Adding to the answer of @ilanman, yes, you can certainly use correlation between a percentage and a numerical variable.
If (some of) the percentages are close to zero% or 100%, though, there could be an "saturation effect". Lets say the variables are
x, and there is really some (causal) connection between
perc, say, which we could have modelled via a logistic regression model. Then the linear relationship is really between
x and the log odds corresponding to
perc. But however, the log odds function is close to linear except near the limits of zero and one, so except in some very extreme cases, the correlations calculated between
perc, and between
(logodds of perc), will be numerically very close.
And, adding to the answer of @Yash, what he shows is a very different phenomenon (and maybe more important). Such a huge difference as 0.1 and 0.9 cannot come from my explanation above, it comes from a large variation in the denominators. If his unemployment data compares countries (or maybe states in the USA), then the denominators will be population size. So his correlation of 0.1 measures correlation between GDP and % unemplyment, his correlation of 0.9 is in reality more of correlation between GDP and population! If his GDP is total (and not per capita, he did'nt specify) that is not surprising. So in that case, the two correlations of 0.1 and 0.9 really measures totally different things.