The ratio of a single case is 1.
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A crude odds ratio is the probability that a case preceeded the control in regard to exposure and history.
The ratio of girls to boys in this case would be 10:1
Case number would be nominal scale; the number has no meaning.
It is not always the case. If you are out in the cold with insufficient clothing, the important thing - to prevent hypothermia - is to MINIMISE the surface to volume ratio.
A fraction is a ratio of two quantities which are measured in the same units. In a simple case, average speed is the ratio between the distance travelled and the time taken. However, the speed is not a fraction of wither the distance nor of the time.