Editing Scientific notation (section)

=== Normalized notation ===
{{main|Normalized number}}
Any real number can be written in the form {{gaps|''m''|e=''n''}} in many ways: for example, 350 can be written as {{val|3.5E2}} or {{val|35E1}} or {{val|350E0}}.<!-- "Any given real number" includes irrational numbers, which can't be represented exactly. It also includes rational numbers, sometimes requiring recurring decimal representation, e.g., 1/3 = 1.333333... -->

In ''normalized'' scientific notation (called "standard form" in the United Kingdom), the exponent ''n'' is chosen so that the [[absolute value]] of ''m'' remains at least one but less than ten ({{nowrap|1 ≤ {{abs|''m''}} < 10}}). Thus 350 is written as {{val|3.5E2}}. This form allows easy comparison of numbers: numbers with bigger exponents are (due to the normalization) larger than those with smaller exponents, and subtraction of exponents gives an estimate of the number of [[orders of magnitude]] separating the numbers.  It is also the form that is required when using tables of [[common logarithm]]s. In normalized notation, the exponent ''n'' is negative for a number with absolute value between 0 and 1 (e.g. 0.5 is written as {{val|5E-1}}). The 10 and exponent are often omitted when the exponent is 0. For a series of numbers that are to be added or subtracted (or otherwise compared), it can be convenient to use the same value of ''m'' for all elements of the series.

Normalized scientific form is the typical form of expression of large numbers in many fields, unless an unnormalized or differently normalized form, such as [[engineering notation]], is desired. Normalized scientific notation is often called '''[[exponentiation|exponential]] notation''' – although the latter term is more general and also applies when ''m'' is not restricted to the range 1 to 10 (as in engineering notation for instance) and to [[radix|base]]s other than 10 (for example, {{gaps|3.15|base=2|e=20}}).