# Terminology of different number representations

## Background:

I am writing an article and trying to find the proper words/terms for different representations of numbers. The article is regarding calculating the SIN, COS and TAN of a number of angles without getting decimal numbers because the "other" form is better for calculations when these are used in other formulas.

Here are two examples:

Two square roots of two can be written in the following two ways:

First: $$2\sqrt 2$$

Second (floating point/decimal): $$2.82842712475$$

## Question

The second example is a decimal number.

What is the name for the representation of two square root of two in the first example?

Thanks!

• Additionally, "simplest radical form" also seems to be an answer. – varlogtim May 20 '18 at 22:00
• One should note that 2\sqrt 2 \neq 2.82842712475$. – Shalop May 20 '18 at 22:23 • Another form:$\sqrt{8}$– Hurkyl May 20 '18 at 23:19 ## 2 Answers When we write$2\sqrt{2}\$ it's simply referred to the exact form.

• Another option would be "symbolic". – Henning Makholm May 20 '18 at 21:36
• Thanks Sean! This is the google search I needed! :) Just to add to this, a few definitions I read of "exact form" were that an "exact number" has a certain value, it cannot be simplified, and there are an infinite amount of significant digits. – varlogtim May 20 '18 at 21:37

In the case of the values of trigonometric functions that can be expressed symbolically, what you have is an algebraic expression (also called radical), which is a special case of a closed-form expression.

https://en.wikipedia.org/wiki/Closed-form_expression#Comparison_of_different_classes_of_expressions