A regular number, also called a finite decimal, is a positive real number that has a terminating decimal expansion.
A number such as 
which is not regular is said to be nonregular.
If 
is a regular number, then
 |  |  |
(1)
|
 |  |  |
(2)
|
 |  |  |
(3)
|
where 
is a nonnegative integer, 
is a positive integer,
and 
,
, ..., 
are decimal digits. Canceling
common factors gives
 |
(4)
|
where 
is a positive integer, 
and 
are nonnegative integers,
and the fraction is reduced
(Havil 2003, p. 25). Conversely, every reduced
fraction of this form has a terminating decimal
expansion.
The denominators of the first few regular unit fractions are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, ... (OEIS A003592),
which have decimal expansions 1, 
, 
, 
, 
, 
, 
, 
, 
, 
, 
, 
, ....
For the reduced fraction above, the number of decimal digits after the decimal
point in its shortest terminating expansion
is 
(Wells 1986, p. 60). In particular, this number is 0 for a positive
integer. Excluding denominator 1, the numbers
of these digits in the regular unit
fractions are 1, 2, 1, 3, 1, 4, 2, 2, 5, 3, 2, 6, 4, 2, 3, ... (OEIS A117920).
