In more detail
Since 1959 the inch has been defined as exactly 2.54 cm, so a foot (12 inches) is exactly 30.48 cm. To convert feet and inches to centimetres, turn everything into inches first and multiply by 2.54: 5 ft 9 in is 69 inches, or 175.26 cm. To go the other way, divide centimetres by 2.54, then split the inches into whole feet and the remainder: 175 cm is 68.9 inches, which is 5 ft 8.9 in.
Why it matters
Height feeds into BMI (body mass index), dosage, clothing and equipment sizing, so a conversion slip changes the result. The common trap is decimal feet: 5.9 ft is not 5 ft 9 in but 5 ft 10.8 in, because a foot has 12 inches, not 10. Rounding too early also adds error; keep the full value until the last step.
Example
6 ft 0 in = 72 in × 2.54 = 182.88 cm
180 cm = 180 / 2.54 = 70.87 in = 5 ft 10.87 in
5.9 ft = 5.9 × 12 = 70.8 in = 5 ft 10.8 in = 179.83 cm
5 ft 9 in = 69 in × 2.54 = 175.26 cm
Reading "5.9 ft" as 5 ft 9 in would give 175.26 cm instead of 179.83 cm, an error of about 4.6 cm.