Farey Approximation

The lemon squeezer icon here is to suggest that you need to 'squeeze' the range in which the irrational number lies making this interval smaller and smaller to get better and better rational approximations.

To decide which interval to choose you may need to know the decimal expansion of the irrational number you are approximating (as in the case of $\pi$). In the case of an irrational number which is a square root you can square the inequalities and you don't need to know the decimal expansion.