The coefficients of a truncated Legendre series are usually used in multigroup cross-section sets to describe the angular distribution for a group-to-group scattering event. Discrete ordinates codes use the truncated Legendre series because this representation of the scattering angle can be used with the addition theorem to conveniently treat the scattering source term. However, the truncated Legendre series has inherent disadvantages for Monte Carlo calculations. In this paper, we examine the truncated Legendre series representation, a discrete angle representation, a step function representation, and an exact representation that is applicable for isotropic scattering in the center-of-mass system. The three approximate representations use the coefficients of a truncated Legendre series as a working base. We show in a sample problem that the step function representation has advantages for multigroup Monte Carlo calculations, and we recommend its inclusion as an option in multigroup codes.