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I will try to make this clear direct me if it is not.In simple scientific solution, the equation contain individual numerical clusters separated by the math functions that will look like e.g. 1234.5 e^3 of defined digits that is 7 digits defining the value. Such as 1,234,500If a particular constant value is introduced that has the fractional portion, which can extend infinitely longer then 7 digits; e.g. Pi or the square root of 2 or the reciprocal of the sin 45 deg 1.4142135623730950488016887242097At which of these digits after the decimal point should the correct rounding out respectfully be 5th, 6th or 7th digit long?

Quote from: tommya300 on 14/07/2010 21:51:27I will try to make this clear direct me if it is not.In simple scientific solution, the equation contain individual numerical clusters separated by the math functions that will look like e.g. 1234.5 e^3 of defined digits that is 7 digits defining the value. Such as 1,234,500If a particular constant value is introduced that has the fractional portion, which can extend infinitely longer then 7 digits; e.g. Pi or the square root of 2 or the reciprocal of the sin 45 deg 1.4142135623730950488016887242097At which of these digits after the decimal point should the correct rounding out respectfully be 5th, 6th or 7th digit long?Your original expression has 5 significan figures so after you add that to, say, pi, then round that to 5 significan figures as well.

Would I need to round out Pi = 3.14159 before the math manipulation?

Quote from: tommya300 on 14/07/2010 23:40:26Would I need to round out Pi = 3.14159 before the math manipulation?You're very welcome, and no. You don't need to round PiRounding is only done at the end of a calculation, not for each step. But keep in mind this assumes that each term used is either exact or has more significan digits than the number input.This topic is covered in text on numerical analysis. Usually in the first chapter. Would you like me to scan one in and post a link to it?

Yes please! There may be other aspects that I may have no knowledge of to ask any questions.

Quote from: tommya300 on 14/07/2010 23:40:26Would I need to round out Pi = 3.14159 before the math manipulation?You're very welcome, and no. You don't need to round Pi

Quote from: Pmb on 15/07/2010 01:11:57Quote from: tommya300 on 14/07/2010 23:40:26Would I need to round out Pi = 3.14159 before the math manipulation?You're very welcome, and no. You don't need to round PiRounding is only done at the end of a calculation, not for each step. But keep in mind this assumes that each term used is either exact or has more significan digits than the number input.This topic is covered in text on numerical analysis. Usually in the first chapter. Would you like me to scan one in and post a link to it?Yes please! There may be other aspects that I may have no knowledge of to ask any questions.

Tommy If you break down your first sum it can demonstrate where problems might arise1.2345 + 3.14159 = 4.37609 But each of those numbers represents a range - as you have above mentioned HI 1.234549 LOW 1.234450 hi 3.1415949 low 3.1415850 When you add the extremes of the range you find that the max potential error swamps the last digits you give HIGH LOWhi 4.376144 4.376045 low 4.376134 4.376035 your range is approximately 4.376035-4.376144 (of course this itself has uncertainties/errors), you cannot be certain of anything past the 3rd decimal place. Personally, in all your examples I would try not to multiply out pi or root two (1.4142) until the very last moment in the hope that they will cancel or multiply out, and unless you need a plain number answer you can leave them in the actual answer. Hope that helped a bit - I would also say that the pages Peter put up are very informative and easily digested. Matthew

Is that why tolerance values are highly observed?

Quote from: tommya300 on 15/07/2010 19:14:05Is that why tolerance values are highly observed?I don't think so. Manufacturing tolerances are more to do with cost than anything else.Computational precision is more about knowing how precise your result needs to be. If you need an answer that's precise to 1% (one part in a hundred), the values that you use in your calculation should probably have a resolution of 0.1% (one part in a thousand).So, it's really a question of knowing how much resolution (precision) you need in your result, and that very much depends on what you are going to do with the result.A 1% error rate might not sound too bad, unless you are talking about midwives dropping babies on the floor when they are born.