Question

Write 2.3181818... as a mixed number.

Answer 1

Assuming the pattern continues, let
`x=2.3181818\ldots=2.3\overline{18}`.

Then
`10x=23.\overline{18}` and
`1000x=2318.\overline{18}`, and we have

`1000x-10x=990x=2295\implies x=(2295)/(990)=(51)/(22)`

Since
`51=2\cdot22+7`, we can write
`x` as the mixed number
`2+\frac7{22}`.

Answer 2

x =
`(51)/(22)`.

Explanation:

Given : 2.3181818...

To find : write as a mixed number.

Solution : We have given that

2.3181818...

Let x = 2.3181818...

We can see the number 18 is repeating 18181818......

So, the bar line is over the two digit 18

`x = 2.318.....`.

On multiplying the number both side by 100.

`100x = 100 * 2.318.....`.

100x = 231.81818.....

We can write the number 231.81818..... in term of x

100x = 229 .5 + x

On subtracting both sides by x

100x -x = 229.5

99x = 229.5

On dividing both sides by 99.

x =
`(229.5)/(99)`.

x =
`(2295)/(990)`.

x =
`(459)/(198)`.

x =
`(51)/(22)`.

Therefore, x =
`(51)/(22)`.