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In this paper we show that numerous patterns exist in the properties of theconvergents formed by truncating the Continued Fraction Expansion (CFE) of theChampernowne Constant in base 10 (C10) immediately before the High Water Marks(HWMs). From these patterns, we have formulated conjectures that may be used topredict the first position in C10 that is incorrect as calculated by theconvergent, the error of the convergent, the denominator of the convergent, andthe number of digits of C10 that are required to give the correct numerator ofthe convergent. The numerator and denominator then provide a very efficientmethod for calculating the CFE coefficients. In addition, we have formulated aconjecture that predicts the exact length in decimal digits of each of the HWMcoefficients of C10 for HWM numbers greater than 3. Furthermore, it isconjectured that the lengths of certain other large coefficients that appear inthe CFE of C10 are related to the lengths of the HWMs and a formula is givenfor this relationship. We designate these other large coefficients 2ndGeneration HWMs, or Child HMWs. It is shown that 3rd, 4th, etc., GenerationHWMs also exist. A conjecture regarding the structure and exact length of thedenominators of the 2nd Generation HWM Convergents is presented. Finally, atable is presented that shows the Coefficient Numbers and the lengths of the3rd and 4th Generation coefficients up to but not including HWM number 12.

On the High Water Mark Convergents of Champernowne's Constant in Base Ten