Final answer:
When solving mathematical problems with units, always use the correct number of significant figures and units, simplify the algebra, check the units cancellation, and ensure the result is reasonable.
Step-by-step explanation:
To solve a mathematical problem correctly, especially involving physical units, it's imperative to express your answers with the correct number of significant figures and proper units. Firstly, identify the equation needed for solving the problem and ensure all values are in the correct units before substituting them into the equation. This will help in obtaining a numerical solution that makes sense and has correct units, which acts as a check for errors.
Eliminate terms wherever possible to simplify the algebra involved in solving the equation. After calculating the answer, make sure the units cancel out appropriately if you're dealing with fractions. This ensures that the remaining units are those desired in the answer. Finally, always check to see if the result is reasonable given the context of the problem.