Question

Find the absolute and percent relative uncertainty and express each answer with a reasonable number of significant figures.

$$\begin{gathered} \mathrm{a})6.2\left(\pm 0.2\right)-4.1\left(\pm 0.1\right)=? \\ \mathrm{b})9.43\left(\pm 0.05\right)\times 0.016\left(0.001\right)=? \\ \mathrm{c})\left[6.2\left(\pm 0.2\right)-4.1\left(\pm 0.1\right)\right]÷9.43\left(\pm 0.05\right)=? \\ \mathrm{d})9.43\left(\pm 0.05\right)\times \left\{\left[6.2\left(\pm 0.2\right)\times {10}^{-3}\right]+4.1\left(\pm 0.1\right)\times {10}^{-3}\right\} \end{gathered}$$

Short answer

To calculate the absolute and percent relative uncertainty.

Step-by-step solution

To calculate absolute and percent relative uncertainty

$$\begin{gathered} \mathrm{Absolute}\mathrm{uncertainty}=3.12(\pm 0.05) \\ \mathrm{a})6.2\left(\pm 0.2\right)-4.1\left(\pm 0.1\right)=2.1\left(\pm 0.2\mathrm{or}\pm 11\%\right) \\ \mathrm{b})9.43\left(\pm 0.05\right)\times 0.016\left(0.001\right)=0.151\left(\pm 0.09\mathrm{or}\pm 6\%\right) \\ \mathrm{c})\left[6.2\left(\pm 0.2\right)-4.1\left(\pm 0.1\right)\right]÷9.43\left(\pm 0.05\right)=0.223\left(\pm 0.024\mathrm{or}\pm 11\%\right) \\ \mathrm{d})9.43\left(\pm 0.05\right)\times \left\{\left[6.2\left(\pm 0.2\right)\times {10}^{-3}\right]+4.1\left(\pm 0.1\right)\times {10}^{-3}\right\}=0.0971\left(\pm 0.0022\mathrm{or}\pm 2.2\%\right) \end{gathered}$$

To calculate the percent relative uncertainty

Percent relative uncertainty with formula (e represents the $\pm$value)

$=\sqrt{e_1^2+e_2^2+e_3^2}$

To obtain the absolute uncertainty

The following is the formula;

$\left(\mathrm{percent}\mathrm{relative}\mathrm{uncertainty}\right)/100\times \mathrm{the}\mathrm{value}\mathrm{of}\mathrm{a})2.1;\mathrm{b})0.151\mathrm{c})0.223\mathrm{d})0.0971$