Editing Scientific notation (section)

{{Short description|Concise notation for large or small numbers}}
{{About|a numeric notation|the musical notation|Scientific pitch notation}}
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'''Scientific notation''' is a way of expressing [[real numbers|numbers]] that are too large or too small to be conveniently written in [[decimal form]], since to do so would require writing out an inconveniently long string of digits. It may be referred to as '''scientific form''' or '''standard index form''', or '''standard form''' in the United Kingdom. This [[base ten]] notation is commonly used by scientists, mathematicians, and engineers, in part because it can simplify certain [[arithmetic operations]]. On [[scientific calculators]], it is usually known as "SCI" display mode.

{| class="wikitable" style="float:right; margin:5px;"
!Decimal notation
!Scientific notation
|-
|{{val|2}}
|{{val|2E0}}
|-
|{{val|300}}
|{{val|3E2}}
|-
|{{val|4321.768}}
|{{val|4.321768E3}}
|-
|{{val|−53000}}
|{{val|-5.3E4}}
|-
|{{val|6720000000}}
|{{val|6.72E9}}
|-
|{{val|0.2}}
|{{val|2E-1}}
|-
|{{val|987}}
|{{val|9.87E2}}
|- 
|{{val|0.00000000751}}
|{{val|7.51E-9}}
|}
In scientific notation, nonzero numbers are written in the form 
{{block indent | em = 1.5 | text = ''m'' × 10{{sup|''n''}}}}
or ''m'' times ten raised to the power of ''n'', where ''n'' is an [[integer]], and the [[coefficient]] ''m'' is a nonzero [[real number]] (usually between 1 and 10 in absolute value, and nearly always written as a [[decimal|terminating decimal]]). The integer ''n'' is called the [[exponent]] and the real number ''m'' is called the ''[[significand]]'' or ''mantissa''.<ref name="Calio_2017"/> The term "mantissa" can be ambiguous where logarithms are involved, because it is also the traditional name of the [[fractional part]] of the [[common logarithm]]. <!-- These are actually floating-point terms, not scientific notation. --> If the number is negative then a minus sign precedes ''m'', as in ordinary decimal notation. In [[#Normalized notation|normalized notation]], the exponent is chosen so that the [[absolute value]] (modulus) of the significand ''m'' is at least 1 but less than 10.

[[Decimal floating point]] is a computer arithmetic system closely related to scientific notation.