Natural Numbers, Whole Numbers and Integers

• Natural numbers are also called the "counting" numbers. They are the numbers that are used to describe quantities, such as 1, 2 ,3, 4 and so on. Fractions, the number 0 and negative numbers are not included in the natural numbers.
  
  Whole numbers are simply the natural numbers with 0 included: 0,1,2,3,4 and so on. As with the natural numbers, fractions and negative numbers are not included in the whole numbers. When negative numbers are included with whole numbers, then the set of numbers would be called "integers."
  
  

Rational Numbers

• Rational numbers include the integers and any fraction that converts to a decimal that ends or has a repetitive pattern. The term "rational" is derived from the term "ratio," which is another representation of a fraction.
  
  To demonstrate the concept, the fraction 2/3 is a rational number because 2/3=.6 repeating, which is a repeating decimal. The fraction 1/2 is a rational number because 1/2=.5, which is a terminating decimal. The fraction 10/1 is rational because 10/1=10, which is an integer.
  
  

Irrational Numbers

• Irrational numbers and rational numbers are mutually exclusive sets of numbers. Irrational numbers are numbers that do not have an exact value as an integer, fraction or decimal. Two common examples of irrational numbers are pi and the square root of 2. These two numbers have decimal or fractional approximations but they are not exact values. For example, pi is commonly estimated as 3.14159, but that approximation never ends, never repeats and has no pattern.
  
  

Number Hierarchy

• The natural numbers is a subset of the whole numbers, the whole numbers is a subset of the integers and the integers is a subset of the rational numbers. The irrational numbers is a completely different set of numbers from the rational numbers. In short, rational numbers include whole numbers. For instance, the number 10 is a both a whole number and a rational number. The only difference between whole and rational numbers is that the rational numbers is the larger grouping that includes whole numbers, negative numbers and fractions with exact decimal values.