NCERT Class 9 Solutions: Number Systems (Chapter 1) Exercise 1.1

Q.1 Is zero a rational number? Can you write it in the form Equation where p and q are integers and Equation ?

Solution:

  • Yes, zero is a rational number.

  • A rational number is a real number that can be written as a simple fraction.

  • In a fraction both the numerator and denominator are whole numbers.

  • Most numbers we use in everyday life are Rational Numbers.

  • Every whole numbers is a rational numbers, because any whole number can be written as a fraction.

    Given the image define the rational number and Irrational numbers

    Given the Table of Real Numbers

    Given the image define the rational number and Irrational numbers

  • For example It can write as Equation etc

    It’s all are form of Equation , where p and q are integers and Equation

Q.2 Find six rational numbers between 3 and 4

Solution:

  • Given 2 rational numbers are 3 and 4

  • To find six rational numbers between 3 and 4

    Denominator should be made equal to Equation

    So multiply in numerator and denominator by 7 we get,

    Equation , Equation

    Six rational numbers between 3 and 4 can be found by varying the numerator between 21 and 28

    We know that Equation

    So, the numbers are Equation

    Hence, six rational number between Equation are:

    Equation

Q.3 Find five rational numbers between Equation .

Solution:

  • Given 2 rational numbers are Equation

  • And to find five rational numbers between Equation

    Denominator should be made equal to Equation

    So multiply in numerator and denominator by 6 we get,

    Equation , Equation

    Five rational numbers between Equation can be found by varying the numerator between Equation and Equation

    We know that Equation

    Therefore, the numbers are Equation

    Hence, five rational number between Equation are:

    Equation

Q.4 State whether the following statements are true or false. Give reasons for your answers.

  1. Every natural numbers is a whole number.

  2. Every integer is a whole number.

  3. Every rational number is a whole number.

Solution:

  1. 1st statement is True, Since the all whole numbers contains all natural numbers and in additional zero

    Given the Rational, Integers, Whole, Natural and Irrational numbers and find the which statement is true or false

    Given the Rational, Integers, Whole, Natural and Irrational Numbers

    Given the Rational, Integers, Whole, Natural and Irrational numbers and find the which statement is true or false

  2. 2nd statement is false, because Integers include Equation but, Whole numbers include Equation

    So, Negatives integers are not whole numbers.

  3. 3rd statement is false, because Rational numbers include Equation but, Whole numbers include Equation

    Therefore, numbers Equation are rational number but not whole numbers.

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