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* The number of digits indicates the precision. For example, {{xt|5 × 10<sup>3</sup>}} means rounded to the nearest thousand; {{xt|5.0 × 10<sup>3</sup>}} to the nearest hundred; {{xt|5.00 × 10<sup>3</sup>}} to the nearest ten; and {{xt|5.000 × 10<sup>3</sup>}} to the nearest unit. | * The number of digits indicates the precision. For example, {{xt|5 × 10<sup>3</sup>}} means rounded to the nearest thousand; {{xt|5.0 × 10<sup>3</sup>}} to the nearest hundred; {{xt|5.00 × 10<sup>3</sup>}} to the nearest ten; and {{xt|5.000 × 10<sup>3</sup>}} to the nearest unit. | ||
===Uncertainty and rounding | ===Uncertainty and rounding=== | ||
* Where explicit uncertainty information (such as a [[margin of error]]) is available and appropriate for inclusion, it may be written in various ways: | * Where explicit uncertainty information (such as a [[Wikipedia:Margin of error|margin of error]]) is available and appropriate for inclusion, it may be written in various ways: | ||
: • {{xt|(1.534 ± 0.035) × 10<sup>23</sup> m}} | : • {{xt|(1.534 ± 0.035) × 10<sup>23</sup> m}} | ||
: • {{xt|12.34{{nbsp}}m<sup>2</sup> ± 5%}} (not used with scientific notation) | : • {{xt|12.34{{nbsp}}m<sup>2</sup> ± 5%}} (not used with scientific notation) | ||
: • {{xt|1.604(48) × 10<sup>−4</sup> J}} (equivalent to {{xt|(1.604 ± 0.048) × 10<sup>−4</sup> J}})<ref>The number in parentheses is the numerical value of the standard uncertainty referred to the corresponding last digits of the quoted result – see [http://www.physics.nist.gov/cgi-bin/cuu/Info/Constants/definitions.html NIST – Use of concise notation]</ref> | |||
: • {{xt|1.604(48) × 10<sup>−4</sup> J}} (equivalent to {{xt|(1.604 ± 0.048) × 10<sup>−4</sup> J}})<ref>The number in parentheses is the numerical value of the standard uncertainty referred to the corresponding last digits of the quoted result – | |||
: • {{xt|Polls estimated Jones's share of the vote would be 55 percent, give or take about 3 percent}} | : • {{xt|Polls estimated Jones's share of the vote would be 55 percent, give or take about 3 percent}} | ||
* Where explicit {{em|uncertainty is unavailable}} (or is unimportant for the article's purposes) round to an appropriate number of [[Wikipedia:Significant digit|significant digits]]; the precision presented should usually be conservative. Precise values (often given in sources for formal or matter-of-record reasons) should be used only where stable and appropriate to the context, or significant in themselves for some special reason. | |||
* Where explicit {{em|uncertainty is unavailable}} (or is unimportant for the article's purposes) round to an appropriate number of [[significant | |||
: • {{xt|The speed of light is defined to be 299,792,458{{nbsp}}m/s}} | : • {{xt|The speed of light is defined to be 299,792,458{{nbsp}}m/s}} | ||
:: {{em|but}} {{xt|Particle velocities eventually reached almost two-thirds the 300-million-metre-per-second speed of light.}} | :: {{em|but}} {{xt|Particle velocities eventually reached almost two-thirds the 300-million-metre-per-second speed of light.}} | ||
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: • {{xt| At least 800 persons died in the ensuing mudslides }} (unlikely that any precise number can be accurate, even if an official figure is issued) | : • {{xt| At least 800 persons died in the ensuing mudslides }} (unlikely that any precise number can be accurate, even if an official figure is issued) | ||
:: {{em|or}} {{xt| Officials listed 835 deaths, but the Red Cross said dozens more may have gone unreported }} (in reporting conflicting information, give detail sufficient to make the contrast intelligible) | :: {{em|or}} {{xt| Officials listed 835 deaths, but the Red Cross said dozens more may have gone unreported }} (in reporting conflicting information, give detail sufficient to make the contrast intelligible) | ||
: • {{xt|The jury's award was $8.5{{nbsp}}million{{nbsp}}...}} (where the actual figure was $8,462,247.63) {{xt| ...{{snd}}reduced on appeal to $3,000,001 (one dollar in [[actual damages]], the remainder in [[punitive damages]])}} | : • {{xt|The jury's award was $8.5{{nbsp}}million{{nbsp}}...}} (where the actual figure was $8,462,247.63) {{xt| ...{{snd}}reduced on appeal to $3,000,001 (one dollar in [[Wikipedia:Actual damages|actual damages]], the remainder in [[Wikipedia:Punitive damages|punitive damages]])}} | ||
* The number of decimal places should be consistent within a list or context ({{xt|The response rates were 41.0 and 47.4 percent, respectively}}, not {{!xt|41 and 47.4 percent}}), unless different precisions are actually intended. | * The number of decimal places should be consistent within a list or context ({{xt|The response rates were 41.0 and 47.4 percent, respectively}}, not {{!xt|41 and 47.4 percent}}), unless different precisions are actually intended. | ||
* It may sometimes be appropriate to note the {{em|lack}} of uncertainty information, especially where such information is normally provided and necessary for full interpretation of the figures supplied. | * It may sometimes be appropriate to note the {{em|lack}} of uncertainty information, especially where such information is normally provided and necessary for full interpretation of the figures supplied. | ||
: • {{xt|A local newspaper poll predicted 52 percent of the vote would go to Smith, but did not publish information on the uncertainty of this estimate}} | : • {{xt|A local newspaper poll predicted 52 percent of the vote would go to Smith, but did not publish information on the uncertainty of this estimate}} | ||
* Avoid using "approximately", "about", and similar terms with figures that have merely been approximated or rounded in a normal and expected way, unless the reader might otherwise be misled. | * Avoid using "approximately", "about", and similar terms with figures that have merely been approximated or rounded in a normal and expected way, unless the reader might otherwise be misled. | ||
: • {{xt|The tallest player was 6 feet 3 inches}} ( | : • {{xt|The tallest player was 6 feet 3 inches}} (not {{!xt|... about 6 feet 3 inches}}{{snd}}heights are conventionally reported only to the nearest inch, even though greater precision may be available in principle) | ||
:: {{em|but}} {{xt|The witness said the assailant was about 5 feet 8 inches tall}} ("about" because here the precise value is unknown, with substantial uncertainty) | :: {{em|but}} {{xt|The witness said the assailant was about 5 feet 8 inches tall}} ("about" because here the precise value is unknown, with substantial uncertainty) | ||
* The reader may be assumed to interpret large round numbers ({{xt|100,000 troops}}) as approximations. Writing a quantity in words ({{xt|one hundred thousand troops}}) can further emphasize its approximate nature. | * The reader may be assumed to interpret large round numbers ({{xt|100,000 troops}}) as approximations. Writing a quantity in words ({{xt|one hundred thousand troops}}) can further emphasize its approximate nature. | ||
===Non-[[radix|base]]-10 notations=== | ===Non-[[radix|base]]-10 notations=== | ||
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