In fact, we use both systems. I surely don’t have to explain the use of the decimal system. However, the use of the duodecimal system, i.e. counting to the base of 12, is hidden in our everyday life. When we are measuring or expressing time intervals, we do so by dividing 1 h by 60 to obtain minutes. For further accuracy we divide the minute again by 60 and call it a second. This division by 60 is in fact based on the duodecimal system, e.g. 5*12=60. If we want to measure time intervals below 1 second, we switch back to the decimal system.
The origin of the decimal system is due to the ten fingers, that each human has. But the numbers 12 and 60 are also present on our hands. If we use our thumb to count the single digits of all four of the remaining fingers, we can count to 12. After that we can use one finger of the other hand to indicate that we’ve already counted to 12 once. If we proceed in this manner, we can count up to 12 digits * 5 fingers, which sums up to 60.
During the french revolution, the supporters of the decimal system set the base for todays SI-unit system. Some purists among them even used decimal clocks and weeks consisting of 10 days.
Nowadays, nearly worldwide the decimal system is used. However, there are quite a few people that support the usage of the duodecimal system, as the number of divisors for 12 is higher, than for 10. 12 has 1,2,3,4,6 and 12 as divisors, whereas 10 only has 1,2,5 and 10. They propose that, when changing to the duodecimal system, mathematics would remain the same, but everyday applications would be easier. One third would not be expressed as 0.3333, but as a convenient 0.4.
– Georges Ifrah: Universalgeschichte der Zahlen, Glb Parkland, Cologne, 1998.