Cambridge Lower Secondary · Grade 7 · Number & Calculation
Counting Sig Figs
0.00470 → 3 sig figs Leading zeros: ignored · Trailing zeros after decimal: count!
Estimation Trick
38.7 × 51.2 ≈ 40 × 50 = 2000 Round each value to 1 sig fig first
Error Interval
6.4 (1 d.p.) → 6.35 ≤ x < 6.45 Half a unit below and above the rounded value
Try it now! Type a number to see its significant digits highlighted:
What you'll learn:
What significant figures are and how to count them
Rounding to 1, 2, and 3 significant figures
The difference between decimal places and significant figures
Using 1 sig fig to estimate calculations quickly
Upper and lower bounds (error intervals)
Checking if an answer is reasonable
📖 Learn: Significant Figures & Estimation
Part 1: What Are Significant Figures?
A significant figure (s.f.) is any digit that carries meaning contributing to the precision of a number.
📌 The Rules for Counting:
1. All non-zero digits are significant. e.g. 4, 7, 2 in 472 → 3 s.f.
2. Zeros between non-zero digits are significant. e.g. 407 → 3 s.f.
3. Leading zeros (before the first non-zero digit) are NOT significant. e.g. 0.0047 → 2 s.f.
4. Trailing zeros after a decimal point ARE significant. e.g. 3.400 → 4 s.f.
5. Trailing zeros in a whole number are ambiguous unless a decimal point is written. e.g. 5000 (1 s.f.?), 5000. (4 s.f.)
💡 Find the first non-zero digit — that is always your 1st significant figure. Count every digit after it (including zeros) as the next significant figures.
Part 2: Rounding to n Significant Figures
Steps to round to n significant figures:
Step 1: Find the n-th significant figure.
Step 2: Look at the digit immediately after it.
Step 3: If that digit is ≥ 5, round up. If < 5, round down (keep the same).
Step 4: Replace all digits after the n-th s.f. with zeros (for whole numbers) or drop them (after a decimal point).
Examples:
72 468 to 1 s.f.: first digit is 7, next is 2 (round down) → 70 000
72 468 to 2 s.f.: second digit is 2, next is 4 (round down) → 72 000
72 468 to 3 s.f.: third digit is 4, next is 6 (round up) → 72 500
0.003 862 to 2 s.f.: 1st s.f. = 3, 2nd s.f. = 8, next = 6 (round up) → 0.0039
💡 When rounding a whole number, the placeholder zeros keep the magnitude correct — don't drop them!
Part 3: Decimal Places vs Significant Figures
These are different ways to express precision:
Number
To 2 d.p.
To 2 s.f.
3.8472
3.85
3.8
0.004 621
0.00
0.0046
148.35
148.35
150
💡 d.p. counts digits after the decimal point. s.f. counts meaningful digits from the first non-zero digit. They can give very different answers for small decimals!
💡 The lower bound is included (≤) but the upper bound is excluded (<) because at exactly 4.75 you'd round up to 4.8, not down to 4.7.
💡 Worked Examples
Example 1: Counting Significant Figures
How many significant figures does each number have?
a) 30 400 → digits: 3, 0, 4, 0, 0 · sandwiched zero (between 3 and 4) counts · trailing zeros in whole number are ambiguous but here we read 3 s.f. Answer: 3 s.f.
b) 0.005 07 → leading zeros (0.00) don't count · 5, 0, 7 all count · Answer: 3 s.f.
c) 1.900 → digits: 1, 9, 0, 0 · all count (trailing zeros after decimal point ARE significant) · Answer: 4 s.f.
d) 0.0600 → leading zeros ignored · 6, 0, 0 all count · Answer: 3 s.f.
📋 Start from the first non-zero digit and count everything after it (including zeros).