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Difference Between Irrational and Rational Numbers

Irrational vs Rational Numbers

Rational number and irrational number are both real numbers. Both are values which represent a certain quantity along a particular continuum. Math and numbers is not everyone’s cup of tea, thus sometimes some people find it confusing to differentiate which one is rational and which one is an irrational number.

Rational Number

A rational number is actually any number which can be expressed as a fraction of two integers x/y where y or the denominator is not zero. Because the denominator can be equal to one, we can conclude that all integers is a rational number. The word rational was originally derived from the word ratio because again they can be expressed as ratio x/y given that both are integers.

Irrational Number

Irrational numbers as what its name may imply are those numbers that are not rational. You cannot write these numbers in fraction form; although you can write it in decimal form. Irrational numbers are those real numbers which are not rational. Examples of irrational numbers include the following: the golden ratio and the square root of 2 because you cannot express all these numbers in fraction form.

Difference between Irrational and Rational Numbers

Here are some differences that one should learn about rational and irrational numbers. First, rational numbers are numbers which we can write as fraction; those numbers that we cannot express as fractions are called irrational, just like pi. The number 2 is a rational number, but its square root is not. One can definitely say that all integers are rational numbers, but one cannot say that all non-integers are irrational. As stated above, rational numbers can be written as fractions; however it can be written as decimals too. Irrational numbers can be written as decimals but not fractions.

Looking at what is stated above can be one’s get away as to mastering what is the difference between these two.

In brief:

• All integers are rational numbers; but it does not necessarily mean that all non-integers are irrational.

• Rational numbers can be expressed as both fraction and decimal; irrational numbers can be expressed as decimal but not in fraction form.


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