Question

Show 0.14285142857.....=1/7

Answer 1

Answer:

x = 0.1428514285....... ....( 1 )

Here , we have five repeating digits after the decimal point. So, we multiply both side of ( 1 ) by 10^5 = 100000 to get

10000x = 14285.14285..... ... ( 2 )

Subtracting ( 1 ) from ( 2 ) , we get

100000x - x =(14285.14284..)-(0.1428514..)

99999x = 14285.0000...

or, x = 14285/99999

or, x = 1/7