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Originally Posted by Mike Betts
Nowadays, there are tools to assist with computing ratios. I use Mathcad which will compute ratios and allow you to adjust for accuracy.
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I just wanted to point out that the TI-89/92 graphing calculator family can also do this with the exact() function:
exact(3.14159265358, 0.00001) = 355/113
The second argument is the tolerance. I'm not sure what other models (if any) are capable of this.