Is this precision is a weighted average precision?
In general, precision is independent of accuracy. The algorithm can be precise but inaccurate, and it also can be accurate but imprecise. This depns on the performance of the algorithm. For more information, have a look at this link:
Precision tells you how accurate you are in predicting positives. With accuracy being low, did you check if recall is acceptable or not. You might have relatively higher false negatives. In general, it is acceptable as long as excess False negatives do not add significant cost.