# Classifying Real Numbers

Wednesday, November 23rd, 2011 at
2:08 pm

# Numbers

## Numbers are either Real or Imaginary.

## Real numbers are either Rational or Irrational. All real numbers can be placed on a real number line.

## Rational numbers include any number that can be written as a fraction or a ratio of two integers, where .

## Irrational numbers cannot be written as a ratio or fraction. When you write an irrational number as a decimal, it does not end in 0 or it does not repeat. Example: = 1.7320508075688772935274463415059…

## The can be placed on the real number line in the space between 1 and 2.

## Rational numbers are subdivided into fractions or integers. On a number line the space in between two integers contains all the fractions or decimal numbers that are between the two integers.

## Fractions are either repeating or terminating. When you write a fraction as a decimal and it ends in 0 it is called a terminating decimal. If it repeats it is called a repeating decimal.

## Examples:

## = 0.50 and = 1.750 are terminating decimals.

## = 1.333… or and = 0.1212121212 or are repeating decimals.

## Integers are rational numbers that make a complete unit. They include all the negative units, 0, and all the positive units.

## Examples:

## -4, , 12/4 = 3, and 0/10 = 0 are all integers.

## Whole numbers are zero and all the positive integers. {0,1,2,3,…}

## Natural numbers are all the positive integers or the numbers you first used to learn to count. {1,2,3,..

## The number 5 is a natural number, a whole number, an integer, a rational number and a real number.

## Classify each of the following numbers: ,-7, and 5/3

## R – real

## I – imaginary

## Ra – rational

## Ir – irrational

## F – fraction

## Term D – terminating decimal

## Repeat D – repeating decimal

## In – integer

## W – whole number

## N – natural number

## is irrational and real [Ir and R]

## 7 is a natural number, a whole number, an integer, a rational number and a real number [N,W,In, Ra, R]

## 5/3 is a fraction, 1.6666… is a repeating decimal, a rational number and a real number [F, Repeat D, Ra, R]

**Filed under: **Pre-requisites for Pre-Calculus • Uncategorized

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