Express the answer to the above operation in the correct number of significant W

Question

Express the answer to the above operation in the correct number of significant Why did you round off your answer to the tenth place? Perform the following operation and report your answer in the proper number of significant figures according to the uncertainty rules. 0.003427 (plusminus 0.000005 cg)/0.03611 (plusminus 0.00003 mu L) = 0.094904459 Find % uncertainty in 0.003427 cg. Find % uncertainty in 0.03611 mu L. Find % uncertainty in the answer to the operation given above. Find the absolute uncertainty in the answer to the operation given above. Express the answer to the operation given above in the correct number of significant figures.

Explanation / Answer

Note that since we have 0.000005 and 0.00003; both having only 1 siginificant figure; then all answers must include only 1 significant figure.

a.

The % uncertainty has the next formula:

% uncertainty = (range) / (actual value) *100%

% uncertainty = (0.000005) / (0.003427) *100% = 0.145900 % to the nearest 1 sig fig --> 0.1 %

b.

Use same formula

% uncertainty = (range) / (actual value) *100%

% uncertainty = (0.00003) / (0.03611) *100% = 0.0830%

round to the to the nearest 1 sig fig --> 0.08 %

c.

The uncertainty of 2 uncertain values is given by

uncertainty = sqrt(value^2 + value^2)

Note that we must use complete values, not rounded values

uncertainty% = sqrt(0.145900^2 + 0.0830^2) = 0.16785 %

uncertainty (1 sig fig) = 0.16785 % --> 0.2 %

d.

For the abs uncertainty, just multiply actual uncertainty by the final product

final product = 0.094904459

uncertainty = 0.16785 %

Uncertainty Vakue = 0.16785% / 100% *0.094904459 = 0.000159297134

round up to 1 sig fig.

0.00007878 --> 0.0002 cg/uL

FINAL NOTE: you used the values in a and b rounded to 1 sig fig for the value in "C". Avoid this since the values should be used complete (i.e. not rounded) thats why we have that slight difference

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