Small number

Within a set positive numbers, a number is small if it is close to zero. A number is smaller if it is less than another number.

Within a set of positive and negative numbers there is ambiguity, because being closer to zero does not correspond to being less, but to being less in absolute value. Depending on context a negative number may be called "smaller" if it is closer to zero, or if it is more negative.

This article deals with positive numbers, and is also applicable to negative numbers by taking the absolute value.

Small numbers are numbers that are small compared with the numbers used in everyday life. Very small numbers often occur in fields such as chemistry, electronics and quantum physics.

As soon as systems of weights and measures were devised, units were subdivided into smaller units: pounds were divided into ounces, pounds into shillings and pence. Beyond the smallest units, there was a need to use vulgar fractions to represent even smaller quantities. In systems such as the degrees-minutes-seconds system, it is possible to represent one second of arc, equal to

of a circle.

Even smaller numbers are often found in science, which are so small that they are not easily dealt with using fractions. Scientific notation was created to handle very small and very large numbers.

Examples of small numbers describing everyday real-world objects are:

Other small numbers are found in particle physics and quantum physics:

Extremely small numbers can be described through their reciprocals, extremely large numbers. The notation is similar, with a minus sign at the first level of exponents, e.g.

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