A result can only be as precise as the least precise measurement behind it. A good conclusion states the value at that precision, gives the uncertainty, and says what the data can and cannot show.
This lesson is part of uncertainty and practical-data reasoning. It uses the spread idea from resolution versus spread.
What rule sets the number of significant figures?
Count the significant figures in each measured value. When you multiply or divide, the answer has the same number as the value with the fewest.
Worked examples
Density. A mass of 54.2 g (3 s.f.) and a volume of 20 cm³ (2 s.f.) give 54.2 ÷ 20 = 2.71 g/cm³. The volume has two significant figures, so write 2.7 g/cm³.
Speed. A distance of 1.50 m (3 s.f.) in a time of 2.3 s (2 s.f.) gives 1.50 ÷ 2.3 = 0.6522… The time has two significant figures, so write 0.65 m/s.
Area. A rectangle of 4.2 cm (2 s.f.) by 3.17 cm (3 s.f.) gives 13.314 cm². Write 13 cm².
What does a full conclusion look like?
Write three parts: the value, the uncertainty and the limit.
An original conclusion for the pendulum data: “The time for 20 swings is 28.5 ± 0.4 s. The spread of the four readings is larger than the stopwatch resolution, so the result is limited by reaction time. Four readings give only a rough estimate of the spread, so more readings would improve it.”
The mistake that costs marks
The common slip is to copy the calculator display, for example 0.652173913 m/s. Such digits claim a precision that a 2.3 s time cannot support.
| Answer | Verdict |
|---|---|
| “Speed = 0.652173913 m/s” | Wrong: far too many digits |
| “Speed = 0.65 m/s” | Right: matches the 2 s.f. of the time |
Another slip is giving a value with no uncertainty and no comment. Add both when a question asks for a conclusion.
Check yourself
A rectangle measures 4.2 cm by 3.17 cm. A student writes the area as 13.314 cm². Correct the answer and explain the change.
Answer
The length 4.2 cm has two significant figures and 3.17 cm has three. The answer should have two significant figures.
Area = 4.2 × 3.17 = 13.314, which is written as 13 cm².
The extra digits in 13.314 suggest a precision that the 4.2 cm measurement does not have.
What to study next
Test the whole section with the section practice set. The graph evidence and fair-comparison lab helps with stating conclusions from graphs.
If you want a teacher to review the wording of your conclusions, see online one-to-one Physics tuition. The mistake log and paper-error review tool helps you log repeat slips.