A few examples of what you can ask Wolfram|Alpha about:
compute properties of an integer
do exact arithmetic with integers
compute a prime factorization
compute properties of a rational number
compute the exact value of a repeating decimal
compute properties of an irrational number
determine whether a number is irrational
determine whether a number is algebraic
identify algebraic integers and units
determine whether a number is transcendental
get information about a transcendental number
do basic arithmetic on complex numbers
find roots of complex numbers
apply functions to complex numbers
do exact arithmetic with large numbers
find a decimal approximation
compute a decimal approximation to a specified number of digits
compute the value of a mathematical constant
do computations involving constants
find possible closed forms for an approximate number
represent an approximate number in terms of specified constants
visualize a set of real numbers on a number line
show multiple sets on a number line
compute properties of an interval of real numbers
compare intervals
convert a decimal number to another base
convert a number in a given base to decimal
do mixed-base computations
do computations with Roman numerals
convert a decimal number to Mayan numerals
find the English name of a large number
specify a number by name