Irrational Numbers Example

There is a group of numbers that cannot be expressed as whole numbers, nor as fractional numbers with a denominator different from 0, this group of numbers is called irrational numbers.

Whole numbers when added, subtracted, or multiplied yield a whole number, which can be positive or negative.

Fractional numbers express a part of a whole, that is, they express a division, which can be added or subtracted from whole numbers or from other fractional numbers. In addition to the products of a division expressed in a fraction, you can produce a decimal result with numbers.

Whole and fractional numbers are easily located on a number line.

Many mathematicians since the time of Pythagoras, realized that there are gaps between fractional numbers. At the same time they found results of mathematical operations that did not express results exact or repeating decimals, but instead produced results with infinite decimals and did not follow a pattern. As these results do not follow Pythagoras' theory of numerical perfection, it is because of this characteristic of not following a pattern that they were called irrational numbers. They also found that these numbers filled in the gaps on the number line between the fractional numbers.

To express an irrational number, it is generally represented as the mathematical formula that gives rise to it. For example, when calculating the square root of the number 2, the result is a number that does not follow any numerical pattern, and whose decimals extend to infinity:

√2 =

Which to simplify is represented as √2.

There are some irrational numbers that have been given specific names as they represent relationships constants, such as the "Archimedean constant", the result of dividing the circumference of a circle enter your radio. In the 18th century this constant was defined as the number pi:

 π = 3.1415926535897932384626433832795028841971693993751058209…

Examples of irrational numbers and their first 20 decimals:

(pi) π = 3.14159265358979323846…

(phi, golden number) φ = 1.6180339887498948482045…

(Euler's number) e = 2.7182818284590452353602…

√2 = 1.41421356237309504880…

√3 = 1.73205080756887729352…

√5 = 2.23606797749978969640…

√7 = 2.64575131106459059050…

√8 = 2.82842712474619009760…

√10 = 3.16227766016837933199…

√11 = 3.31662479035539984911…

√12 = 3.464101615137754587054…

√13 = 3.605551275463989293119…

√14 = 3.741657386773941385583…

√15 = 3.872983346207416885179…

√17 = 4.123105625617660549821…

√18 = 4.2426406871192851464050…

√19 = 4.3588989435406735522369…

√20 = 4.47213595499957939281834…

√26 = 5.099019513592784830028224…

√30 = 5.477225575051661134569697…

√35 = 5.916079783099616042567328…

√40 = 6.324555320336758663997787…

√50 = 7.071067811865475244008443…

√99 = 9.949874371066199547344798…

√101 = 10.049875621120890270219264…

√201 = 14.177446878757825202955618…

√500 = 22.360679774997896964091736…

√713 = 26.702059845637377344148367…

√888 = 29.799328851502679438663632…

√999 = 31.606961258558216545204213…