Class 9 Maths - Number System Previous Year Questions

(i) Every point on the number line corresponds to a real number which may be either rational or irrational.

(ii) The decimal form of an irrational number is neither recurring nor terminating.

(iii) The decimal representation of the rational number $\frac{8}{27}$  is 0.296.

(iv) 0 is a rational number.

Sol:

Sol:

Sol:The rational number lying between 13  and  12 is calculated as follows:

12 × ( 13 + 12 )  =  1 × (2 + 3)3 × 2  =  512.

Therefore, 13  < 512  < 12.

Now, the rational number lying between 13 and 512 is calculated as:

12 × ( 13 + 512 )  =  1 × (4 + 5)12 × 2  =  38.

Therefore, 13  <  38  <  512.

The rational number lying between 512 and 12 is:

12 × ( 512 + 12 )  = 1 × (5 + 6)12 × 2  = 1124.

Therefore, 512 < 1124 < 12.

Hence, the three rational numbers lying between 13  and  12  are:  38,  512,  and  1124.

Sol: 0 is a rational number.

Sol:
Here,using (a+b)² = a² + 2ab +b²
we get, 
(√5 + √2)²= (√5²+ 2√5√2 + (√2)²
= 5 + 2√10 + 2 = 7 + 2√10

Sol: Simplify each square root.Substitute these value in given equation : √45 – 3√20 + 4√5 
we get , 
= 3√5 – 6√5 + 4√5 
= √5.

Sol: Let x =1.8181… …(i)
[multiplying eqn. (i) by 100] 
we get , 
100x = 181.8181… …(ii) 
99x = 180 
[subtracting (i) from (ii)] 
we get, 
x = 180/99
Hence, 1.8181… = 180/99 = 20/11

Sol:Using Identity: (a – b) (a+b) = a² – b²

(i) (11 + √11) (11 – √11)

= 11² – (√11)²

= 121 – 11

= 110

Sol:Multiply and divide the given number by 2√5 + 3

Sol:
(a) (729)^1/6
Prime factorize 729 = 3 × 3 × 3 × 3 × 3 × 3 = 3⁶( Used : Rule of exponents used: (a^x)^y = a^xy) 
(b) (64)^2/3
Prime factorize 64 = 2 × 2 × 2 × 2 × 2 × 2 = 2⁶Rule of exponents used: (a^x)^y = a^xy) 
(c) (243)^{6/5
( Used : Rule of exponents used: (ax)y = axy)} 
(d) (21)^3/2 x  (21)^5/2
Rule of exponents used: (a^x) × (a^y) = a^{x + y}
Prime factorize 81 = 3 × 3 × 3 × 3 = 3⁴
Rule of exponents used:

Sol: Multiply and divide by the  (8 - 3√5): 

Sol: 

Thus, 1/17 = 0.0588235294117647….
Therefore, 1/17 has 16 digits in the repeating block of digits in the decimal expansion.