Question

Question #a1e8f

Answer 1

`0.6bar(12) = 101/165`

Explanation:

Let `x = 0.6bar(12)`

Note that the repeating portion of the decimal is `2` digits long, so we multiply `x` by `10^2 = 100`.

`100x = 61.2bar(12)`

`=> 100x-x = 61.2bar(12)-0.6bar(12)`

`=> 99x = 61.2-0.6`

`=> 99x = 60.6`

`=> 99x = 606/10`

`=> x = 606/10 * 1/99`

`:. x = 101/165`

For a detailed approach to general questions of this type, see this question.

Answer 2

`101/165`

Explanation:

Note that `0.6bar(12)` is the same as `0.612121212...`

Let `x=0.6bar(12)`

Then `10x=6.121212...`

and `1000x=612.121212...`

So `1000x-10x= 612.121212...`
`" "ul(color(white)(61)6.121212...) larr" subtract"`
`" "1000x-10x=606.000000.....`

`=>x(1000-10)=990x=606`

`=>x=606/990 = 101/165`