An excellent point Audioguru.The datasheet for the CD4511 LED driver shows that its output high is not to the supply voltage but is about 1V less than the supply voltage so calculate the current-limiting resistors with that in mind.
Looking at the Fairchild datasheet, the typical output is roughly 0.4V below Vcc. Thus,
9 - 0.4 = 8.6V (output voltage of 4511 to segments)
Then,
8.6 - 2.1 = 6.5V (voltage we need resistor to take up)
6.5 = 0.012 x R
R = ~542Ω
So a typical value to use would be either 510Ω or 560Ω.
You may opt to "play" with a few different values until you're happy with the display. The calculations give you an idea of where you should be so you don't damage anything. For instance, if you need the display really bright, the display datasheet says the segments can accept 20mA. You could then use a resistor as low as 325Ω (330Ω is a typical value), but nothing less than that.
Also note you can sharpen the display by putting a colored piece of plastic over the digits. A dark transparent red sheet 0.010" in thickness would work well or a piece of dark red acrylic ~1/8" thick. This helps hide the unlit segments and really makes the display "pop". You'll notice a piece of colored plastic over a digital alarm clock display for this reason.