Question

Rewrite the number 3.123 56 (±0.167 89%) in the forms (a) number (± absolute uncertainty) and (b) number (± percent relative uncertainty) with an appropriate number of digits.

Short answer

$\mathrm{Absolute}\mathrm{uncertainty}=3.12\left(\pm 0.005\right)\mathrm{and}\%\mathrm{relative}\mathrm{uncertainty}=0.168\%$

Step-by-step solution

To solve for:

⦁ Number $\pm$absolute uncertainty =?

⦁ Number$\pm$ percentage relative uncertainty =?

Calculation of absolute uncertainty

Given information:

3.12356$\left(\pm 0.16789\%\right)$

⦁ To solve for the absolute uncertainty as shown below:

$$\begin{gathered} \mathrm{absolute}\mathrm{uncertainty}=3.12356\times 0.16789\% \\ \hspace{0.17em}=3.12356\times \frac{0.16789}{100} \\ =0.00524415 \\ \mathrm{Absolute}\mathrm{uncertainty}=3.12(\pm 0.005) \end{gathered}$$

Calculation of percentage relative uncertainty

b) To solve the percentage relative uncertainty as shown:

% relative uncertainty = 0.16789%
% relative uncertainty = 0.168%

Therefore, the $\mathrm{Absolute}\mathrm{uncertainty}=3.12\left(\pm 0.005\right)$and$\%\mathrm{relative}\mathrm{uncertainty}=0.168\%$