In physics we come across expressions like ° C = 5/9 (° F - 32)
K = ° C + 273 Used for temperature conversion from one scale to other. Also we come across expressions like Velocity of a body as a function of time is $v=3t^2$. Or the displacement travelled in nth second in case of uniform acceleration is given by the expression: $$Snth =u+(1/2) (a)(2n−1).$$ Do all they need to be dimensionally correct or they are just numerical equations and not generalized physical equations which need not to be dimensionally correct? I had searched the same on net but did not find any satisfactory answers. As some sources say in displacement equation Snth t is hidden in some terms but how can something be hidden in a generalized physical equation.