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Define (i) rational number, (ii) irrational number (iii) real numbers

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This is the basic and conceptual question from real numbers chapter in which we have to give the definition of rational number, irrational number and real number.

RS Aggarwal, Class 10, chapter 1D, question no 1


1 Answer

  1. (i) rational number

    The rational numbers are numbers which can be expressed as a fraction and also as positive numbers, negative numbers and zero. It can be written as p/q, where q is not equal to zero.

    1. number 9 can be written as 9/1 where 9 and 1 both are integers.
    2. 0.5 can be written as 1/2, 5/10 or 10/20 and in the form of all termination decimals.
    3. 81  is a rational number, as it can be simplified to 9 and can be expressed as 9/1.
    4. 0.7777777 is recurring decimals and is a rational number.

    (ii) irrational numbers

    The numbers which are not a rational number are called irrational numbers. Now, let us elaborate, irrational numbers could be written in decimals but not in fractions which means it cannot be written as the ratio of two integers.
    Irrational numbers have endless non-repeating digits after the decimal point.

    1. 5/0 is an irrational number, with the denominator as zero.
    2. π is an irrational number which has value 3.142…and is a never-ending and non-repeating number.
    3. 2  is an irrational number, as it cannot be simplified.
    4. 0.212112111…is a rational number as it is non-recurring and non terminating.

    (iii) real numbers

    The real numbers include all the rational numbers, such as the integer −5 and the fraction 4/3, and all the irrational numbers, such as 2 (1.41421356…, the square root of 2, an irrational algebraic number).

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