The use of continued fractions as an important tool in number theory began with 17^th century results of Schwenter, Huygens and Wallis and came to maturity with the work of Euler in 1737 and the subsequent use of continued fractions as a number theoretic tool by Lagrange, Legendre, Gauss, Galois and their successors. In this paper, we will find the continued fraction representation of quotients of different powers of consecutive numbers between 2 and 10.