Question

How do you convert 0.27 (7 being repeated) to a fraction?

Answer 1

`0.27bar7=5/18`

Explanation:

The way to write a repeating decimal is like this:

For your question `0.2bar7" or 0.27bar7` if you wish to emphasis it.

Another form of repeating decimal could be ( picked at random)
`437.234234234.... -> 437.bar234`

On The Socratic site the format is hashkey 437.bar237 hashkey

In the same way if I actually used the hash key then hash 2x^2 hash
look like: `2x^2`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Solving your question")`

Let `x=0.277bar7`
Then `10x=2.77bar7`

Then `10x-x=2.5`

`=> x(10-1)=2.5`

`x=2.5/9`

I do not like the decimal numerator so I am going to get rid of it!

1 can be written in many ways. For example, `2/2=1`

So `x" "=" "2.5/9" " =" " 2.5/9xx2/2" "=" "(2.5xx2)/(9xx2)`

`x=5/18`

So `x=0.27bar7=5/18`