# Thread: Calculating the period of a decimal

1. ## Calculating the period of a decimal

Find the delay and period of $\frac{60}{336}$.

How I started:

$\frac{60}{336}=\frac{5}{2^2 \cdot 7}$.

Hence the delay $\mu=\max \{0,2 \}=2$.

I've run into a bit of a problem when I try and find the delay.

I need to find n s.t $10^n=1 \bmod 7$.

Comparing this to Euler's theorem $\Rightarrow n= \phi(7)=6\Rightarrow \nu=6.$.

My mark scheme also agrees with this result. However, can it always be done in this way? ie. will the delay always be reduced to $10^n=1 \bmod p$ where p is prime?

2. you are talking about period..right.