Rational Numbers: Definition, Examples

What is a Rational Number?

In Math, rational numbers are a highly prevalent sort of number that students learn. These numbers are in the form p/q, where p and q are integers q ≠ 0.The Rational numbers are not as same as the fraction, there is a slight difference between the two. Whole numbers make up fractions, whereas integers make up the numerator and denominator of rational numbers.

The set of rational numbers also includes all integers, which can be expressed as a quotient with the integer as the numerator and 1 as the denominator. Rational numbers are either terminating or recurring decimals in decimal form. Irrational numbers are real numbers that cannot be written as a quotient of two integers.

Rational Number: Definition

A rational number is a number that can be expressed as the quotient p/q of two numbers with q ≠ 0. The set of rational numbers also includes all integers, which can be expressed as a quotient with the integer as the numerator and 1 as the denominator. Rational numbers are either terminating or recurring decimals in decimal form. Irrational numbers are real numbers that cannot be written as a quotient of two integers.

Every Rational Number is a proper or improper fraction

In the same way that whole numbers and integers are represented on the number line, rational numbers can be represented on the number line. The number zero (0) is known as the origin on the number line. The positive values are shown on the right side of the origin, whereas the negative values are shown on the left. Let’s look at how to express rational numbers on a number line now.

There are two main sorts of representations for rational numbers. The rational number can be expressed as a proper or improper fraction.

Representation of a Proper Fraction

If it’s a proper fraction, the numerator is smaller than the denominator, so the supplied rational number should be less than 1 and more than 0, and we can simply express it on the number line.

Representation of a Improper Fraction

Because the numerator is bigger than the denominator in an improper fraction, the given rational number should be greater than 1. In this scenario, turn the improper fraction into a mixed fraction first. This conversion aids in determining the precise location of a given fraction on the number line. It’s useful to know where the fraction falls between two integers.

Rational Number: Examples

A rational number is one that can be written as a fraction with both the numerator and denominator being integers. Here are some examples of rational numbers:

  1. -13, 0
  2. 1/3
  3. -3/7
  4. 0.9 or 9/10
  5. -0.01 or -1/100
  6. 14/9

Is 0 a Rational number?

Yes, 0 (zero) is a rational number.

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Rational Number: FAQs

Ques. What is rational number example?

Ans. A rational number is one that has the form p/q, with p and q being integers and q not equal to 0. 1/3, 2/4, 1/5, 9/3, and so on are some examples of rational numbers.

Ques. Is 7 a rational number?

Ans. The number seven is a logical one. When two integers are divided, the result is called a rational number. 7 can be written in the form of p/q as 7/1, and here q should not be equal to 0, and 1 is not equal to 0.

Ques. How can you identify a rational number?

Ans. A rational number is one that is stated in p/q form or in fraction form with both the numerator and denominator parts being integers. The number “0” is a rational number as well.

Ques. Is Pi a rational or irrational number?

Ans. Pi is an irrational number, meaning it is a real number that cannot be stated as a fraction. Pi’s value is stated in decimal form, which is non-terminating and non-repeating. The non-terminating value demonstrates the nature of irrational numbers. As a result, is an irrational number. It’s an unreasonable decision.

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