We study the quality of approximation of a given number $x\in[0,1]$ by its integer base expansion. We prove the Jarnik type theorem about approximation with base $b$ convergents. Further, we compare the rate of approximation of integer base expansions with continued fraction expansions, as the latter is known to provide the best approximations in a certain sense. We introduce an integer-base Diophantine exponent and show that it can differ from the well-known irrationality exponent coming from approximation by $b^n$.