Question

What is the fraction `6/11` written as a decimal?

Answer 1

`6/11=0.bar(54)`

Explanation:

One way to determine this is by long division:

`color(white)("XXX"11)ul(color(white)("xx")0 .color(white)("x")5color(white)("x")4color(white)("x")5color(white)("x")4color(white)("x")....)`
`color(white)("XXX")11)color(white)("x")6. color(white)("x")0color(white)("x")0color(white)("x")0color(white)("x")0color(white)("x")....`
`color(white)("XXXXxX")ul(5color(white)(."x")5`
`color(white)("XXXXXXxX")5color(white)("x")0`
`color(white)("XXXXXXxX")ul(4color(white)("x")4`
`color(white)("XXXXXXXXX")6color(white)("x")0`
`color(white)("XXXXXXXXX")ul(5color(white)("x")5`
`color(white)("XXXXXXXXXX")5color(white)("x")0`
`color(white)("XXXXXXXXXX")ul(4color(white)("x")4`
`color(white)("XXXXXXXXXXX")6color(white)("x")0`

...and as we can see, the pattern `54` will continue forever.