Question

List all the numbers from the given set that are, a.natural numbers b.whole numbers c.integers d.rational numbers, e.irrational numbers

{-9,-4/5,0,0.25,ã3,9.2,ã100}

Answer 1

a.natural numbers
Numbers that are non-negative integers, such as 1,2,12,201,...
There are two definitions of natural numbers, one that includes 0, and the other one does not. Most high-school definitions include 0.

b.whole numbers
Whole numbers do not have decimals nor fractions. They can be positive, negative, or zero. Examples are -100, -23, 0, 40, 47,1729,...

c.integers
Integers are whole numbers. This term is a more technical term than "whole numbers".

d.rational numbers,
Rational numbers are whole numbers or fractions that can be represented by division of two integers, m/n. Whole numbers can be represented by an integer divided by 1.
Examples: 0, 3, 4/5, 144/17, 355/113, -45/13..., 0.4, 3.̅3 (=10/3),

e.irrational numbers
Irrational numbers are real numbers that are not rational, i.e. real numbers that cannot be represented as a quotient of two integers. Examples are: √2, -√94, π and e.

This should give you a good idea of how to classify numbers. Proceed with the exercise and post your answers for checking if you wish.

Note:
If you are wondering what a real number is:
a real number is a number that is not complex. A complex number includes an imaginary component, i. A real number is a subset of complex numbers, which has the general form <b>a+bi</b>, where a and b are real numbers, and i is the square-root of -1. When b=0, the number becomes a real number.