Geometry.

The first clocks were sundials, which worked by putting a line on the ground. As soon as you comparing two different lines on the ground, you are doing geometry to represent time.

When you start messing around with geometry, you need an easy way to describe the angle of an equilateral triangle. 1/6th of a circle, or 1/3rd of a line. Trying to represent 1/3 or 1/6th in base 10 is fugly. Trying to divide a circle into 10 equal sections is just as fugly.

Dividing a circle into 6 equal sections is trivial: after you draw the circle with your compass, walk the compass around the perimeter. You have just inscribed a hexagon.

You're still missing the angle of 1/4 of a circle: the angles of a square. Those are pretty important in geometry as well. It's fairly trivial to draw another 6 points between the first 6 on your circle.

We use a 12-hour clock because of basic geometry. The 360-degree circle is the bastard child of basic geometry and a base-10 number system.

The decimalization of money is its own fun history, with a lot of different countries undergoing their own transitions at different times.

The Spanish dollar, which was the world reserve currency in its heyday, was divided into 8 reals (see how pirates used to refer to money in the form of "pieces of eight") but issues with the supply of silver led to the introduction of the lesser real de vellón, which eventually settled at 20 to the dollar after over 100 years of uncertainty and confusion.