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One hand is 101.6 mm, exactly four inches, and the subdivision is base 4 — so 62 inches is 15.2 hands and 15.5 hands is impossible.
The hand is a non-SI unit standardised to four inches (101.6 mm), used to measure the height of horses in many English-speaking countries. The fixed length is what makes conversion from centimetres exact.
The subdivision of the hand is base 4, not decimal. A horse measuring 62 inches is 15.2 hands, because 15 × 4 + 2 = 62. The notation 15.5 hands is an impossible value, since the inches after the point only run 0, 1, 2 and 3.
The hand was standardised at four inches by a statute of King Henry VIII, the Horses Act 1540. That statute is the reason the modern figure is 101.6 mm rather than some other traditional length.
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To convert a height in centimetres, divide by 10.16 to get hands and a decimal fraction, then read the fraction back into inches using the base-4 rule. A horse of 162 cm is about 15.9 hands, which is written 15.3.
The same rule applies in reverse. A horse listed at 16.0 hands is 64 inches, or about 162.6 cm, while a horse at 14.2 hands is 58 inches, or about 147.3 cm.
Beginners most often go wrong by reading the fraction as a decimal. Treating 15.2 as 15.2 tenths of a hand gives the wrong height; the correct reading is 15 hands and 2 inches.
Further reading