Question

express of the Infinity repeating decimal in the form of decimal in the form of a/b is 0.154 . question number e

Answer 1

Let x be 0.154 ( bar on 54 ).
x = 0.1545454........ - ( i )

Multiplying 10 on both sides :

10x = 1.545454........ - ( ii )

Multiplying 10 to both sides :

100 x = 15.4545454....... - ( iii )

Multiplying 10 again on both sides :

1000 x = 154.545454........ - ( iv )

Eq ( iv ) - ( ii )

1000 x - 10x = 154.54 (bar on 54) - 1.54 (bar on 54 )

990 x = 153
x = 153/990

Hence , 0.154 ( bar on 54 ) can be written as 153/990 in a/b form.