Comprehension When numbers having uncertainties or errors are used to compute other numbers, the...

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Comprehension
When numbers having uncertainties or errors are used to compute other numbers, these will be uncertain. It is especially important to understand this when a number obtained from measurements is to be compared with a value obtained from theoretical prediction. Assume a student wants to verify the value of \( \pi \) as the ratio of circumference to diameter of a circle. The correct value of ten digits is 3.141592654 . He draws a circle and measures its diameter and circumference to its nearest millimeter obtaining the values \( 135 \mathrm{~mm} \) and \( 424 \mathrm{~mm} \), respectively. Using a calculator he finds \( \pi=3.140740741 \).
If diameter and circumference both have an error of \( 1 \% \), what is the error in value of \( \pi \) ?
(a) \( 2 \% \)
(b) \( 1 \% \)
(c) \( 0.5 \% \)
(d) \( 0 \% \)
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