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 pq, where p and q are integers and q0 ?

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 12,03,42, etc

    It’s all are form of pq , where p and q are integers and q0

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 6+1=7

    So multiply in numerator and denominator by 7 we get,

    3=3×77=217 , 4=4×77=287

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

    We know that 21<22<23<24<25<26<27<28

    So, the numbers are 217<227<237<247<257<267<277<287

    Hence, six rational number between 3=217and4=287 are:

    227,237,247,257,267,277

Q.3 Find five rational numbers between 35and45 .

Solution:

  • Given 2 rational numbers are 35and45

  • And to find five rational numbers between 35and45

    Denominator should be made equal to 5+1=6

    So multiply in numerator and denominator by 6 we get,

    35=3×65×6=1830 , 45=4×65×6=2430

    Five rational numbers between 35and45 can be found by varying the numerator between 1830 and 2430

    We know that 18<19<20<21<22<23<24

    Therefore, the numbers are 1830<1930<2030<2130<2230<2330<2430

    Hence, five rational number between 35=1830and45=2430 are:

    1930,2030,2130,2230,2330

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 {,2,1,0,1,2,} but, Whole numbers include {0,1,2,3,}

    So, Negatives integers are not whole numbers.

  3. 3rd statement is false, because Rational numbers include 52,35,0.63,etc. but, Whole numbers include {0,1,2,3,}

    Therefore, numbers 52,35,0.63,etc are rational number but not whole numbers.

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