Any rational number can be expressed as a repeating decimal. The length of the repeating segment is called the period of the decimal. So 1/7 = 0.142857142857... has period 6, while 1/11 = 0.9090909... has period 2.
What prime numbers have reciprocals with period five or less? This problem can be tackled crudely with a computer, but a technology-free solution is also possible.