Since 100 cm = 1 m (100 centimeter equals 1 meter), when we divide 100 cm by 1 m we get 1 as a result. Then, we can multiply a measure by this fraction (equivalent to one) without changing the measure, but converting the units.
So, let's multiply 9 m by the fraction 100cm/(1m):
[tex]9m=9m\cdot1=9m\cdot\frac{100\operatorname{cm}}{1m}=9\cdot100cm\frac{m}{m}=900\operatorname{cm}[/tex]
