A quantity is defined by the relation

PHYSICS · Multi-part · A Level · Physics · Measurements and their errors · Measurements and their errors

Problem

A quantity

Z

is defined by the relation

Z=\dfrac{A+B}{C^{2}}

, where the measured values are:

A=(12.46\,\pm0.05)\,\text{cm}

B=(7.32\,\pm0.03)\,\text{cm}

and

C=(3.18\,\pm0.02)\,\text{cm}

. (i) Distinguish between absolute uncertainty and relative uncertainty, giving one example of each from the data above. (ii) Describe, in a logical sequence, the steps a student should follow to obtain the numerical value of

Z

together with its absolute uncertainty. (iii) Explain how the rules of significant figures would be applied to round off the final value of

Z

and its uncertainty.

Related theory

Precision & Reporting
Measurement Errors
Errors in measurement
Arithmetic operations and uncertainty propagation

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