You choose the number of useful digits by knowledge of the situation. A person who is properly taught how to apply the rules of significant digits knows how many digits apply. A number left in fractional form is not an answer. If I have a number like 2/3, what does that mean if I'm trying to build something with it?
2/3 is no less an anwer than 0.67
Admittedly the problem presented is purely numerical with no context.
Even if you have a number such as 2/3, you still have to assign a level of accuracy to it. There is no way you can make something exactly 2/3 of something. You are always going to have to state a plus/minus something else.
Alright, but it may not be an end result. It could be an intermediate step involving a fractional coeifficient. Take as an example the formulae for the volume of a sphere - 4/3 * pi * r^3
In any case, if the figure of 2/3 was an approximation for something, with a known error bound, then by substituting a decimal approximation you introduce a further error.
Phil Hall
