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ScientificNotationThreshold
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ScientificNotationThreshold

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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)Summary of the most common use cases

This number is shown by default in scientific notation:

In[1]:=1
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https://wolfram.com/xid/0d2nbj0uvjx84t0sv3ceht-ow107i

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

In[2]:=2
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https://wolfram.com/xid/0d2nbj0uvjx84t0sv3ceht-pniixh

This number is shown by default in scientific notation:

In[1]:=1
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https://wolfram.com/xid/0d2nbj0uvjx84t0sv3ceht-r4wegd

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

In[2]:=2
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https://wolfram.com/xid/0d2nbj0uvjx84t0sv3ceht-nwtvrb

Scope  (2)Survey of the scope of standard use cases

Use ScientificNotationThreshold with NumberForm:

In[1]:=1
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https://wolfram.com/xid/0d2nbj0uvjx84t0sv3ceht-svic02
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0d2nbj0uvjx84t0sv3ceht-xmvcml

ScientificForm:

In[3]:=3
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https://wolfram.com/xid/0d2nbj0uvjx84t0sv3ceht-mhg1t1
In[4]:=4
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https://wolfram.com/xid/0d2nbj0uvjx84t0sv3ceht-mot2wc

DecimalForm:

In[5]:=5
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https://wolfram.com/xid/0d2nbj0uvjx84t0sv3ceht-bnmlfp
In[6]:=6
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https://wolfram.com/xid/0d2nbj0uvjx84t0sv3ceht-l80xzj

AccountingForm:

In[7]:=7
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https://wolfram.com/xid/0d2nbj0uvjx84t0sv3ceht-lzc7b8
In[8]:=8
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https://wolfram.com/xid/0d2nbj0uvjx84t0sv3ceht-ny0vc8

EngineeringForm:

In[9]:=9
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https://wolfram.com/xid/0d2nbj0uvjx84t0sv3ceht-polot2
In[10]:=10
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https://wolfram.com/xid/0d2nbj0uvjx84t0sv3ceht-oqm0gw

PaddedForm:

In[11]:=11
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https://wolfram.com/xid/0d2nbj0uvjx84t0sv3ceht-9h1eow
In[12]:=12
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https://wolfram.com/xid/0d2nbj0uvjx84t0sv3ceht-564jly

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

In[1]:=1
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https://wolfram.com/xid/0d2nbj0uvjx84t0sv3ceht-uv1haj
Out[1]=1

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

In[2]:=2
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https://wolfram.com/xid/0d2nbj0uvjx84t0sv3ceht-yr4g3a
Out[2]=2

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

In[3]:=3
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https://wolfram.com/xid/0d2nbj0uvjx84t0sv3ceht-wqb37g
Out[3]=3

Properties & Relations  (1)Properties of the function, and connections to other functions

The functions related to NumberForm have different defaults for ScientificNotationThreshold:

In[1]:=1
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https://wolfram.com/xid/0d2nbj0uvjx84t0sv3ceht-i4wo41
In[2]:=2
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https://wolfram.com/xid/0d2nbj0uvjx84t0sv3ceht-iahldm
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0d2nbj0uvjx84t0sv3ceht-e617wb
Out[3]=3
Wolfram Research (2017), ScientificNotationThreshold, Wolfram Language function, https://reference.wolfram.com/language/ref/ScientificNotationThreshold.html.
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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.

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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.

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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

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

BibTeX

@misc{reference.wolfram_2025_scientificnotationthreshold, author="Wolfram Research", title="{ScientificNotationThreshold}", year="2017", howpublished="\url{https://reference.wolfram.com/language/ref/ScientificNotationThreshold.html}", note=[Accessed: 06-June-2025 ]}

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@misc{reference.wolfram_2025_scientificnotationthreshold, author="Wolfram Research", title="{ScientificNotationThreshold}", year="2017", howpublished="\url{https://reference.wolfram.com/language/ref/ScientificNotationThreshold.html}", note=[Accessed: 06-June-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_scientificnotationthreshold, organization={Wolfram Research}, title={ScientificNotationThreshold}, year={2017}, url={https://reference.wolfram.com/language/ref/ScientificNotationThreshold.html}, note=[Accessed: 06-June-2025 ]}

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@online{reference.wolfram_2025_scientificnotationthreshold, organization={Wolfram Research}, title={ScientificNotationThreshold}, year={2017}, url={https://reference.wolfram.com/language/ref/ScientificNotationThreshold.html}, note=[Accessed: 06-June-2025 ]}