Computers vary in their representation of numbers and the optimizations provided for their manipulation. With internet programming we've come to think of numbers as strings and convert freely from this machine independent form to those preferred on a host.
Here I suggest for various classes of numbers their preferred representations as a string.
An integer can count from zero to any finite limit.
0|[1-9][0-9]*
A signed integer can count up or down.
0|-?[1-9][0-9]*
A rational number counts in small but non-zero steps.
0|-?[1-9][0-9]*(/[2-9]|[1-9][0-9]+)?
A vector counts in multiple dimensions.
0|-?[1-9][0-9]*(/[2-9]|[1-9][0-9]+)?(,( 0|-?[1-9][0-9]*(/[2-9]|[1-9][0-9]+)?))+
Each of these classes of numbers includes the previous values maintaining uniqueness of representation. That is, unequal strings mean unequal numbers. This expectation excludes some familiar expressions.
0001 -0 3/1 1.5 ∞ π 05/26/49
We've intentionally excluded floating point and its common representations such as scientific notation which is best applied only to Measurement.