Mathematics is a basic science, and the concept of "number" is abstract, and its "quantity" is generally expressed only by numbers, and units of measurement will be used in specific applications. For example, the ratio of 8 to 2 is 4, and the units of measurement of 8 and 2 need not be considered.

As for the length of bow and arrow, it belongs to mathematical application and needs length unit. The length of the line segment in the vector direction represents the size of the vector, which is abstract and has no unit.