Express the following decimal expression into rational numbers. \(0.\overline { 24 } \)

Express the following decimal expression into rational numbers. \(2.\overline { 327 } \)

Express the following decimal expression into rational numbers \(3.1\overline { 7 } \)

Express the following decimal expression into rational numbers \(0.\overline { 0001 } \)

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

Locate an irrational number between two rational numbers\(\frac { 23 }{ 10 } \) and\(\frac { 12 }{ 5 } \)

Identify the type of numbers needed to solve the simple equations given here. Question 1 and 2 are solved for you, as examples. (Perhaps -the number systems developed gradually depending on the needs of 'answers' during such problem solving!)

S.No	Equation	Solution	Type of number in the solution
1	x - 7 = 17	x = 24	Natural number
2	x + 5 = 5	x = 0	Whole number
3	x + 1 = 9
4	x + 9 = 1
5	7x = 19
6	5x = -3
7	x2 - 2 = 0

If \(\sqrt{2}\) =1.414, \(\sqrt{3}\) = 1.732, \(\sqrt{5}\) = 2.236, \(\sqrt{10}\) = 3.162 then find the values of the following correct to 3 places of decimals.
(i) \(\sqrt { 40 } -\sqrt { 20 } \)
(ii) \(\sqrt { 300 } -\sqrt { 90 } -\sqrt { 8 } \)

Can you get a rational number when you compute
(i) the sum of two surds
(ii) the difference of two surds
(iii) the product of two surds
(iv) the quotient of two surds
Justify each answer with an example.

Represent the following numbers in scientific notation:
(i) (300000)² \(\times\) (20000)⁴
(ii) (0.000001)¹¹ ÷ (0.005)³
(iii) \( \{ (0.00003 ) ^{ 6 }\times (0.00005)^{ 4 }\} \div \{ (0.009)^{ 3 }\times (0.05)^{ 2 }\} \)