Lua numbers are 64-bit floating point, they don't store any extra information like TI-Nspire Basic does about whether it's the square root of 3 or pi or whatever.

I would suggest to use math.eval and call basic function to do the calculation. But sadly enough getNum and getDenom don't work good through math.eval.
But ... gcd() (greatest common divisor) does, so I made my own function:
function exact(n)
local n_int, n_float = math.modf(n)

local n_size = math.pow(10, #tostring(n_float)-2)

local num = n_float * n_size
local denom = n_size

local gcd = math.eval("gcd(" .. num .. "," .. denom .. ")")

num = num/gcd
denom = denom/gcd

return n_int, num, denom
end

It works like this:
big, num, denom = exact(13.125)big will be 13
num will be 1
denom will be 8
So, 13 1/8 .

It doesn't do any error checking though, thats your task :p