Irrational Number Definition
It is one of the two major types of real numbers. The set of irrational numbers includes all those numbers that can’t be written in the form of a fraction. It means a number that has no defined denominator will be termed an irrational number.
Note:
Read about Real Numbers here.
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For example, √2 ,√5 ,√7,√3 are included in a set of irrational numbers. There are many other numbers that are irrational when we solve them. “Pi”, a famous constant in Mathematics, is also an irrational number.
Fun Facts about Irrational Number
- The Sum of an irrational number with a rational number will always be an irrational number.
- The product of a rational number with an irrational number will be an irrational number.
- The multiplication of two irrational numbers gives a rational number as the output.
How to check if a number is irrational or not?
For a Mathematics student, it is important to learn how he can check if a number is irrational or not. Many students try to find this by dividing which takes a lot of time and effort. The simplest approach to check this is by evaluating the decimal part of the solution.
If the decimal part of the solution is neither recurring nor terminating, it means that the given number is irrational. But if the decimal part has been terminated after some digits, it shows that the number is not irrational.
Common sets included in irrational numbers
An irrational number is a type of real number that can’t be defined in terms of ratio or fraction. It includes multiple sets of numbers that we are going to mention here.
- Natural numbers
- Whole numbers
- Integers
Note:
Read about Natural Numbers, Whole Numbers, and Integers here.
What is the difference between Rational and Irrational Numbers?
The main difference between Rational and Irrational numbers is their appearance. If a number can be written in the form of a fraction, it will be termed a Rational number otherwise the number will be irrational.
Note:
Read about Rational Numbers here.
FAQ's
Is Pi an irrational number?
Yes, Pi is an irrational number because its decimal part is neither recurring nor terminating.
What is the opposite of an irrational number?
The opposite of an irrational number is a rational number. Both sets are two major types of real numbers.
Is 2/3 a rational number or an irrational number?
2/3 is a rational number because its decimal part includes repeated terms.
Are all integers are irrational?
No, all integers are not irrational. The set of integers includes both rational and irrational numbers.
