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Approximation
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The special number pi is about 3, but using 3 in calculations is not very accurate. Using 3·14 instead is more useful, whilst scientific calculators are usually pre-programmed with pi as 3·14159265359
Let's use these different approximations of pi to calculate the circumference of a circle, diameter d=10 cm.
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The circumference c is given by: c = pi × d.
1. c = pi × d = 3 × 10 = 30 cm
2. c = pi × d = 3·14 × 10 = 31·4 cm
3. c = pi × d = 3·14159265359 × 10 = 31·4159265359 cm
(1) is about right; (2) is quite accurate (nearest millimetre); whereas (3) is excessively accurate: do we need an answer to the nearest billionth of a cm?!
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Vital Question: how accurate was the 10 cm diameter?
Did we assume it was perfect, or to the nearest cm or mm? |
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