157/50
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0.314 = 314/1000 = 157/500
3.14 = 314/100 = 157/50
1 x 314 and 2 x 157
There are many, many, fractions equal to 3.14314/100 for instance. Or 22/7 which is smaller and almost as close. It gives you 3.1428571 which is closer then 314/100. Uh, no. 314/100 is much closer to 3.14 than 22/7. Also, 22/7 is not smaller than 314/100, it is larger. 3.1428571 > 3.14.
sqrt(314) cannot be simplified.