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
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.