Answer:
3.5%
Explanation:
You want the percent error in a measured value of 4.16 g/cm³ in relation to a handbook value of 4.018 g/cm³.
Percent error
The percentage error is calculated as ...
% error = ((measured) - (actual))/actual × 100%
= (4.16 -4.018)/4.018 × 100%
= 0.142/4.018 × 100% ≈ 3.5%
Significant figures
The given numbers, 4.16 and 4.018 have 3 and 4 significant figures, respectively. Their difference will have 2 significant decimal places, as does 4.16, so should be considered to be 0.14. This value has 2 significant figures, so the final answer will have 2 significant figures.
You will note that we kept all of the digits available throughout the computation, rounding to 2 significant figures only at the end.
You will also note that taking differences of numbers of approximately the same value can result in a loss of significant figures.