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in Number System by (33.1k points)
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Write the following numbers in \(\frac p{q}\) form. 

i. 0.555 

ii. \(29.\overline{568}\)

1 Answer

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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

∴ \(x=\frac{29539}{999}\) 

∴ \(29.\overline{568}\) \(\frac{29539}{999}\)

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