This paper presents a multiplication reduction technique through near-zero approximation, enabling embedded learning in resource-constrained IoT devices. The intrinsic resilience of neural network and the sparsity of data are identified and utilized. Based on the analysis of leading zero counting and adjustable threshold, intentional approximation is applied to reduce near-zero multiplications. By setting the threshold of the multiplication result to 2-5 and employing ReLU as the neuron activation function, the sparsity of the CNN model can reach 75% with negligible loss in accuracy when recognizing the MNIST data set. Corresponding hardware implementation has been designed and simulated in UMC 65nm process. It can achieve more than 70% improvement of energy efficiency with only 0.37% area overhead of a 256 Multiply-Accumulator array.