* Know the relationship: There are 10 mm (millimeters) in 1 cm (centimeter).

* Set up a fraction: We want to find the fraction of 1 cm that 6 mm represents. So, the fraction is 6 mm / 1 cm.

* Convert to the same unit: Since we want a fraction of centimeters, we need to convert millimeters to centimeters. Divide 6 mm by 10 mm/cm to get 0.6 cm.

* Simplify the fraction: The fraction becomes 0.6 cm / 1 cm.

* Result: The fractional part of 1 cm that 6 mm represents is 6/10 or 3/5.