is stock price a continuos random variable?

Suppose we have the possible stock value between 1 and 2. Since stock values are quoted in dollars and pennies, we can have values of 1.33, 1.34, 1.35 upto 1.99 but not 1.33333

Doesnt this make it a discrete RV rather than a continuos RV?

Question needs to be rephrased as - are stock returns CRV or DRV. That would be interesting. Absolute prices on its own has no deeper meaning.