Express the following in the form  \({p\over q},\)  where p and q are integers and q \(\ne\) 0.
\(0.2\overline{45}\)

Without actual division classify the decimal expansion of the following numbers as terminating or non-terminating and recurring.
\({17\over 200}\)

Express the following in the form 3ⁿ: 243

Use a fractional index to write \(\left( 5\sqrt { 125 } \right) ^{ 7 }\)

Express the surds in the simple form \(\sqrt { 27 } \)

Express the surds in the simple form \(\sqrt [ 3 ]{ 128 } \)

Find any five rational numbers between
(i) \(\frac { 1 }{ 4 } \) and \(1\over 5\)
(ii) 0.1 and 0.11
(iii) -1 and -2

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) \(0.5\overline { 68 } \)

Find whether x and y are rational or irrational in the following
(i) a = 2 + \(\sqrt { 3 } \) , b = 2 - \(\sqrt { 3 } \) ; x = a + b, y = a+ b
(ii) a = \(\sqrt { 2 } \)  + 7, b = \(\sqrt { 2 } \) - 7 ; x = a + b, y = a - b
(iii) a = \(\sqrt { 75 } \), b = \(\sqrt { 3 } \), x = ab, y = \(\frac { a }{ b } \)
(iv) a = \(\sqrt { 18 } \), b = \(\sqrt { 3 } \), x = ab, y = \(\frac { a }{ b } \)

Verify that 1 = \(0.\overline { 9 } \)

Convert the following rational numbers into decimal
(i) \(3\over 4\)
(ii) \(5\over 8\)
(iii) \(9\over 25\)

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

We used to write \(\pi\) as \(\frac{22}{7}.\) Can we say \(\pi\) is a rational number?

Create a word problem whose solution is an irrational number.

Find any 3 irrational numbers between 0.12 and 0.13.