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Is 22/7 a rational or irrational number?

  • Difficulty Level : Basic
  • Last Updated : 06 Aug, 2021

Do you know where the term “rational” came from? It gets its name from the word “ratio.” As a result, rational numbers are closely linked to the idea of ratio. Both rational and irrational numbers are real numbers, but they have different characteristics. A rational number is one that can be written as p⁄q, where p and q are integers and q is not equal to zero. However, an irrational number cannot be expressed using simple fractions. √2 is an irrational number, whereas 2⁄3 is an example of a rational number.

What are Rational Numbers?

Numbers that may be represented as a fraction, as well as positive, negative, and zero, are known as rational numbers. It may be expressed as p/q, where q is not zero. The term “rational” comes from the word “ratio,” which refers to a comparison of two or more values or integer numbers, and is also known as a fraction. It is the ratio of two numbers in simple terms. All whole numbers, natural numbers, fractions of integers, integers, and terminating decimals are rational numbers.

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Examples of Rational Numbers



3, 4, 5, and so on are some examples of rational numbers as they can be expressed in fraction form as 3/1, 4/1, and 5/1. The number “0” is also rational since it may be represented in a variety of ways, including 0/1, 0/2, 0/3, and so on.

What are Irrational Numbers?

Irrational numbers are any numbers that are not rational numbers. Irrational numbers may be represented in decimals but not fractions, which implies they can’t be stated as a ratio of two integers. After the decimal point, irrational numbers have an infinite amount of non-repeating digits.

Examples of Irrational Numbers

√2, √3, √5, and so on are some examples of irrational numbers as they cannot be expressed in form of p⁄q. Euler’s Number, Golden Ratio, π, and so on are also some examples of irrational numbers. 1/0, 2/0, 3/0, and so on are irrational because they give us unlimited values.

Is 22/7 a rational or irrational number?

Solution:

Rational numbers are one of the most prevalent types of numbers that we learn in math after integers. A rational number is a sort of real number that has the form p/q where q≠0. All whole numbers, natural numbers, fractions of integers, integers, and terminating decimals are rational numbers.

When a rational number is split, the result is a decimal number, which can be either a terminating or a recurring decimal. All rational numbers can be expressed as a fraction whose denominator is non-zero. Here, the given number, 22⁄7 is a fraction of two integers and has recurring decimal value (3.142857). Hence, it is a rational number.

Similar Questions

Problem 1: Determine whether √3 is a rational number.

Solution:

A rational number is a sort of real number that has the form p/q where q≠0. When a rational number is split, the result is a decimal number, which can be either a terminating or a recurring decimal. Here, the given number, √3 cannot be expressed in the form of p/q. Hence, it is an irrational number.

Problem 2: Determine whether 1.232323…. is a rational number.

Solution:

A rational number is a sort of real number that has the form p/q where q≠0. When a rational number is split, the result is a decimal number, which can be either a terminating or a recurring decimal. Here, the given number, 1.232323… has recurring digits. Hence, 1.232323…. is a rational number.

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