101st digit of a period-200 reciprocal

University · ●●●○○ 50 pts

Let

p

be a prime number such that the period of the decimal expansion of

\frac{1}{p}

is 200. That is,

\frac{1}{p}=0.XXXX\ldots

for some block

X

of 200 digits, but

\frac{1}{p}\neq 0.YYYY\ldots

for every block

Y

with fewer than 200 digits. Find the 101st digit, counting from the left, of

X