Starting from the success of Glove and Word2Vec in natural language processing, continuous representations are widely deployed in many other domain of applications. These applications span over encoding textual information to modeling user and items in recommender systems, using embedding vectors to represent a large number of objects. As the cardinality of the object sets increases, the embedding components quickly become the bottleneck in training memory footprint. In this work, we focus on building a system to train continuous embeddings in low precision floating point representation. Specifically, our system performs SGD-style model updates in single precision arithmetics, casts the updated parameters using stochastic rounding and stores the parameters in half-precision floating point. Theoretically, we prove that for strongly convex objectives, our SGD-based training algorithm retains the same convergence rate up to constants. We also present a system-friendly implementation for faster random number generator that increases runtime performance by 30%. We deploy our training system to deep neural networks with low precision embedding tables for recommender systems on top of both public dataset Criteo and an internal dataset at Facebook. We empirically demonstrate that our half-precision floating point training system can achieve generalization performance matching that of single precision training system, with up to 2X memory saving and 1.2X faster training speed.