Question

Express 0.254 5454 dotdotdot as fraction in simplest form

Answer 1

stepwise answer is given

Answer 2

Let x = 0.25454545 . . . . . (a)


Multiply eqn (a) by 10


10 x = 10 x 0.25454545 . . . .


10 x = 2.54546454 . . . .eqn (1)


Multiply eqn (a) by 100


1000 x = 1000 x 0. 2545454 ....


1000 x = 254.545454 .... eqn (2)

Substract equation 2 from 1


I.e

1000 x = 254.545454 ....
10 x = 2.545454 ....
______________________
990 x = 252.0

Therefore

x = 252/990 Cancel using 2 table



x = 126/495 Cancel using 3 table

x = 42/ 165 Cancel using 3 table

x = 14/ 55


Hope it helps