What is the Difference Between a Rational and an Irrational Number? What is an Easy Way to Remember Them?

Numbers are everywhere. They are the key to a successful business and they are the formula that can take you to outer space. The better you understand them, the better you will do in life. Even if you do not become a businessman or a scientist, numbers will help you manage your earning and savings better.

Rational and irrational numbers are two types of numbers under real numbers. You know what real numbers are, right? Real numbers can be both positive and negative, therefore, both rational and irrational numbers can also be both negative and positive. Read on to know more about the difference between rational and irrational numbers and how to identify them.

Rational Numbers

The word rational has been derived from ratio which denotes the comparison of two numbers or their representation in a simple form of a fraction. Rational numbers can be expressed in the form of a/b where both a and b are integers. Always remember that the denominator can never be 0, this means, b can never be 0. Which types of numbers are known as rational numbers? The answer is finite decimals, recurring decimals, mixed fractions, integers, etc. Examples of rational numbers include ½, 3/10, -14, etc.

Irrational Numbers

Irrational numbers are numbers that cannot be represented as a ratio of integers. Their ratio is neither terminating nor repeating. In other words, if you write an irrational number in the ratio form and divide the numbers the division will go on and so will the quotient. The numbers in the quotient also do not repeat themselves.

Examples of irrational numbers include the square root of non-square numbers such as √5. If you solve it you get, 2.2360….. you will have to round up the answer to present limited numbers. Some other examples include pi, e, a product of rational and an irrational number 2√2, etc.

What is an Easy Way to Remember Them?

You do not have to remember rational numbers or irrational numbers. If you can classify them and identify them, that is enough to work with them. As already discussed, rational numbers can be written as a ratio of two numbers or in a fraction form. Whereas, an irrational number can never be written as a ratio of two numbers and its decimal form does not stop and does not repeat.

So, every time you come across a question where you have to identify a number as a rational or irrational number, you have to write it as a ratio. If you succeed, you can identify that number as a rational number and if you don’t the number is irrational. 

In general, the square roots of numbers that are not perfect squares are irrational numbers and the number pi is always irrational. Square roots of perfect squares are always rational. You can use this to quickly identify the numbers without dividing them to find out if their decimals end or if they can be represented as fractions.

Another quick way of identifying the numbers is to divide the given ratio and notice the quotient. If it stops or the numbers in it start repeating, the number is rational. If the division does not stop and the numbers do not repeat in the quotient, the number is irrational. Easy? Maybe not but you will get better with practice. The math gets easy and magical only if you work hard with it, make time for it, and don’t approach it with a negative mindset.