Number of Repeating Digits in Base b Expansion of Fractions

numerator

1

size

10

color scheme

DarkBands

In base 10 the fraction 1/3 has 1 repeating digit, 3, while 1/7 has 6 repeating digits: {

1,

4,

2,

8,

5,

7

}. This plot shows the number of repeating digits in the base

b

representation of a fraction with a specified numerator and with denominators from 1 up to a specified size for bases

b=2

to a specified size.