One centimetre is 0.0328083990 feet, which is a clumsy number for a reason: this conversion is almost never used as a straight decimal. In practice it is a height conversion, and heights in feet are written as feet and inches rather than as decimal feet.
About the units
The centimetre is a hundredth of a metre, and it is the unit in which most of the world states a person's height: 175 cm, 183 cm, 160 cm. The foot is a twelfth of a yard, exactly 0.3048 metres since 1959, and in the English-speaking world heights are given as a whole number of feet plus a remainder in inches. That mixed-radix notation is the real source of difficulty here. Converting 178 cm gives 5.84 feet, which is a number nobody uses — the useful answer is 5 feet 10 inches, and getting there means taking the fractional part and multiplying by twelve.
The exact factor
One foot is exactly 30.48 cm, so centimetres to feet is 1 ÷ 30.48 = 0.032808398950131..., repeating. To reach the conventional form, divide the centimetres by 30.48 to get whole feet, then multiply whatever is left over by 12 to get inches. For 178 cm: 178 ÷ 30.48 = 5.8399, so five feet, and 0.8399 × 12 = 10.08, so five feet ten inches. The rounding at the last step matters more than it looks, because an inch is 2.54 cm and rounding to the nearest inch can shift the answer by more than a centimetre.
Where you meet this conversion
Height is the dominant case by a wide margin — passports, medical records, dating profiles, sports rosters and driving licences all state it, and they switch units at national borders. Basketball and American football listings give player heights in feet and inches while the same athletes appear in centimetres in European coverage. Doorways, ceiling clearances and vehicle height restrictions are the other common encounter, and there the conversion matters practically: a 2.1 m clearance is 6 feet 11 inches, and vans have been wedged under bridges over less.