Recall that 1 in. = 2.54 cm -- (1)
From RHS of (1), we have 2.54 to be expressed as 254/100 (This fraction is equivalent to 2.54)
So, the fractional unit considered in converting 15 in. to cm is 254/100, and this is simply done by multiplying 15 by 254/100 cm, i.e.
15 in. -> cm: 15 × (254/100) cm