The inch is defined in centimetres
Since the international yard and pound agreement of 1959, one inch is exactly 2.54 centimetres. That is not a measured approximation that might be refined later — it is the definition, agreed by the United States, United Kingdom, Canada, Australia, New Zealand and South Africa to end decades of national inches that disagreed in the sixth decimal place. Every conversion on this page is therefore exact arithmetic, not an estimate.
Why the answer is also shown as a fraction
A decimal inch is correct and frequently useless. Tape measures, drill sets, spanners and timber are marked in binary fractions — halves, quarters, eighths, sixteenths — so an answer of 11.811 inches has to be translated before you can cut anything. The fraction row does that translation, rounding to the nearest sixteenth, which is the finest gradation on a standard tape.
Rounding to a sixteenth introduces at most about 0.8 mm of error. For joinery that is usually invisible; for machining it is not, which is why engineering drawings stay in decimal inches or thousandths.
The approximations people use
The common mental shortcut is to divide centimetres by 2.5, which overstates the answer by about 1.6% — fine for judging whether a parcel fits a shelf, poor for anything cumulative. Over a 200 cm span the shortcut is out by more than an inch. The other familiar rule, that 30 cm is about a foot, is closer than it looks: 30 cm is 11.811 inches, so a 30 cm ruler is a shade under a real foot.