Practice Dimensional Consistency in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
The principle that every term added or equated in a valid equation must share the same physical dimensions or units.
You can't add meters to seconds — dimensionally inconsistent equations don't make physical sense.
Example 1
easyIs the equation v = d + t (velocity = distance + time) dimensionally consistent?
Example 2
mediumCheck: E = mc^2 where E is energy (kg·m²/s²), m is mass (kg), c is speed (m/s).
Example 3
easyIs A = l + w a valid formula for area?
Example 4
mediumIn the equation x^2 + 3x = 10 (where x is in meters), are all terms dimensionally consistent?