How the conversion works
A foot is 12 inches, and an inch is exactly 2.54 cm. So 6 ft 8 in is 6 × 12 + 8 = 80 inches, and 80 × 2.54 = 203.2 cm. Nothing is rounded: because the inch is defined as 2.54 cm, a height in whole or half inches always comes out in centimeters with two decimals at most.
Asked the other way round: How tall is 80 inches in feet? Rounded to the nearest centimeter: How tall is 203 cm in feet?
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