i. 0.555= \(\frac{0.555\times1000}{1\times1000}\) =\(\frac{555}{1000}\) = \(\frac{5\times111}{5\times200}\) = \(\frac{111}{200}\)
ii. Let x = \(29.\overline{568}\)…(i)
x = 29.568568…
Since, three numbers i.e. 5, 6 and 8 are repeating after the decimal point.
Thus, multiplying both sides by 1000,
1000x = \(29568.\overline{568}\)…(ii)
Subtracting (i) from (ii),
1000x – x =\(29568.\overline{568}\) - \(29.\overline{568}\)
∴ 999x = 29539
∴ \(x=\frac{29539}{999}\)
∴ \(29.\overline{568}\) \(\frac{29539}{999}\)