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# Classify numbers

Numbers can be classified into groups:

Natural Numbers
Natural numbers are what you use when you are counting one to one objects. You may be counting pennies or buttons or cookies. When you start using 1,2,3,4 and so on, you are using the counting numbers or to give them a proper title, you are using the natural numbers.

Whole Numbers
Whole numbers are easy to remember. They're not fractions, they're not decimals, they're simply whole numbers. The only thing that makes them different than natural numbers is that we include the zero when we are referring to whole numbers. However, some mathematicians will also include the zero in natural numbers and I'm not going to argue the point. I'll accept both if a reasonable argument is presented. Whole numbers are 0, 1, 2, 3, 4, and so on.

Integers
Integers can be whole numbers or they can be whole numbers with a negative signs in front of them. Individuals often refer to integers as the positive and negative numbers. Integers are -4, -3, -2, -1, 0, 1, 2, 3, 4 and so on.

Rational Numbers
Rational numbers have integers AND fractions AND decimals (except decimal values that continues forever without a pattern). Now you can see that numbers can belong to more than one classification group. Rational numbers can also have repeating decimals which you will see be written like this: 0.54444444... which simply means it repeats forever, sometimes you will see a line drawn over the decimal place which means it repeats forever, instead of having a ...., the final number will have a line drawn above it.

Irrational Numbers
Irrational numbers don't include integers OR fractions. However, irrational numbers can have a decimal value that continues forever WITHOUT a pattern, unlike the example above. An example of a well known irrational number is pi which as we all know is 3.14 but if we look deeper at it, it is actually 3.14159265358979323846264338327950288419.....and this goes on for somewhere around 5 trillion digits!

Real Numbers
Here is another category where some other of the number classifications will fit. Real numbers include natural numbers, whole numbers, integers, rational numbers and irrational numbers. Real numbers also include fraction and decimnal numbers.

In summary, this is a basic overview of the number classification system, as you move to advanced math, you will encounter complex numbers. I'll leave it that complex numbers are real and imaginary.

Classify the following numbers as rational or irrational:

i. $\frac{1}{3}$    ii. 7    iii. $\sqrt{7}$    iv. $\sqrt{25}$   v. $\pi$

Solution:

 i. $\frac{1}{3}$ rational ii. 7 rational iii. $\sqrt{7}$ irrational iv. $\sqrt{25}$ rational v. $\pi$ irrational

Classify the following numbers as rational, irrational, natural, whole and/or integer. (A number may belong to more than one set).

i. -2    ii. $4\frac{1}{3}$    iii. $\sqrt{5}$    iv. 0

Solution:

 i. -2 rational, integer ii. $4\frac{1}{3}$ rational iii. $\sqrt{5}$ irrational iv. 0 rational, integer, whole number

Explain the difference between a rational and an irrational number.

A rational number can be expressed as the ratio of two integers. An irrational number is any
real number that is not rational.