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Integration with pi - Rational Approximation?

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I'm having trouble understanding the difference between these two integration commands:
clear; syms y;
int(1000*9.8*(10-y)*(pi*6^2),0,10)
int(9.8*1000*(pi*6^2)*(10-y),0,10)
On my machine (2019b - Windows) and MATLAB Online, using format short I get:
ans =
17640000*pi
ans =
14876074069235525/268435456
I often receive odd rational approximations when integrating using pi (note that leaving pi out of the integral fixes the issue). I haven't been able to find an answer as to why this happens. I'm assuming MATLAB computes a decimal answer using pi, cuts the approximation at the 14 or 15th decimal place, then creates a fraction out of the result, but why does this happen some times and not others?

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Paul Dostert
Paul Dostert 2 Nov 2019
Thanks so much. Makes perfect sense!

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