant figures scale sensibly across very large and very small numbers, so the same rounding instruction (3 sf) makes sense whether the answer is 0.0000452 or 45200, numbers that in real contexts are often written with metric prefixes instead of long strings of zeros. Decimal places would need a different instruction for every size of number, which is why dp is mostly reserved for angles and money, where the scale of the answer is predictable.
I rounded correctly but still lost a mark. What happened?
Check whether you rounded too early in your working, not just at the final line. Examiners specifically penalise premature rounding because it can shift the final significant figure, exactly as in worked example 2 above. Keep full calculator values until the line where you state your final answer.
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