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ScientificNotationThreshold

is an option for NumberForm and related functions that specifies the threshold between the use of decimal notation and scientific notation to represent real numbers.

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ScientificNotationThreshold

ScientificNotationThreshold

is an option for NumberForm and related functions that specifies the threshold between the use of decimal notation and scientific notation to represent real numbers.

Details

  • The setting ScientificNotationThreshold{min,max} for integer values min<max indicates that a real number x will be represented in decimal form in base b if bmin≤|x|<bmax, or in scientific form otherwise.

Examples

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Basic Examples  (2)

This number is shown by default in scientific notation:

Wolfram Language code: NumberForm[1234567.89]

Increase the upper threshold to 109 to show it still in decimal form:

Wolfram Language code: NumberForm[1234567.89, ScientificNotationThreshold -> {-5, 9}]

This number is shown by default in scientific notation:

Wolfram Language code: NumberForm[-0.0000001234]

Decrease the lower threshold to 10-8 to show it still in decimal form:

Wolfram Language code: NumberForm[-0.0000001234, ScientificNotationThreshold -> {-8, 6}]

Scope  (2)

Use ScientificNotationThreshold with NumberForm:

Wolfram Language code: p = 0.987654321{10 ^ -8, -10 ^ -4, 1, -10 ^ 4, 10 ^ 8}
Wolfram Language code: NumberForm[p, ScientificNotationThreshold -> {-3, 2}]

ScientificForm:

Wolfram Language code: ScientificForm[p]
Wolfram Language code: ScientificForm[p, ScientificNotationThreshold -> {-6, 7}]

DecimalForm:

Wolfram Language code: DecimalForm[p]
Wolfram Language code: DecimalForm[p, ScientificNotationThreshold -> {-6, 7}]

AccountingForm:

Wolfram Language code: AccountingForm[p]
Wolfram Language code: AccountingForm[p, ScientificNotationThreshold -> {-3, 2}]

EngineeringForm:

Wolfram Language code: EngineeringForm[p]
Wolfram Language code: EngineeringForm[p, ScientificNotationThreshold -> {-6, 5}]

PaddedForm:

Wolfram Language code: PaddedForm[p]
Wolfram Language code: PaddedForm[p, ScientificNotationThreshold -> {-3, 2}]

For any base b, positive real numbers larger than b-5 and smaller than or equal to b6 are typeset in decimal form:

Wolfram Language code: Options[NumberForm, ScientificNotationThreshold]

These are pairs {b6-1,b6} for bases b from 2 to 17, showing the threshold at exponent 6:

Wolfram Language code: NumberForm[BaseForm[N[{# ^ 6 - 1, # ^ 6}], #], 8]& /@ Range[2, 17]//Column

Raising the threshold to exponent 7 makes powers b6 be displayed in decimal form, for all bases:

Wolfram Language code: NumberForm[BaseForm[N[{# ^ 6 - 1, # ^ 6}], #], 8, ScientificNotationThreshold -> {-5, 7}]& /@ Range[2, 17]//Column

Properties & Relations  (1)

The functions related to NumberForm have different defaults for ScientificNotationThreshold:

Wolfram Language code: forms = {AccountingForm, DecimalForm, EngineeringForm, NumberForm, PaddedForm, ScientificForm};
Wolfram Language code: OptionValue[#, ScientificNotationThreshold]& /@ forms
Wolfram Language code: Transpose[{forms, %}]//Dataset
Wolfram Research (2017), ScientificNotationThreshold, Wolfram Language function, https://reference.wolfram.com/language/ref/ScientificNotationThreshold.html.

Text

Wolfram Research (2017), ScientificNotationThreshold, Wolfram Language function, https://reference.wolfram.com/language/ref/ScientificNotationThreshold.html.

CMS

Wolfram Language. 2017. "ScientificNotationThreshold." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ScientificNotationThreshold.html.

APA

Wolfram Language. (2017). ScientificNotationThreshold. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ScientificNotationThreshold.html

BibTeX

@misc{reference.wolfram_2026_scientificnotationthreshold, author="Wolfram Research", title="{ScientificNotationThreshold}", year="2017", howpublished="\url{https://reference.wolfram.com/language/ref/ScientificNotationThreshold.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_scientificnotationthreshold, organization={Wolfram Research}, title={ScientificNotationThreshold}, year={2017}, url={https://reference.wolfram.com/language/ref/ScientificNotationThreshold.html}, note=[Accessed: 13-June-2026]}