In order to design robust and stable zone fire modeling algorithms, the numerical properties of computer arithmetic and the modeling differential equations must be understood. This report examines some of these properties and provides tools for their analysis. Many sets of differential equations for zone fire modeling can be derived using the conservation of mass and energy. A comparison between various possible formulations is made in terms of numerical properties. One property that many formulations possess is the presence of multiple time scales. Pressures equilibrate much faster than other quantities such as density and temperature. Numerically, this property is known as stiffness. Stiffness, in the context of fire modeling, and numerical methods for handling it are discussed.