Ensuring computations are unit-wise consistent is an important task in software development. Numeric computations are usually performed with primitive types instead of abstract data types, which results in very weak static guarantees about correct usage and conversion of units. This paper presents PUnits, a pluggable type system for expressive units of measurement types and a precise, whole-program inference approach for these types. PUnits can be used in three modes: (1) modularly check the correctness of a program, (2) ensure a possible unit typing exist, (3) annotate a program with units. Annotation mode allows human inspection and is essential since having a valid typing does not guarantee that the inferred specification expresses design intent. PUnits is the first units type system with this capability. Compared to prior work, PUnits strikes a novel balance between expressiveness, inference complexity, and annotation effort. We implement PUnits for Java and evaluate it by specifying the correct usage of frequently used JDK methods. We analyzed 234k lines of code from eight open-source scientific computing projects with PUnits, which inferred 87 scientific units and generated well-specified applications. The experiments show that PUnits provides an effective, sound, and scalable alternative to using encapsulation-based units APIs (like javax.measure), enabling Java developers to reap the performance benefits of using primitive types instead of abstract data types for unit-wise consistent scientific computations.