The first significant figure is the first non-zero digit, reading left to right. Leading zeros are never significant.

The Cambridge method: round every single number in the calculation to 1 significant figure before doing any arithmetic — not after.

Example: estimate $\dfrac{38.7 \times 5.14}{0.198}$.

1. Round each number: $38.7 \to 40$, $5.14 \to 5$, $0.198 \to 0.2$.
2. Substitute: $\dfrac{40 \times 5}{0.2}$.
3. Numerator: $40 \times 5 = 200$.
4. Divide by $0.2$ (same as multiplying by $5$): $200 \div 0.2 = 1000$.

Beyond estimating, you also need to round final answers to whatever accuracy a question specifies. Look at the digit immediately after the place you're rounding to: if it's $5$ or more, round up; otherwise, round down.

Example (a): round $5764$ to the nearest thousand. The digit after the thousands place is $7$, so round up: $6000$.

Example (b): round $0.04763$ to 2 significant figures. The first two significant figures are $4$ and $7$; the next digit is $6$, so round up: $0.048$.

The same rule applies — round everything to 1 s.f. first, then follow BIDMAS as normal.

Example: estimate $\sqrt{99.2} + 21.6 \times 0.48$.

1. Round: $99.2 \to 100$, $21.6 \to 20$, $0.48 \to 0.5$.
2. Substitute: $\sqrt{100} + 20 \times 0.5$.
3. $\sqrt{100} = 10$ and $20 \times 0.5 = 10$.
4. Add: $10 + 10 = 20$.

Estimation questions are testing a specific skill — checking that an answer is a sensible size — not testing whether you can get the most accurate possible value. If you were allowed to calculate exactly and round the final answer, you'd never actually demonstrate that you can spot a wildly wrong calculator answer (e.g. from a mistyped bracket) using quick mental arithmetic. That's precisely why examiners can tell from your working whether you rounded first: the two methods usually give visibly different numbers, since rounding early loses some accuracy on purpose in exchange for speed.

Example: the exact value of $\dfrac{38.7 \times 5.14}{0.198}$ is $1004.3\ldots$, close to — but not identical to — the estimate of $1000$ found earlier by rounding first. Both are "correct" for their own purpose: the exact value for accuracy, and $1000$ for demonstrating the estimation method the question actually asked for.

• Calculating exactly first, then rounding — this doesn't demonstrate the estimation method the mark scheme wants.
• Treating leading zeros as significant, which shifts the rounded value to the wrong size entirely.
• Rounding down when the next digit is $5$ or more — e.g. $65$ rounds to $70$, not $60$.