Editing Number line (section)

==Extensions of the concept==
===Logarithmic scale===
{{main|Logarithmic scale}}
[[Image:LogLog exponentials.svg|thumb|A log-log plot of ''y''&nbsp;=&nbsp;''x''&nbsp;(blue), ''y''&nbsp;=&nbsp;''x''<sup>2</sup>&nbsp;(green), and ''y''&nbsp;=&nbsp;''x''<sup>3</sup>&nbsp;(red).<br />Note the logarithmic scale markings on each of the axes, and that the log&nbsp;''x'' and log&nbsp;''y'' axes (where the logarithms are 0) are where ''x'' and ''y'' themselves are 1.]]

On the number line, the distance between two points is the unit length if and only if the difference of the represented numbers equals 1. Other choices are possible. 

One of the most common choices is the ''logarithmic scale'', which is a representation of the ''positive'' numbers on a line, such that the distance of two points is the unit length, if the ratio of the represented numbers has a fixed value, typically 10. In such a logarithmic scale, the origin represents 1; one inch to the right, one has 10, one inch to the right of 10 one has {{nowrap|1=10×10 = 100}}, then {{nowrap|1=10×100 = 1000 = 10<sup>3</sup>}}, then {{nowrap|1=10×1000 = 10,000 = 10<sup>4</sup>}}, etc. Similarly, one inch to the left of 1, one has {{nowrap|1=1/10 = 10<sup>–1</sup>}}, then {{nowrap|1=1/100 = 10<sup>–2</sup>}}, etc.

This approach is useful, when one wants to represent, on the same figure, values with very different [[order of magnitude]]. For example, one requires a logarithmic scale for representing simultaneously the size of the different bodies that exist in the [[Universe]], typically, a [[photon]], an [[electron]], an [[atom]], a [[molecule]], a [[human]], the [[Earth]], the [[Solar System]], a [[galaxy]], and the visible Universe.

Logarithmic scales are used in [[slide rule]]s for multiplying or dividing numbers by adding or subtracting lengths on logarithmic scales.
[[File:slide rule example3.svg|frame|center|The two logarithmic scales of a slide rule]]

===Combining number lines===
A line drawn through the origin at right angles to the real number line can be used to represent the [[imaginary number]]s. This line, called [[imaginary line (mathematics)|imaginary line]], extends the number line to a [[complex number plane]], with points representing [[complex number]]s.

Alternatively, one real number line can be drawn horizontally to denote possible values of one real number, commonly called ''x'', and another real number line can be drawn vertically to denote possible values of another real number, commonly called ''y''. Together these lines form what is known as a [[Cartesian coordinate system]], and any point in the plane represents the value of a pair of real numbers. Further, the Cartesian coordinate system can itself be extended by visualizing a third number line "coming out of the screen (or page)", measuring a third variable called ''z''. Positive numbers are closer to the viewer's eyes than the screen is, while negative numbers are "behind the screen"; larger numbers are farther from the screen. Then any point in the three-dimensional space that we live in represents the values of a trio of real numbers.