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Multiple Choice
Determine the absolute and relative uncertainty to the following multiplication and division problem. 1.12(±0.01) x 0.546 (±0.01) / 3.12(±0.02) x 1.12 (0.03)
A
0.003 absolute; 0.01 relative
B
0.03 absolute; 0.006 relative
C
0.006 absolute; 0.03 relative
D
0.006 absolute; 0.01 relative
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1
Identify the given values and their uncertainties: 1.12(±0.01), 0.546(±0.01), 3.12(±0.02), and 1.12(±0.03).
For multiplication and division, the relative uncertainties are added. Calculate the relative uncertainty for each value by dividing the absolute uncertainty by the measured value.
Add the relative uncertainties of all the values involved in the multiplication and division to find the total relative uncertainty.
Multiply the total relative uncertainty by the calculated result of the multiplication and division to find the absolute uncertainty.
Express the final result with its absolute and relative uncertainties, ensuring the significant figures are consistent with the precision of the measurements.