When I compute a number where an approximation is needed but no accuracy is specified, I usually scan the first few digits and if I find a zero, then I truncate the decimals before the first zero. For example, when a number is $$0.3893600616808018504240555127216653816499614494988434849653045489,$$ I wrote the result as approximately $0.38936$.
I understand that there is a zero probability that this algorithm is not well-defined. For example, when the number is equal to $\frac{1}{3}=0.333\ldots$.
But in practice, is there a (possibly informal) name for this process (when it is defined)?