What is irrational and rational

People have calculated Pi to over a quadrillion decimal places and still there is no pattern. The first few digits look like this:. The number e Euler's Number is another famous irrational number.

People have also calculated e to lots of decimal places without any pattern showing. The Golden Ratio is an irrational number.

Apparently Hippasus one of Pythagoras' students discovered irrational numbers when trying to write the square root of 2 as a fraction using geometry, it is thought. Instead he proved the square root of 2 could not be written as a fraction, so it is irrational. But followers of Pythagoras could not accept the existence of irrational numbers, and it is said that Hippasus was drowned at sea as a punishment from the gods! A number is an arithmetical value that can either be an object, word or symbol representing a quantity that has multiple implications in counting, measurements, labelling etc.

Numbers can either be integers, whole numbers, natural numbers, real numbers. Real numbers are further categorized into rational and irrational numbers. In this article, we will discuss rational numbers, irrational numbers, Rational and irrational numbers examples, the difference between irrational and rational numbers etc. Rational Numbers. The term ratio came from the word ratio which means the comparison of any two quantities and represented in the simpler form of a fraction.

The denominator of a rational number is a natural number a non-zero number. Integers, fractions including mixed fraction, recurring decimals, finite decimals etc all come under the category of rational numbers. Irrational Numbers. A number is considered as an irrational number if it cannot be able to simply further to any fraction of a natural number and an integer.

The decimal expansion of irrational numbers is neither finite nor recurring. A surd is a non-perfect square or cube which cannot be simplified further to remove square root or cube root. Rational and Irrational Numbers Examples.

Some of the examples of rational numbers. Irrational numbers, in contrast to rational numbers, are pretty complicated. As Wolfram MathWorld explains, they can't be expressed by fractions, and when you try to write them as a number with a decimal point , the digits just keep going on and on, without ever stopping or repeating a pattern.

So what sort of numbers behave in such a crazy fashion? Basically, ones that describe complicated things. As mathematician Steven Bogart explained in this Scientific American article that ratio will always equal pi, regardless of the size of the circle.

Since the earliest attempts to calculate pi were performed by Babylonian mathematicians nearly 4, years ago, successive generations of mathematicians have kept plugging away, and coming up with longer and longer strings of decimals with non-repeating patterns. In , Google researcher Hakura Iwao managed to extend pi to 31,,,, digits, as this Cnet article details.

Sometimes, a square root — that is, a factor of a number that, when multiplied by itself, produces the number that you started with — is irrational number, unless it's a perfect square that's a whole number, such as 4, the square root of One of the most conspicuous examples is the square root of 2 , which works out to 1.

That value corresponds to the length of the diagonal within a square, as first described by the ancient Greeks in the Pythagorean theorem. Why do we call them rational and irrational? That seems to be a little murky. If you trace both 'rational' and 'ratio' back to their Latin roots, you find that in both cases the root is about 'reasoning,' broadly speaking.

What's clearer is that both rational and irrational numbers have played important roles in the advance of civilization.

While language probably dates back to around the origin of the human species, numbers came along much later, explains Mark Zegarelli , a math tutor and author who has written 10 books in the "For Dummies" series.

Hunter-gatherers, he says, probably didn't need much numerical precision, other than the ability to roughly estimate and compare quantities.