All terms in this list:

rational number: A real number that can be expressed as the ratio of two integers.

scientific notation: a method of writing, or of displaying real numbers as a decimal number between 1 and 10 followed by an integer power of 10

whole number: all natural numbers including zero.
0, 1, 2, 3, 4, ...9,372, 9,373...

integer: An element of the infinite and numerable set {...,-3,-2,-1,0,1,2,3,...}.
a number on the number line

natural number: a member of the set of natural numbers - a positive integer (set of [1,2,3,...])
number your niece would count

irrational number: Any real number that cannot be expressed as a ratio of two integers.
non-repeating, non-terminating decimals and non-perfect square roots.