Math Help - missing digits in decimal expansion

Are there any interesting irrational numbers whose decimal expansions have no 9s in them. Certainly one can construct such a number (take the square root of two in base 9. The onlydidgits will be 0-8. Then declare it to be in base 10. The number will still be irrational, and will only have digits 0-8. But do such numbers ever arise outside of this context?

I'm not sure what you mean by "outside this context". What "context" are you talking about?

One common example of an irrational number that does NOT have a "9" in its decimal expansion is where there is "another 0" between each pair of "1"s.