The decimal period of a repeating decimal is the number of digits that repeat. For example, 
has decimal period one, 
has decimal period two, and 
has decimal period three.
Any nonregular fraction 
is periodic and has decimal period 
independent of 
, which is at most 
digits long. If 
is relatively prime to
10, then the period 
of 
is a divisor of 
and has at most 
digits, where 
is the totient function.
It turns out that 
is the multiplicative order of 10 (mod 
) (Glaisher 1878, Lehmer 1941). The number
of digits in the repeating portion of the decimal expansion of a rational
number can also be found directly from the multiplicative
order of its denominator.
A prime 
such that 
is a repeating decimal with decimal period shared
with no other prime is called a unique prime.
