Traditional decision theory assumes that people use precise representations of involved probabilities and outcomes to evaluate options, but observed behavior seems much less precise. Khaw et al. (2020) take an essential step by introducing imprecision into modeling decision-making. Specifically, their model assumes that people mentally form imprecise representations of numerosity after seeing a number, and such inexact number representations result in small-stake risk aversion and stochastic choices simultaneously. This project aims to provide empirical evidence for this model. Package 1 adopts cognitive load manipulation, designed to occupy subjects' cognitive resources and thus make their number representations noisier, to test whether treated subjects' choices become more risk-averse and random. Related studies show that the acuity of mental number representations is determined by approximate numeracy, a numerical competence that contains two separate elements. Package 2 randomly assigns two treatments (brain stimulation and brain training) to subjects to enhance these two elements respectively and then tests the hypothesis that the treated subjects should behave more risk-neutrally and consistently while further comparing the relative role of these two elements of approximate numeracy in decision-making. Finally, Package 3 studies whether and how noisy number representations lead to violations of stochastic dominance and tests two treatments' effects on the violations.