inci sözlüğün aynştaynını seçiyoruz beyler

a physical quantity can be expressed as the product of a number and a physical unit. a formula expresses a relationship between physical quantities. a necessary condition for a formula to be valid is that all terms have the same dimension, meaning every term in the formula could be potentially converted to contain the identical unit (or product of identical units).
in the example above, for the volume of a sphere, we may wish to compute with r = 2.0 cm, which yields

there is vast educational training about retaining units in computations, and converting units to a desirable form, such as in units conversion by factor-label.
however, the vast majority of computations with measurements is done in computer programs with no facility for retaining a symbolic computation of the units. only the numerical quantity is used in the computation. this requires that the universal formula be converted to a formula that is intended to be used only with prescribed units, meaning the numerical quantity is implicitly assumed to be multiplying a particular unit. the requirements about the prescribed units must be given to users of the input and the output of the formula.
for example suppose the formula is to require that , where tbsp is the u.s. tablespoon (as seen in conversion of units) and vol is the name for the number used by the computer. similarly, the formula is to require . the derivation of the formula proceeds as:

given that , the formula with prescribed units is

the formula is not complete without words such as: "vol is volume in tbsp and rad is radius in cm". other possible words are "vol is the ratio of v to tbsp and rad is the ratio of r to cm."
the formula with prescribed units could also appear with simple symbols, perhaps even the identical symbols as in the original dimensional formula:

and the accompanying words could be: "where v is volume (tbsp) and r is radius (cm)".
if the physical formula is not dimensionally homogeneous, and therefore erroneous, the falsehood becomes apparent in the impossibility to derive a formula with prescribed units. it would not be possible to derive a formula consisting only of numbers and dimensionless ratios.