Read it aloud: three dollars and sixty-nine cents and nine tenths, the price of a gallon of gasoline.

The decimal-positional system can be tweaked in various ways. This hybrid notation is decimal, but not positional, or maybe half-positional. Its decimal-positional counterpart would be 3.699 (if you like approximations, this is almost indistinguishable from a price of three point seven. Your wallet won’t notice the difference.)

So, 9/10 of what? Of a cent, that is 9 thousandths of a dollar. One can try to improve (improve?) this notation in various ways.

3/10. 6/10 9/10 9/10

three tenths of a ten dollar bill, plus six tenths of a dollar, plus nine tenths of a dime, plus nine tenths of a cent

Try also: 3. 699/1000 (three dollars and six hundred ninety nine thousandths of a dollar).

Try some hybrids (the fractional notation in the second position only, say).

The whole point of this innovation in design is to keep your eye away from the approximation. You read three point six, and you pay three point seven: the extra dime is the price for your cognitive inattention.

Still, there is something deeply intuitive about the fraction in the last position.