![]() ![]() The last seven digits are meaningless – they imply a greater accuracy than is possible with the measurements. If you draw a circle, measure its diameter to be 168 mm and its circumference to be 527 mm, their quotient, representing, is 3.136904762. The accuracy of an answer is determined by the accuracy of the physical measurement on which the answer is based. Including more digits in an answer does not necessarily increase its accuracy. For example, if a sign was placed where the elevation was really 1000 m to the nearest meter, then the sign could read “1000 m (3280 ft)”. The signs could also be moved to different locations, where the number of meters was more exact. Or, the number of feet could be expressed with the same precision as the number of meters, as “914 m (2999 ft)”. The number of meters could be expressed in one significant figure, as “900 m (3000 ft)”. There are various ways to alter the signs. The standard would be almost indestructible in that there is essentially a limitless supply of feet to be used. That also renders the standard as not reproducible, because there could be many reproductions that were quite different from each other. The standard would be extremely variable – perhaps by a factor of 2. ![]() The standard would be very accessible, because wherever a measurement was needed, it would be very easy to find someone with feet. (b) If any person’s foot were to be used as a standard, “standard” would vary significantly depending on the person whose foot happened to be used most recently for a measurement. The standard could be reproducible – tracings or plaster casts could be made as secondary standards. The standard would not be indestructible – the foot would not last forever. The standard would be somewhat invariable if the person were an adult, but even then, due to swelling or injury, the length of the standard foot could change. A particular person’s foot would not be very accessible, since the person could not be at more than one place at a time. (a) Fundamental standards should be accessible, invariable, indestructible, and reproducible. CHAPTER 1: Introduction, Measurement, Estimating Answers to Questions 1. ![]()
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