Significant Figures — Lab Measurement Math (Worked Example)

Easy

Problem

In a lab you measure a plate as 12.5 cm by 8.24 cm. (a) What is its area, with correct significant figures? (b) You also weigh two samples: 15.2 g and 3.45 g. What is their total mass, with correct significant figures?

Given

length = 12.5 cm (3 s.f.)
width = 8.24 cm (3 s.f.)
masses = 15.2 g and 3.45 g

Find

Area and total mass rounded per sig-fig rules.

Principle

A result is only as precise as its weakest input: multiplication follows fewest significant figures; addition follows fewest decimal places.

Formula

\text{Area} = l \times w

Area = l × w (fewest s.f.); sum rounded to fewest decimal places

Solution

Raw area: $12.5 \times 8.24 = 103.0\ \mathrm{cm^2}$
Both inputs have 3 significant figures → keep 3: $103\ \mathrm{cm^2}$
Raw sum: $15.2 + 3.45 = 18.65\ \mathrm{g}$
15.2 limits us to one decimal place → $18.7\ \mathrm{g}$

Area = 103 cm²; total mass = 18.7 g

Unit check

cm × cm = cm²; g + g = g. Units are straightforward here — the lesson is precision, not dimensions.

What this means physically

Writing 103.0 cm² would claim precision you never measured, and 18.65 g pretends the scale knew hundredths it didn't. Sig figs keep your reported precision honest — a core lab skill.

Common mistake

Applying the multiplication rule to addition. 15.2 + 3.45 → 18.7 is decided by decimal places (tenths), not by counting 3 vs 3 significant figures.