A numerical characteristic of large random numbers is studied. Let F be a distribution on the real numbers with infinite endpoint. X denotes a random variable with distribution F. Consider the transformation for a decimal number d(1)d(2)d(3) ... d(n).d(n+1) ... in [10(n-1), 10(n)) to 0.d(2)d(3) ... in [0, 1). We are interested in the distribution of transformed X for large X, which implies the behavior of the large random number except the first figure. It is shown that the distribution of transformed X conditioned by the first figure converges as X becomes large for most distributions. Moreover, it turns out that the limit distribution depends on the tail behavior of F and the first figure. A similar problem for distributions with finite endpoints is also considered. In this case, the distance until the endpoint is a matter of concern and parallel results to the ones for infinite endpoint case are given.