If n is a natural number then \(\sqrt { n } \) is ________.

(a)

always a natural number

(b)

always an irrational number

(c)

always a rational number

(d)

may be rational or irrational

An irrational number between 2 and 2.5 is ________.

(a)

\(\sqrt { 11 } \)

(b)

\(\sqrt { 5 } \)

(c)

\(\sqrt { 2.5 } \)

(d)

\(\sqrt { 8 } \)

The number \(0.\bar { 3 } \) in the form \(\frac { p }{ q } \) where p and q are integers and \(q\neq 0\)

(a)

\(\frac { 33 }{ 100 } \)

(b)

\(\frac { 3 }{ 10 } \)

(c)

\(\frac { 1 }{ 3 } \)

(d)

\(\frac { 3 }{ 100 } \)

The value of  \(0.\bar { 23 } +0.\bar { 22 } \) is ____________

(a)

\(0.\bar { 43 } \)

(b)

0.45

(c)

\(0.4\bar { 5 } \)

(d)

\(0.\bar { 45 } \)

Find the odd one out of the following.

(a)

\(\sqrt { 32 } \times \sqrt { 2 } \)

(b)

\(\frac { \sqrt { 27 } }{ \sqrt { 3 } } \)

(c)

\(\sqrt { 72 } \times \sqrt { 8 } \)

(d)

\(\frac { \sqrt { 54 } }{ \sqrt { 18 } } \)

Represent the following as decimal form 
(i) \(\frac { -4 }{ 11 } \)
(ii) \(\frac { 11 }{ 75 } \)

Convert the following decimal numbers in the form of \(\frac { p }{ q } (p,q\in Z\ and\ q\neq 0)\)
(i) \(0.\overline { 3 } \)
(ii) \(2.\overline { 124 } \)
(iii) \(0.4\overline { 5 } \)
(iv) \(0.5\overline { 68 } \)

Can we write 0.25 as 0.250000 ...? Can a terminating decimal be written as a recurring decimal?

Express the following decimal expression into rational numbers. 0.86

Express the following decimal expression into rational numbers \(17.2\overline { 15 } \)

Find the decimal expansion of \(\sqrt { 3 } \)

Find any two irrational numbers between \(\sqrt { 2 } \) and \(\sqrt { 3 } \)

Express the rational number \(\frac { 1 }{ 33 } \) in recurring decimal form by using the recurring decimal expansion of \(\frac { 1 }{ 11 } \). Hence write \(\frac{71}{33}\) in recurring decimal form