It is very important to understand the basics of the number system, first is the classification of numbers. This is similar to classifying people. People can be put into groups like male, female, tall, short, etc… Here is a diagram of the number system.

Real Numbers

 

 

 

 

 

 

 

 

 

 

 

 

 

 

By looking at the diagram, notice that all real numbers are either rational or irrational. All rational numbers can be written in the form as a/b (a divided by b). Irrational numbers cannot be written in that form.

 

If a number is rational, it may also be an integer, whole number, and/or a natural number. Irrational numbers cannot be broken into smaller classes, state that they are irrational. Usually, when one has a square root that is not easily found (very large decimal) it will be irrational.

 

All natural numbers are whole numbers, but not all whole numbers are natural numbers. This is a very important concept to grasp, re-read it and look at the diagram above until it is understood. Basically, think about the number 0 it is the only number that is a whole number and not a natural number (refer to the above diagram). When taking this concept on a larger scale and trying to compare the numbers that are integers to the naturals, it is more easily understood that every natural is an integer, but not every integer is a natural (negative numbers).

 

Example

 

Classify

 

 

Irrational Answer!

 

Example

Classify 0

Rational, Integer, Whole number Answer!

 

Example

Classify 1

Rational, Integer, Whole number, Natural number

Answer!

 

Example

Classify 1/5

Rational Answer!