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Ancient Babylonians divided days sexagesimally meaning in fractions of 1/60. They measured days by 6 subdivisions (1/60 x 1/60 x 1/60 etc.) to measure units of time as small as 2 milliseconds. Hellenistic astronomers also divided days sexagesimally but also used a mean hour (1/24).
Please see the related link for the answer. In brief, now we use multiples of 10. The Egyptians used a multiple of 60. This has been adopted since, as far as I believe.
Because somebody decided to call one-sixtieth of a minute, one second. Earlier on, somebody decided to call one-sixtieth of an hour, one minute. Guess why there are exactly twenty-four hours in a day!
It is thought that there are 60 seconds in a minute because we have inherited measures based on 60 (the sexagesimal system) from the Sumerians, who developed it around 2,000 B.C.

The sexagesimal system is used in both astronomical measurements (degrees, minutes and seconds of angle) and time measurements because these are historically connected, from when time was measured by the motion of the sun and the stars.

60 was probably originally used by the Sumerians because it is a number that can be divided many different ways, by 2, 3, 4, 5 and 6, and also by 10, 12, 15, 20 and 30.

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Q: Why are there sixty seconds in a minute?
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