Question

Write the following number in `p/q` form.

0.555 

Answer 1

0.555

= `(0.555xx1000)/(1xx1000)`

= `555/1000`

`= (5xx111)/(5xx200)`

`= 111/200`

Answer 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`