Advances in high-throughput sequencing have increased the availability of microbiome sequencing data that can be exploited to characterize microbiome community structure in situ. We explore using word and sentence embedding approaches for nucleotide sequences since they may be a suitable numerical representation for downstream machine learning applications (especially deep learning). This work involves first encoding ("embedding") each sequence into a dense, low-dimensional, numeric vector space. Here, we use Skip-Gram word2vec to embed k-mers, obtained from 16S rRNA amplicon surveys, and then leverage an existing sentence embedding technique to embed all sequences belonging to specific body sites or samples. We demonstrate that these representations are meaningful, and hence the embedding space can be exploited as a form of feature extraction for exploratory analysis. We show that sequence embeddings preserve relevant information about the sequencing data such as k-mer context, sequence taxonomy, and sample class. Specifically, the sequence embedding space resolved differences among phyla, as well as differences among genera within the same family. Distances between sequence embeddings had similar qualities to distances between alignment identities, and embedding multiple sequences can be thought of as generating a consensus sequence. In addition, embeddings are versatile features that can be used for many downstream tasks, such as taxonomic and sample classification. Using sample embeddings for body site classification resulted in negligible performance loss compared to using OTU abundance data, and clustering embeddings yielded high fidelity species clusters. Lastly, the k-mer embedding space captured distinct k-mer profiles that mapped to specific regions of the 16S rRNA gene and corresponded with particular body sites. Together, our results show that embedding sequences results in meaningful representations that can be used for exploratory analyses or for downstream machine learning applications that require numeric data. Moreover, because the embeddings are trained in an unsupervised manner, unlabeled data can be embedded and used to bolster supervised machine learning tasks.