Question

A student cut a leaf into rectangles 50mm x 30mm. Measurements were made using a ruler (1mm graduations). The student calculated the area of the leaf. What is the percentage uncertainty for the calculated area?

Answer 1

Solution:

Percentage uncertainty for the calculated area:

$\epsilon=\frac{\Delta{}A}{A}100\%$

Area of the leaf:

$A=a\cdot{}b$

Absolute uncertainty:

$\Delta{}A\approx{}dA=A'_ada+A'_bdb=b\Delta{}a+a\Delta{}b$

Then:

$\epsilon=\frac{b\Delta{}a+a\Delta{}b}{ab}100\%=(\frac{\Delta{}a}{a}+\frac{\Delta{}b}{b})100\%$

Measurements were made using a ruler with 1mm graduations. Therefore:

$\Delta{}a=\Delta{}b=0.5 mm.$

Let's calculate:

$\epsilon=(\frac{0.5}{50}+\frac{0.5}{30})100\%\approx3$

Answer: 3%