a computer - executable ratiometric analysis method determines integer components of a rational number ratio or a close approximation of an irrational number ratio . in one embodiment the method uses a ratio of rotational speeds of two rotating assets in a machine or process , generates a new rational number based on the ratio of speeds , and calculates the integer components of the new rational number . the result is the integer ratio relationship between the initial two rational numbers . the method may be used in machinery analysis applications to determine whether a low - order integer ratio relationship exists between two machinery rotating components . low - order integer ratio relationships in machinery are generally harmful in related machinery rotating components , and detection of such relationships is an important tool in preventing damage to machinery components . in a more general embodiment the algorithm can be used to determine the closest integer roots of any fractional number where this information would be of interest to an analyst in understanding the fractional number .