Don't think about equations first, think about the rules-of-thumb for the method that's most appropriate. You can get the equations from a book or Wikipedia.
Probably the biggest partition in the data you described is understanding that nominal scale is for group numbers for which there is no mathematical relationship between groups: cereal types (A=cheerios, B=fruit loops, C=grape nuts), or trucks (A=chevy, B=dodge, C=ford). Next, you can measure anything within the groups to obtain continuously-scaled results, i.e. for cereal groups (concentration of sugar in cereal, particle size, etc.) or truck(gas mileage, weight, length, etc.) and then compare e.g. averages of these measurements between the groups.
Everything you stated really boils down to the first question that's always asked by a statistician: "How are the data distributed?" This question requires knowing about nominal, ordinal, interval, continuous scales and several discrete (binomial, Poisson) and continuous (normal, Student's t, chi-square, F-ratio, uniform) probability distributions because any method used commonly depends on the probability distribution which is most appropriate given the data (variable). So first, you have to know the various probability distributions.
Next, the main types of analysis (inferential tests of hypotheses) for the above are typically:
A. categorical data analysis: based on counts (frequencies); ideal for nominal data, example is chi-squared contingency table analysis.
B. methods which employ continuously-scaled data: equality of means testing, association (correlation, covariance), dependency and prediction, (regression,classification), etc. However, ordinal and interval data can be used here as well.
If you're interested in digit precision for numbers like age=32, weight=23.1769 pounds, protein concentration=1.24E-07 (decimal precision), then you have to focus on measurement accuracy, which has nothing to do with equations. Also, 32 is a positive integer, 23.1769 is a real-valued number with 4 digit decimal precision, sqrt(2) is an irrational number, the fraction 1/3=0.333333333..... has never-ending digit precision, etc. -- and these are types of numbers defined by mathematics.
So there you go: your initial question requires knowing about probability distributions, scales of outcomes, inferential hypothesis testing, and types of numbers. Would recommend reading an introductory level textbook on statistics or biostatistics (e.g. Pagano) and then ramp up to foundations/intermediate level textbooks (e.g. Rosner). You can't focus on only equations, but rather need to be like a stone mason or brick layer who knows the materials and correct sequence of work required to build a walkway or a brick wall.