The 46th digit after the decimal in the decimal expansion of 11996 is
Choose the correct choice from the following choices
A) 0 B) 1 C) 4 D) 6 E) 8
Let dj denote the jth digit of 1/1996 after the decimal. In other words, we write   1/1996=0.d1d2d3....The problem is to determine d46. Observe that   (*)   10in45*1/1996=d1d2d3...d45d46d47...   We compute 1045 modulo 1996. Since 1996 5 = (2000 - 4) 5 = 104 -20, we get   that 104* 20 (mod 1996). Since 1996 4 = (2000- 4) 4 = 8000 - 16, we obtain   1012*(104)3 *203 * 8000*6 (mod 1996). Continuing in this manner, we get 1036 *   (1012)3* 16*212 * 4096 * 104 (mod 1996), 1044* 1036 104 104 *104 20 20 *   2080 20*84 20 * 1680 (mod 1996), and 1045 * 1044 10* 16800* 8 (1996 +   4) + 800 * 832 (mod 1996). This means that the remainder when we divide 1045 by 1996   is 832. If q denotes the quotient, we deduce that   1045/1996= q +832/1996= q.4168...   where the digits after the decimal are computed by long division. We are only interested   in the first of these, the digit 4 since it follows from () that this digit must be d46.   correct answer 4
<result>C</result>
The 46th digit after the decimal in the decimal expansion of 11996 is