herbison@ultra.DEC (B.J.) (08/27/85)
The original question was the area of a table 3 meters by 4 meters. >> Anyway, it turns out the "correct" answer is 1 * 10^1 meters^2; >> since the initial data only had 1 digit of accuracy, that's all the final >> answer can have. Steven Bird says: >Getting even more off the point, suppose we were to compute 3*4 in base 12. >The answer of course is 10(base 12) which has 1 significant figure as required. >10(base 12) translates to 12 +/- 6 (base 10) which I think is more acceptable >than the 10 +/- 5 implied by 1 * 10^1 metres^2 above. And if the calculation is done in hexadecimal, the answer is 3*4=C. This translates to decimal as 12 +/- 0.5. In binary the problem is 11*100=1100. There are two significant digits (bits) from the `11', so the decimal version of this is 12 +/- 2. >Error analysis should be *independent* of the base used to represent numbers. >For this reason I think there is something fundamentally wrong with the use >of significant figures to express accuracy. I agree with you Steven, thanks for pointing that line of reasoning out. B.J.