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Rational or Irrational calculator 

Enter the values required in the rational and irrational numbers calculator and select the operation to identify the nature of numbers.

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Rational and Irrational numbers calculator 

Rational and irrational expression calculator/ checker identifies whether the inputted number is rational or irrational. For a fraction, it uses a numerator and denominator. And for rooted values, it requires index and number.

What are rational numbers?

The numbers which can be expressed in the ratio of two integers form a set of rational numbers. It is denoted by Q.

I.e Q = {x|x =p/q; p,q z q 0}

7, 2/6, √25 are some examples of real numbers.

What are irrational numbers?

The numbers which cannot be expressed as a ratio (quotient) of integers are called irrational numbers. The set of irrational numbers are denoted by Q’.

, √7, 1.370256…. are some examples of irrational numbers

Note:

For each prime number n, n is an irrational number.

Types of rational and irrational numbers:

The set of both rational and irrational numbers are called real numbers. Every real number can be written in the form of decimals. 

Learning these types helps to identify rational and irrational numbers.

On the basis of decimal representation, types of rational and irrational numbers are as follows. 

Rational numbers:

It has two types:

Terminating:

A terminating decimal is one that has a finite number of digits after its decimal point.

Example:

  •  1/10 = 0.2
  •  ¾ = 0.75

Recurring:

Those numbers that are non-terminating but in which the same digit or group of digits repeat themselves indefinitely are also rational numbers.

Example:

  • 4/9 =0.444444… = 4
  • 9/11 =0.818181… = 0.81

Irrational numbers:

The numbers which are neither terminating nor recurring are described as irrational numbers. 

Example:

  • √5  
  • √7

The rational and irrational equation calculator can be used to know the decimal form of the expressions as well.