Question

What, approximately, is the percent uncertainty for a measurement given as$1.57{\mathrm{m}}^2$?

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 $A_1=1.57{\mathrm{m}}^2$.

The uncertainty in measurement is $A_2=0.01{\mathrm{m}}^2$.

Writing the formula of percent error

The formula of percent error is:

$∆A=\frac{A_2}{A_1}\times 100\%$ ....... (i)

Calculating the percent uncertainty

From equation (i), the percent uncertainty is

$$\begin{gathered} ∆A=\frac{0.01}{1.57}\times 100\% \\ ∆A=0.6369\% \\ ∆A\approx 0.6\% \end{gathered}$$

Thus, the final value of multiplication is 0.6%.