Question

What, approximately, is the percent uncertainty for a measurement given as\({\bf{1}}{\bf{.57 }}{{\bf{m}}^{\bf{2}}}\)?

Short answer

The correct answer of percent uncertainty is 0.6%.

Step-by-step solution

Writing the given data

The uncertainty in measurement is defined as the variation of the values that are assigned to a particular quantity.

The data given is\({A_1} = 1.5{\rm{7 }}{{\rm{m}}^2}\).

The uncertainty in measurement is \({A_2} = 0.0{\rm{1 }}{m^2}\).

Writing the formula of percent error

The formula of percent error is

\(\Delta A = \frac{{{A_2}}}{{{A_1}}} \times 100\% \) … (i)

Calculating the percent uncertainty

From equation (i), the percent uncertainty is

\(\begin{aligned}{c}\Delta A = \frac{{0.01}}{{1.57}} \times 100\% \\ = 0.6369\% \\ \approx 0.6\% \end{aligned}\).

Thus, the final value of multiplication is 0.6%.