The article considers a model for determining the correct numbers when performing arithmetic operations and calculating analytical functions. At the output of the model there are received an exact number of correct digits as a result of operations with inaccurate numbers. Applied astronomical problems used to study the model can be solved by using tools that, due to errors in floating point calculations, receive inaccurate numbers. The lack of control over the correct digits can lead to setting an underestimated value of the argument in the output methods resulting in a loss of the correct digits or to an excessive value of the argument which creates the illusion of high accuracy. Inaccurate numbers that are used in different operations in the astronomical problems get the exact quantitative values of the correct numbers with the help of the proposed model and can get rid of dubious numbers that do not contribute to the accuracy of the result. Formulas for determining the number of correct digits are considered, with and without taking into account the first significant digits. The research may be directed to further extension of the model for complex calculations of non-analytical functions.