Question

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

Short answer

The correct answer of percent uncertainty is 0.6%.

Step-by-step solution

Step 1. 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 $A_2=0.01m^2$.

Writing the formula of percent error

The formula of percent error is

$\Delta A=\frac{A_2}{A_1}\times 100\%\dots \left(i\right)$

Step 3. Calculating the percent uncertainty

From equation (i), the percent uncertainty is

$\begin{array}{c}\Delta A=\frac{0.01}{1.57}\times 100\%\\ =0.6369\%\\ \approx 0.6\%\end{array}$

Thus, the final value of multiplication is0.6%.