This paper deals with the problem of explaining the optimality of vague expressions in language. According to Frazee and Beaver (2010), vague terms like ``tall'' or ``many'' are vague in so far as they constrain ``some measure relative to a value which cannot be known in principle or in practice''. On their approach, in agreement with standard theories of the meaning of gradable expressions (Kennedy 2007), ``tall'' semantically means ``taller than t'', and ``many'' means ``more than m'', but speaker and hearer are typically uncertain about those threshold values t and m. What the speaker communicates, therefore, is in fact a statistical distribution over those values, and the sentence is informative when the hearer gets a better indication of the true state of affairs than prior to the utterance (see also Lassiter and Goodman 2017).The goal of this paper is to give a more specific account of the rationale for lexical vagueness in relation to speaker-uncertainty about the world, putting emphasis on the interpretation of approximator words such as ``around'' and ``about'' (Sauerland and Steva 2011). The central argument of this paper is that in cases in which the speaker is uncertain about the observation of a precise quantity, the use of a vague approximator like ``around'' provides an optimal resource for truthfulness: basically, any more precise alternative would commit the speaker either to error or to unwarranted truth. Vague expressions, more generally, may be argued to provide an optimal tradeoff between the need to be truthful and the need to be informative, given our discriminative limitations.