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Mathematics frequency table is a graph that is used for data value. This makes it easier for things to be graded.
A double number line is very similar to a ratio table in that you use them to solve problems requiring proportions. The ratio table is more flexible in that you do not need to position the numbers in the "correct" position. If you google using models in realistic mathematics education you will find references to these and ideas how they might be used in the classroom
The present value annuity formula is used to simplify the calculation of the current value of an annuity. A table is used where you find the actual dollar amount of the annuity and then this amount is multiplied by a value to get the future value of that same annuity.
Ratios are used to compare numbers. When you're working with ratios, it's sometimes easier to work with an equivalent ratio.
Pi is an irrational number, meaning that it cannot be written as the ratio of two integers (fractions such as 22/7 are commonly used to approximate pi; no common fraction (ratio of whole numbers) can be its exact value).