In practical applications, how many decimal places does Pi realistically need to be used?
by 
Mawgan
ANSWERS: 12
-
It depends entirely on the situation you are using it for. "Practical applications" is too vague.
-
I think it would be great to know the amount of pie I get to eat.
-
I always use 3.14159 when I do calculations, unless there is a need for more precise results. For the most part that is all I will ever use. But when I do need more precise calculations I use : decimal: 3.14159265358979323846264338327950288419716939937510 Binary: 11.00100100001111110110 Hexadecimal: 3.243F6A8885A308D31319
-
3.1415 is more than enough... It depends on where the largest error is... If you have, say, a 10% error in the value of a radius, then 3.14 is going to be easily more accurate (it's about a 0.1% error there)... Whereas if your radius is calculated to, say, 1 in 1,000,000 then you'll need to use Pi to be like, 3.14156925... The percentage variation from your value and the actual value is easy to calculate... Pi / Your value of pi - 1, then *100 to get the percentage error
-
Well for general calculations at school five decimal places is quite acceptable. For engineering you'd need a few more, perhaps ten or twenty. For micro-engineering you'd need to be extremely accurate, perhaps fifty or a hundred decimal places. If you wanted to go to the extreme then that would involve calculations to do with space travel, you'd need millions of decimal places to calculate something accurately enough to make whatever you're bulding safe to use.
-
Most computer calculations, which is where most engineering is done, use either Single Length floating point, which has an accuracy of about 7 decimal places, or double length floating, which has an accuracy of about 16 decimal places. There is therefore no point in representing pi in real world calculations to much more than the latter accuracy - say about 18 decimal places.
-
In real practical applications, eg cutting a piece of flexible grommet to fit a small hole, 3 and a bit is accurate enough. For a bigger hole, you might want to go 3.14. I'd still rather just use my calculator and get all 8 or 16 digits or whatever it gives me. Four times the arctangent of one in radians is always my favourite answer.
-
Well, π to just 11 decimal places is accurate enough to calculate the circumference of the earth with a precision of a millimeter, and π to 39 decimal places is sufficient to work out the circumference of any circle that fits in the observable universe to a precision comparable to the size of a hydrogen atom. Just think about that. If you wanted to build a space ship that could fly to the accuracy of an atom on the furthest star you can see in the sky, you would only need 39 decimal places.
-
two decimal places. 3.14
-
Bit of random history: My kids' dad had memorized Pi to the 50th place, just for fun. It was right. I checked. I don't think I could ever do that.
-
Depends on the application; if you're constructing your own thing not very much, if you're an expert engineer then more, and if you're trying to calculate which day of the week the Big Bang occured on then you may need it to the million of decimals.
-
I have read that 5 decimal places is sufficient to measure anything on the Earth. And 10 decimal places is sufficient to measure anything in the observable universe to the same degree.
RELATED QUESTIONS
Copyright 2023, Wired Ivy, LLC