In converting 10 inches to centimeters, what unit (omit the number) would you place in the numerator of your ratio?

  centimeters

Step-by-step explanation:

The numerator of the conversion factor always has the "to" units. The denominator has the "from" units. That way, when you multiply, the "from" units cancel:

  (xx from) · (yy to)/(zz from) = xx·yy/zz · (from/from) · to = xx·yy/zz · to

Here, you want to convert to centimeters, so centimeters will be the units in the numerator.

  10 in · (2.54 cm)/(1 in) = 25.4 cm

The conversion factor is always "1". That is, the numerator and denominator are always equal in value. Here, 2.54 cm = 1 in, so (2.54 cm)/(1 in) = 1. You can multiply by 1 anytime you like. For units conversion, it only has the effect of changing the units.