Question

Someone please help im stuck on this question

Answer 1

`(91)/(22)`

Explanation:

Given: 4.1363636...

Let x=4.1363636...

We can see number 36 ( 2 digit repeating ) so we will multiply it by 100

On multiplying both sides by 100

100x=100*4.1363636...

100x=413.63636 .....

We can write it in term of x

100x=x+409.5

On subtracting both sides by x

100-x=409.5

99x = 409 .5

On dividing both sides by 99

x=
`(409.5)/(99)`

x=
`(4095)/(990)`

x=
`(819)/(198)`

On dividing both number by 9

x=
`(91)/(22)`

Therefore, x =
`(91)/(22)`

Answer 2

Explanation:

x = 4.13636363

100x = 413.636363

100x - x = 413.636363 - 4 .13636363

99x = 409.5

x = 409.5 / 99