Mathematics • Year 10 • Unit 1 • Lesson 12
Significant Figures — Skill Drill
Build fluency with the four rules from Lesson 12: non-zero digits always count, sandwiched zeros always count, leading zeros never count, and trailing zeros count only when a decimal point is present. Then round confidently to a given number of significant figures.
1. I do — fully worked example
Read every step. Each one has a short reason on the right so you can see why, not just what.
Problem. How many significant figures does 0.00340 have, and what is it rounded to 2 significant figures?
Step 1 — Apply Rule 3 (leading zeros).
0.003 40 — the two zeros before the 3 are LEADING zeros.
Reason: leading zeros are never significant — they only mark the place value.
Step 2 — Apply Rule 1 (non-zero digits).
3 and 4 are non-zero → both significant.
Reason: all non-zero digits are always significant.
Step 3 — Apply Rule 4 (trailing zero with a decimal point).
The final 0 sits after the decimal point → significant.
Reason: trailing zeros are significant only if there is a decimal point. There is one here, so the 0 counts.
Step 4 — Count the significant figures.
Significant digits: 3, 4, 0 → 3 sig figs.
Step 5 — Round to 2 sig figs.
First two sig figs are 3 and 4. Next digit is 0, which is < 5, so 4 stays. → 0.0034.
Answer: 0.00340 has 3 significant figures. Rounded to 2 sig figs it is 0.0034.
2. We do — fill in the missing steps
Same structure as Section 1, but with the working faded. Fill in each blank line. 4 marks
Problem. How many significant figures does 0.004030 have, and what is it rounded to 2 significant figures?
Step 1 — Identify the leading zeros (Rule 3). The zeros before the 4 are __________ zeros and are __________ (never / always) significant.
Step 2 — Identify the non-zero digits (Rule 1). The non-zero digits here are __________ and __________, both of which are __________ (significant / not significant).
Step 3 — Identify the sandwiched zero (Rule 2). The 0 between the 4 and the 3 is a __________ zero and is __________ (always / never) significant.
Step 4 — Identify the trailing zero (Rule 4). The final 0 sits after the decimal point, so it is __________ (significant / not significant).
Step 5 — Count. The number of significant figures is __________.
Step 6 — Round to 2 sig figs. The first 2 sig figs are __________ and __________. The next digit is __________, which is less than 5, so the kept digit stays the same. Rounded value = ______________.
3. You do — independent practice
Show your working in the space under each problem. The first four are foundation. The middle two are standard. The last two are extension.
Foundation — count the sig figs
3.1 How many significant figures in 0.00560? 1 mark
3.2 How many significant figures in 5008? 1 mark
3.3 How many significant figures in 100. (the decimal point is part of the number)? 1 mark
3.4 How many significant figures in 4.50 × 10³ (a measurement in scientific notation)? 1 mark
Standard — round to a stated precision
3.5 Round 6.549 to 2 significant figures. Show the digit you used to decide. 2 marks
3.6 Round 96,450 to 3 significant figures. Show the digit you used to decide. 2 marks
Extension — push your thinking
3.7 Round 2.995 to 3 significant figures. (Watch for the cascading round-up.) 3 marks
3.8 A student writes "450 has 3 significant figures". Their friend writes "450 has 2 significant figures". Both can be defended. Explain why, and show how to write each version unambiguously using scientific notation. 2 marks
How did this worksheet feel?
What I'll revisit before next class:
Section 2 — We do (faded 0.004030)
Step 1: leading zeros, never significant.
Step 2: non-zero digits 4 and 3, both significant.
Step 3: sandwiched zero, always significant.
Step 4: trailing zero after a decimal point → significant.
Step 5: total = 4 sig figs (4, 0, 3, 0).
Step 6: first 2 sig figs are 4 and 0. Next digit is 3, less than 5, so the kept digit stays. Rounded value = 0.0040.
3.1 — 0.00560
Leading zeros not significant; 5 and 6 are non-zero; trailing 0 is after the decimal point so significant. → 3 sig figs.
3.2 — 5008
5 and 8 are non-zero; the two 0s are sandwiched between non-zero digits and are always significant. → 4 sig figs.
3.3 — 100.
The decimal point makes the trailing zeros significant. → 3 sig figs.
3.4 — 4.50 × 10³
In scientific notation, every digit of the mantissa is significant. 4, 5, 0 → 3 sig figs.
3.5 — Round 6.549 to 2 sig figs
First 2 sig figs are 6 and 5. The next digit is 4, which is < 5, so the 5 stays unchanged. → 6.5.
3.6 — Round 96,450 to 3 sig figs
First 3 sig figs are 9, 6, 4. The next digit is 5, which rounds the 4 up to 5. Replace remaining digits with zeros. → 96,500.
3.7 — Round 2.995 to 3 sig figs (cascade)
First 3 sig figs are 2, 9, 9. Next digit is 5 → round 9 up. But 9 + 1 = 10, so we carry: the second 9 becomes 0 and the previous 9 also becomes 10 → carry again. Result: 3.00 (we keep the trailing 0 because that's what shows 3 sig figs).
The trailing 0 is essential — "3" alone would only be 1 sig fig.
3.8 — Why 450 is ambiguous
Without a decimal point, the trailing 0 in 450 might be a real measured digit or just a placeholder. Both readings are defensible.
3 sig figs: write 450. or 4.50 × 10².
2 sig figs: write 4.5 × 10².
Scientific notation resolves the ambiguity by making every digit in the mantissa significant.