You measure a square plate’s side as L = 10.0 ± 0.1 cm (1% uncertainty) and compute the area A = L². What is the uncertainty of the area?

Exactly 0.1 cm², matching the ruler

About 1%, squaring changes nothing

Physics I / Propagation of Errors

Practice question · Multiple choice

You measure a square plate’s side as $L = 10.0 \pm 0.1$ cm (1% uncertainty) and compute the area $A = L^{2}$ . What is the uncertainty of the area?

Hints

Perturb it: compute $(10.1)^{2}$ and compare with $10.0^{2}$ in percent.
For $A = L^{n}$ , the relative errors obey $\frac{\Delta A}{A} \approx n\frac{\Delta L}{L}$ .

Show the answer

C. About 2%: powers multiply relative error

Why

$(10.1)^2 = 102.01$ , about 2% above 100. Powers are error amplifiers: exponent × relative error. This is why a period measured to 1% gives $g$ (which involves $T^{2}$ ) only to 2%, and why precise exponents demand very precise inputs.

Read the lesson: Propagation of Errors →

Practise Propagation of Errors

The app has 7 more questions on this lesson, and keeps your place in the course. Physics I is free to start.

Start Physics I free Get it onGoogle Play

You measure a square plate’s side as L=10.0±0.1L = 10.0 \pm 0.1L=10.0±0.1 cm (1% uncertainty) and compute the area A=L2A = L^{2}A=L2. What is the uncertainty of the area?

Practise Propagation of Errors

More questions on Propagation of Errors

You measure a square plate’s side as $L = 10.0 \pm 0.1$ cm (1% uncertainty) and compute the area $A = L^{2}$ . What is the uncertainty of the area?