
Approximation

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 preprogrammed with pi as 3·14159265359
Let's use these different approximations of pi to calculate the circumference of a circle, diameter d=10 cm.
 
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?!

Vital Question: how accurate was the 10 cm diameter?
Did we assume it was perfect, or to the nearest cm or mm? 
