left column: Decimal (base-10) digits: 0-9

right column: Hexadecimal (base-16) equivalent, digits: 0-9, A-F

`1/2 = 0.5 1/2 = 0.8`

1/4 = 0.25 1/4 = 0.4

1/8 = 0.125 1/8 = 0.2

3/4 = 0.75 3/4 = 0.C

3/8 = 0.375 3/8 = 0.6

5/8 = 0.625 5/8 = 0.A

7/8 = 0.875 7/8 = 0.E

1/16 = 0.0625 1/10 = 0.1

3/16 = 0.1875 3/10 = 0.3

5/16 = 0.3125 5/10 = 0.5

7/16 = 0.4375 5/10 = 0.7

9/16 = 0.5625 9/10 = 0.9

11/16 = 0.6875 B/10 = 0.B

13/16 = 0.8125 D/10 = 0.D

15/16 = 0.9375 F/10 = 0.F

1/32 = 0.03125 1/20 = 0.08

7/24 = 0.29166… 7/18 = 0.4AAA…

5/12 = 0.4166… 5/C = 0.6AAA…

1/3 = 0.3333… 1/3 = 0.5555…

2/3 = 0.6666… 2/3 = 0.AAAA…

1/6 = 0.1666… 1/6 = 0.2AAA…

1/64 = 0.015625 1/40 = 0.04

25/64 = 0.380625 19/40 = 0.64

1/128 = 0.0078125 1/80 = 0.02

Look at how much simpler hex is for representing fractions! This is because 16 has many more divisors than 10.

This comes from

Table 3 (p. 21) of Nystrom's 1862

*Project of a New System of Arithmetic, Weight, Measure and Coins: Proposed to Be Called the Tonal System, With Sixteen to the Base*, modified to use conventional hex digits (0-9,A-F). So as to distinguish numerals from letters, Nystrom invents his own symbols for hex's 9 & B-F and uses the symbol "9" for hex's A.