Problem
NT-B1-M11-P011 Period of a Fraction
#11
★★☆☆☆ Level 2 of 5
Find the period length of \(\frac{1}{11}\).
Use \(10\equiv-1\pmod{11}\).
Since \(10 ot\equiv1\pmod{11}\), but \(10^2\equiv1\pmod{11}\), the order of \(10\) modulo \(11\) is \(2\). Thus the period is \(2\).
Link between periods and order.