A unit converter is multiplying by a 1 but it is defined by units.  So multiplying by (1m)/(100cm) is numerically equation to '1' and allows you to convert from cm to m, or (100cm)/(1m) converts from m to cm.  That is the concept of a unit converter. 

Applying a unit converter does include the unit 'cm' for centimeters or 'm' for meters, simply multiply by 1/100 or 100/1 because the solver will see 'cm' as two variables multiplied together "c*m". 

Finally, since a conversion from cm^2 to m^2 leads to a value less than 1, then change the 'Calculate using:' choice to real numbers:

Click to see all the steps