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Question
Write the following number in `p/q` form.
0.555
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Solution 1
0.555
= `(0.555xx1000)/(1xx1000)`
= `555/1000`
`= (5xx111)/(5xx200)`
`= 111/200`
Solution 2
0.555... = 0.5
Let, x = \[\ce{0.\overset{\bullet}{5}}\]
In this, only one digit 5 is recurring. Therefore, multiplying both sides by 10,
∴ 10x = \[\ce{0.\overset{\bullet}{5}}\]
∴ 10x - x = \[\ce{5.\overset{\bullet}{5} - \ce{0.\overset{\bullet}{5}}}\]
∴ 9x = 5
∴ x = `5/9`
∴ 0.555... = `5/9`
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