In a newer version of WordPress (3.8.3) the version number wasn't anywhere in plain sight on the dashborad for some reason (someone might have changed something on the site that I had to fix), but the WordPress logo in the upper left corner leads to an about page which says WordPress 3.8.3 (or the one you have) in huge letters.
This question might be 2 years old, but it's quite high on google, so I thought that if I drop this answer here, someone else might find it useful. After all, I got here after searching for an answer for this very question.