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Is 2 a rational number?

  • Difficulty Level : Medium
  • Last Updated : 17 Aug, 2021

The method to represent and work with numbers is understood as a numeration system or number system. A number system may be a system of writing to represent numbers. it’s the notation to represent numbers of a given set by using digits or other symbols. It allows us to work on arithmetic operations like division, multiplication, addition, subtraction. Some important number systems are as follows,

  • Decimal Number System
  • Binary Number System
  • Octal Number System
  • Hexadecimal Number System

Let’s see about decimal number systems intimately.

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Decimal Number System

The decimal numeration system consists of ten digits i.e. from 0 to 9. The bottom of the decimal numeration system is 10. These digits are often represented or expressed as any numeric value. For example, the decimal number 163 consists of the digit 3 in one place, the digit 5 in the tens place, and the digit 1 in hundreds place which can be represented as,

(1×102) + (6×101) + (3×100)

= (1×100) + (6×10) + (3) { where, 100 = 1}

= 100 + 60 + 3

= 163

The decimal number system is widely used in mathematics and there are different types of numbers based on the characteristics shown by them in the decimal system, for instance, there are real, complex, rational, irrational numbers, the following problems statement consist of knowledge related to irrational number, lets solve the problem,

Is 2 a Rational or Irrational number?

The above problem statement first requires to have the knowledge about what exactly rational and irrational numbers in the decimal number system are, therefore, lets first learn about rational and irrational numbers,

Rational Number

Rational numbers are numbers that may be represented as fractions and also as positive numbers, negative numbers, and 0. The real number is written within the p/q form, where q isn’t adequate to zero. For example, 3/2,5/3, and 1/7 are rational numbers.

Irrational Number

Irrational numbers are numbers that cannot be written in the form of fractions. They are represented in decimal form. For example, √19 = 4.35889, √2 = 1.424 are irrational numbers.

2 is a rational number because it satisfies the condition for rational number and  can be written in p/q form which is mathematically represented as 2/1, where 1≠0. 

Similar Problems

Question 1: Is 1/4 rational or an irrational number?


1/4 is a rational number because it satisfies the condition for rational number and can be written in p/q form where, 4≠0.

Question 2: Is 1.5 a rational or an irrational number?


1.5 is a rational number as it satisfies the condition for rational number and can be written as 3/2 which is in p/q form where, 2≠0.

Question 3: Is √2 a rational or irrational number?


√2 is irrational number because it satisfies the condition for irrational number which is written in decimals i.e., the value of √2 = 1.4142135623730950… 

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