Due to resource constraint of WSNs, it may be unnecessary or impossible to provide full coverage in many applications. Instead, partial coverage is enough to satisfy user requirements. Meanwhile, by applying partial coverage, network lifetime can be prolonged remarkably which is a primary goal of WSNs. In this paper, we investigate the p-Percent Coverage Problem which only requires that p% of the whole area to be monitored at any time and the Connected p-Percent Coverage Problem which enforces connectivity in addition. We propose two algorithms. One is pPCA which is a greedy algorithm to solve the p-Percent Coverage Problem. The other is CpPCA-CDS, which is a total distributed algorithm based on Connected Dominating Set to address Connected p-Percent Coverage Problem. The Sensing Void Distance after using CpPCA-CDS can be bounded by a constant. Theoretical analysis as well as simulation results are provided to evaluate our algorithms.