RATIONAL NUMBERS

Definition of Rational Numbers

A Rational Number is a real number written as a ratio of integers with a non-zero denominator.

More About Rational Numbers

Rational numbers are indicated by the symbol Q
Rational number is written in form, where p and q are integers and q is a non-zero denominator.
All the repeating or terminating decimal numbers are rational numbers.
Rational numbers are the subset of real numbers.

Examples of Rational Numbers

3/5,10.3,0.6,12/5,3/4 - All these are examples of rational numbers as they terminate.


Video Examples: Definition of Rational Numbers


Solved Example on Rational Numbers

Ques: Identify a number that is a rational number but not an integer.

Choices:
  • A.
  • B. 10.3
  • C. - 3.523...
  • D. -

Correct Answer: B

Solution:

  • Step 1: - 3.523... is a non-terminating and a non-repeating decimal number, so it is not a rational number.
  • Step 2: = - 5 is a rational number and also an integer.
  • Step 3: cannot be expressed as a quotient of two integers, so it is not a rational number.
  • Step 4: 10.3 = 103 / 10 is a rational number, but not an integer.

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