One hour is exactly 60 minutes. The sixty is not a decimal accident that history failed to clean up — it is a deliberate inheritance from Babylonian mathematics, and it has survived every attempt to replace it.
About the units
The division of the hour into sixty parts comes from the sexagesimal number system used in Mesopotamia from around 2000 BC. Sixty was chosen because it has twelve divisors — 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60 — which makes thirds, quarters, fifths and sixths all come out as whole numbers. Decimal time has been tried and rejected: revolutionary France introduced a ten-hour day with 100-minute hours in 1793, mandated it in 1794, and abandoned it in 1795 after the public simply refused. The clocks made for it are museum pieces. The hour itself has no natural basis at all; it is a twenty-fourth of a day by convention.
The exact factor
The factor is exactly 60, and both directions are exact. The divisibility is what makes the unit useful in practice: a third of an hour is 20 minutes, a quarter is 15, a fifth is 12, and a sixth is 10 — all whole numbers, where a decimal hour would give 33.33, 25, 20 and 16.67. That property is why scheduling, transport timetables and billing in tenths of an hour coexist without much friction. Note that decimal hours do appear in payroll and legal billing, where 1.5 hours means 90 minutes and 1.25 means 75 — and reading 1.30 as an hour and a half is the standard error there.
Where you meet this conversion
Everywhere, but the conversion is worth attention in payroll and project time tracking, where hours are recorded as decimals and worked in minutes. A timesheet showing 7.75 hours means 7 hours 45 minutes, and reading it as 7:75 or 7:45 gives different answers, only one of which is right. Cooking times, exercise durations and travel schedules all move between the two. Aviation and maritime logs record time in hours and decimal fractions rather than minutes precisely to avoid the mixed-radix arithmetic.