So then you notice that if you measure more precisely you get a different fraction... and even more precisely another different fraction. It's natural to ask w

So then you notice that if you measure more precisely you get a different fraction... and even more precisely another different fraction. It's natural to ask what ratio you'd get if you measured with endless precision. In some cases there is such an answer and you can reason it out without conducting a series of increasingly precise measurements (though you could also find it with a sufficiently precise measurement), but in other cases there is no such answer. Isn't that interesting?