As one of the cornerstones of computing, dynamic random-access memory (DRAM) is prevalent across digital systems. Over the years, researchers have proposed modifications to DRAM macros or explored alternative uses of existing DRAM chips to extend the functionality of this ubiquitous media. This work expands on the latter, providing new insights and demonstrating new functionalities in unmodified, commodity DRAM. FracDRAM is the first work to show how fractional values can be stored in off-the-shelf DRAM. We propose two primitive operations built with specially timed DRAM command sequences, to either store fractional values to the entire DRAM row or to masked bits in a row. Utilizing fractional values, this work enables more modules to perform the in-memory majority operation, increases the stability of the existing in-memory majority operation, and builds a state-of-the-art DRAM-based PUF with unmodified DRAM. In total, 582 DDR3 chips from seven major vendors are evaluated and characterized under different environments in this work. FracDRAM breaks through the conventional binary abstraction of DRAM logic, and brings new functions to the existing DRAM macro.