Question

What is `0.66666...` as a fraction?

Answer 1

`6/10` or `6/99`

Explanation:

I would say from your sentence the possible fractions is;

`6/99`

Which gives the repeated sequence of `6`

That's for geometric progression in finding the least fraction..

But in converting the decimal `0.6` into fraction is following due process..

`0.6`, `rArr6` there is representing tenth, in other words its `6/10`

Hence,

`0.6 = 6/10 -> "As a fraction"`

But with `6` as a repeating fraction is `6/99`

Answer 2

`0.66666... = 2/3`

Explanation:

I think you intended `0.66666...` which can be written `0.bar(6)`

In which case see what happens when we multiply by `10`:

`10 * 0.66666... = 6.66666...`

So if we subtract the original, we get an integer. That is:

`(10 - 1) * 0.66666.... = 6.66666... - 0.66666... = 6`

Dividing both ends by `(10-1)` we find:

`0.66666... = 6/(10-1) = 6/9 = 2/3`