Significant Figures
Significant figures are all certain digits in a measured value plus the first uncertain digit; leading zeros are not significant, embedded zeros are significant, and trailing zeros are significant when decimal notation makes them explicit.
Why this shows up in the exam
Reporting laboratory measurements · Reading specifications · Comparing precision of recorded values
Learn the idea
Significant figures communicate the resolution justified by a measured numeral, including meaningful zeros. Digits are evidence: leading zeros only locate the decimal point, while captive and explicitly written trailing decimal zeros can carry measurement information.
🧠 Memory hook: Leading zeros locate; captive zeros count; written decimal tails can count.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- N = a x 10ⁿ with 1 <= |a| < 10 — scientific notation exposes significant digits
- relative rounding scale roughly 0.5 x 10^(place)/|N| — scale of last-place rounding uncertainty
How to approach it
- 1Rewrite ambiguously in scientific notation
- 2Count from the first nonzero digit
- 3Preserve explicitly measured trailing zeros
Common slip-ups that cost marks
- •Counting leading zeros
- •Dropping significant trailing decimal zeros
- •Inferring significance from an ambiguous integer without notation
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A quantity Q is defined as Q = force^1 / speed^2. Which dimensional formula represents Q?
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