Important NCERT Examples 9th

 

Important NCERT Examples for class 9th 

                chapter - 1     Number System 

Example 1 : Are the following statements true or false? Give reasons for your answers.

(i) Every whole number is a natural number.

(ii) Every integer is a rational number.

(iii) Every rational number is an integer .

Example 2 : Find five rational numbers between 1 and 2.

Example 3 : Locate √2 on the number line.

Example 4 : Locate √3 on the number line.

Example 5 : Find the decimal expansions of 10/3 , 7/8 and 1/7 .

Example 6 : Show that 3.142678 is a rational number. In other words, express 3.142678 in the form p/q ,  where p and q are integers and q ≠ 0.

Example 7 : Show that 0.3333... = 0. ⁻⁻3   can be expressed in the form p/q , where p and q are integers and q ≠ 0.

Example 8 : Show that 1.272727... = 1.27 can be expressed in the form p/q , where p and q are integers and q ≠ 0.

Example 9 : Show that 0.2353535... = 0.235 can be expressed in the form p/q , where p and q are integers and q ≠ 0.

Example 10 : Find an irrational number between 1/7 and 2/7 .

 Example 11 : Check whether 7√5, 7/√5 , √2+21 , π−2 are irrational numbers or not. 

Example 12 : Add 2√2 + 5√3 and √2 – 3√3.

Example 13 : Multiply 6√5 by 2√5.

Example 14 : Divide 8√15 by 2√3.

Example 15 : Simplify the following expressions:

  (i) (5+ √7)(2+ √5)                  (ii) (5+ √5)(5− √5)

  (iii)(√3+ √7)²                         (iv)(√11− √7)(√11+ √7)

Example 16 : Rationalise the denominator of 1/√2 ⋅

Example 17 : Rationalise the denominator of 1/ (2 + √3) . 

Example 18 : Rationalise the denominator of 5 / (√3 - √5) . 

Example 19 : Rationalise the denominator of 1 / (7 + 3√2 ) .