Math Olympiad Test: Number System- 2 - Class 9 MCQ

Since,
- = 0.875 (Terminating decimal)
 (Irrational)
93/300 = 31/100 = 0.31 (Terminating decimal)
190/30 = (Repeating decimal)
∵ Repeating and terminating decimals are rational numbers.

Here

⇒ (3)^3(n-m) = (3)^-x
⇒ x = 3(m – n)     as  [m - n = 1]
⇒ x = 3 x 1 = 3

We have

= 3(2.236+1.732)
= 3(3.968)
= 11.904

= 10 + 3 – 7√3 = α + b
= 13 – 7√3 = α + b√3
⇒ α = 13, b = –7

2^-m x 2^-m =2^-2
⇒ (2)^-2m = (2)^-2
⇒ m = 1
Substituting the value of m in,

Here 


Similarly 


Rearranging all the terms in the required pattern, we have 

= 3 + 2 = 5

∵ 10^x = 64 ⇒ (10^x)^1/2 = (64)^1/2 = 8
∴ 10^x/2 = 8 ⇒

both side multiplied by 10

(10)^x/2 X 10  =  (64)^1/2 X 10

  =  8 X 10 = 80

∵ x^–2 = 64
⇒ x^-1 = 8
⇒ x = 1/8

Given x = 2 + √3 then

​​​​​​
∴  x = 5, y = 3

Given n = then x = 0.24545
 10x = 2.4545 ...(i)
and 100x = 24.54545
and 1000x = 245.454545 ...(iii)
Subtracting eq (i) and eq (iii), we get
990x = 243
⇒ x = 243/990 = 27/110