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

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

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 etc

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

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

    So multiply in numerator and denominator by 7 we get,

    ,

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

    We know that

    So, the numbers are

    Hence, six rational number between are:

Q.3 Find five rational numbers between .

Solution:

  • Given 2 rational numbers are

  • And to find five rational numbers between

    Denominator should be made equal to

    So multiply in numerator and denominator by 6 we get,

    ,

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

    We know that

    Therefore, the numbers are

    Hence, five rational number between are:

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 but, Whole numbers include

    So, Negatives integers are not whole numbers.

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

    Therefore, numbers are rational number but not whole numbers.