order of magnitude

• 桁

関

digit、order

WordNet

1. one of the elements that collectively form a system of numeration; "0 and 1 are digits" (同)figure
2. a finger or toe in human beings or corresponding body part in other vertebrates (同)dactyl
3. make a request for something; "Order me some flowers"; "order a work stoppage"
4. bring order to or into; "Order these files"
5. established customary state (especially of society); "order ruled in the streets"; "law and order"
6. place in a certain order; "order the photos chronologically"
7. a degree in a continuum of size or quantity; "it was on the order of a mile"; "an explosion of a low order of magnitude" (同)order_of_magnitude
8. the act of putting things in a sequential arrangement; "there were mistakes in the ordering of items on the list" (同)ordering
9. (architecture) one of original three styles of Greek architecture distinguished by the type of column and entablature used or a style developed from the original three by the Romans
10. a group of person living under a religious rule; "the order of Saint Benedict" (同)monastic order
11. a commercial document used to request someone to supply something in return for payment and providing specifications and quantities; "IBM received an order for a hundred computers" (同)purchase order
12. a body of rules followed by an assembly (同)rules of order, parliamentary law, parliamentary procedure
13. (biology) taxonomic group containing one or more families
14. (often plural) a command given by a superior (e.g., a military or law enforcement officer) that must be obeyed; "the British ships dropped anchor and waited for orders from London"
15. a request for something to be made, supplied, or served; "I gave the waiter my order"; "the companys products were in such demand that they got more orders than their call center could handle"
16. issue commands or orders for (同)prescribe, dictate
17. give instructions to or direct somebody to do something with authority; "I said to him to go home"; "She ordered him to do the shopping"; "The mother told the child to get dressed" (同)tell, enjoin, say
18. the property of relative size or extent (whether large or small); "they tried to predict the magnitude of the explosion"; "about the magnitude of a small pea"
19. relative importance; "a problem of the first magnitude"
20. having a systematic arrangement; especially having elements succeeding in order according to rule; "an ordered sequence"
21. logical or comprehensible arrangement of separate elements; "we shall consider these questions in the inverse order of their presentation" (同)order, ordination

PrepTutorEJDIC

1. (手足の)指 / アラビア数字(0から9までの一つ;0を除くこともある)
2. 〈C〉《しばしば複数形で》『命令』,指図,指令 / 〈U〉(物事の)『順序』,順番 / 〈U〉(自然界の)『秣序』 / 〈U〉(社会の)治安,秣序 / 〈U〉整頓(せいとん)された状態,きちんとしていること《good,badなどを伴って》(一般に物事の)調子, 状態 / 〈U〉(商品などの)『注文』《+『for』+『名』》 / 〈C〉調文品 / 〈C〉(レストランなどでの料理の)一盛り / 〈C〉種類,等級,品資(kind, sort) / 〈C〉(動植物分類の)目(もく) / 〈C〉聖職者の階級;《複数形で》聖職 / 〈C〉《しばしばO-》教団,教派;(ある特殊な)社会 / 〈C〉《しばしばO-》勲位,勲章 / 〈C〉(古代ギリシャの)建築様式,柱式 / …‘を'『命令する』,指図する;〈人〉‘に'命令する / 《方向を表す副詞[句]を伴って》〈人〉‘に'行くように命じる / 〈商品など〉‘を'『注文する』;…‘を'あつらえる / …‘を'整頓(せいとん)する,きちんとする / 命令する;注文する
3. 《所有・所属》…『の』,…のものである,…に属する・《材料・要素》…『でできた』,から成る・《部分》…『の』[『中の』] ・《数量・単位・種類を表す名詞に付いて》…の・《原因・動機》…『で』,のために(because of) ・《主格関係》…『の』,による,によって・《目的格関係》…『を』,の・《同格関係》…『という』・《関係・関連》…『についての』[『の』],の点で・《抽象名詞などと共に》…の[性質をもつ] ・《『It is』+『形』+『of』+『名』+『to』 doの形で,ofの後の名詞を意味上の主語として》・《分離》…『から』・《起原・出所》…『から』[『の』](out of) ・《『名』+『of』+『a』(『an』)+『名』の形で》…のような・《『名』+『of』+『mine』(『yours, his』など独立所有格)の形で》…の…・《時》(1)《副詞句を作って》…に《形容詞句を作って》…の・《時刻》《米》…前(to,《米》before)
4. 『大きさ』,規模 / 『重要さ』(importance);(精神的な)偉大さ,高潔 / (星の)光度,等級 / マグニチュード(地震の強さなどの数量的単位)
5. 整然とした,規則正しい

Wikipedia preview

出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2013/05/21 22:25:29」(JST)

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An order of magnitude is the class of scale or magnitude of any amount, where each class contains values of a fixed ratio to the class preceding it. In its most common usage, the amount being scaled is 10 and the scale is the (base 10) exponent being applied to this amount (therefore, to be an order of magnitude greater is to be 10 times as large). Such differences in order of magnitude can be measured on the logarithmic scale in "decades" (i.e. factors of ten).

The order of magnitude of a physical quantity is its magnitude in powers of ten when that physical quantity is expressed in powers of ten with one digit to the left of decimal.

"We say two numbers have the same order of magnitude of a number if the big one divided by the little one is less than 10. For example, 23 and 82 have the same order of magnitude, but 23 and 820 do not." - John Baez

Use

Orders of magnitude are generally used to make very approximate comparisons, and reflect very large differences. If two numbers differ by one order of magnitude, one is about ten times larger than the other. If they differ by two orders of magnitude, they differ by a factor of about 100. Two numbers of the same order of magnitude have roughly the same scale: the larger value is less than ten times the smaller value.

In words (long scale)	In words (short scale)	Prefix	Symbol	Decimal	Power of ten	Order of magnitude
quadrillionth	septillionth	yocto-	y	0.000,000,000,000,000,000,000,001	10−24	−24
trilliardth	sextillionth	zepto-	z	0.000,000,000,000,000,000,001	10−21	−21
trillionth	quintillionth	atto-	a	0.000,000,000,000,000,001	10−18	−18
billiardth	quadrillionth	femto-	f	0.000,000,000,000,001	10−15	−15
billionth	trillionth	pico-	p	0.000,000,000,001	10−12	−12
milliardth	billionth	nano-	n	0.000,000,001	10−9	−9
millionth	millionth	micro-	µ	0.000,001	10−6	−6
thousandth	thousandth	milli-	m	0.001	10−3	−3
hundredth	hundredth	centi-	c	0.01	10−2	−2
tenth	tenth	deci-	d	0.1	10−1	−1
one	one	–	–	1	100	0
ten	ten	deca-	da	10	101	1
hundred	hundred	hecto-	h	100	102	2
thousand	thousand	kilo-	k	1,000	103	3
million	million	mega-	M	1,000,000	106	6
milliard	billion	giga-	G	1,000,000,000	109	9
billion	trillion	tera-	T	1,000,000,000,000	1012	12
billiard	quadrillion	peta-	P	1,000,000,000,000,000	1015	15
trillion	quintillion	exa-	E	1,000,000,000,000,000,000	1018	18
trilliard	sextillion	zetta-	Z	1,000,000,000,000,000,000,000	1021	21
quadrillion	septillion	yotta-	Y	1,000,000,000,000,000,000,000,000	1024	24

The order of magnitude of a number is, intuitively speaking, the number of powers of 10 contained in the number. More precisely, the order of magnitude of a number can be defined in terms of the common logarithm, usually as the integer part of the logarithm, obtained by truncation. For example, the number 4,000,000 has a logarithm (in base 10) of 6.602; its order of magnitude is 6. When truncating, a number of this order of magnitude is between 10⁶ and 10⁷. In a similar example, with the phrase "He had a seven-figure income", the order of magnitude is the number of figures minus one, so it is very easily determined without a calculator to be 6. An order of magnitude is an approximate position on a logarithmic scale.

An order-of-magnitude estimate of a variable whose precise value is unknown is an estimate rounded to the nearest power of ten. For example, an order-of-magnitude estimate for a variable between about 3 billion and 30 billion (such as the human population of the Earth) is 10 billion. To round a number to its nearest order of magnitude, one rounds its logarithm to the nearest integer. Thus 4,000,000, which has a logarithm (in base 10) of 6.602, has 7 as its nearest order of magnitude, because "nearest" implies rounding rather than truncation. For a number written in scientific notation, this logarithmic rounding scale requires rounding up to the next power of ten when the multiplier is greater than the square root of ten (about 3.162). For example, the nearest order of magnitude for 1.7 × 10⁸ is 8, whereas the nearest order of magnitude for 3.7 × 10⁸ is 9. An order-of-magnitude estimate is sometimes also called a zeroth order approximation.

An order-of-magnitude difference between two values is a factor of 10. For example, the mass of the planet Saturn is 95 times that of Earth, so Saturn is two orders of magnitude more massive than Earth. Order-of-magnitude differences are called decades when measured on a logarithmic scale.

Non-decimal orders of magnitude

See also: Logarithmic scale

Other orders of magnitude may be calculated using bases other than 10. The ancient Greeks ranked the nighttime brightness of celestial bodies by 6 levels in which each level was the fifth root of one hundred (about 2.512) as bright as the nearest weaker level of brightness, so that the brightest level is 5 orders of magnitude brighter than the weakest, which can also be stated as a factor of 100 times brighter.

The different decimal numeral systems of the world use a larger base to better envision the size of the number, and have created names for the powers of this larger base. The table shows what number the order of magnitude aim at for base 10 and for base 1,000,000. It can be seen that the order of magnitude is included in the number name in this example, because bi- means 2 and tri- means 3 (these make sense in the long scale only), and the suffix -illion tells that the base is 1,000,000. But the number names billion, trillion themselves (here with other meaning than in the first chapter) are not names of the orders of magnitudes, they are names of "magnitudes", that is the numbers 1,000,000,000,000 etc.

order of magnitude	is log10 of	is log1000000 of	short scale	long scale
1	10	1,000,000	million	million
2	100	1,000,000,000,000	trillion	billion
3	1000	1,000,000,000,000,000,000	quintillion	trillion

SI units in the table at right are used together with SI prefixes, which were devised with mainly base 1000 magnitudes in mind. The IEC standard prefixes with base 1024 were invented for use in electronic technology.

The ancient apparent magnitudes for the brightness of stars uses the base and is reversed. The modernized version has however turned into a logarithmic scale with non-integer values.

Extremely large numbers

For extremely large numbers, a generalized order of magnitude can be based on their double logarithm or super-logarithm. Rounding these downward to an integer gives categories between very "round numbers", rounding them to the nearest integer and applying the inverse function gives the "nearest" round number.

The double logarithm yields the categories:

..., 1.0023–1.023, 1.023–1.26, 1.26–10, 10–10¹⁰, 10¹⁰–10¹⁰⁰, 10¹⁰⁰–10¹⁰⁰⁰, ...

(the first two mentioned, and the extension to the left, may not be very useful, they merely demonstrate how the sequence mathematically continues to the left).

The super-logarithm yields the categories:

, or

negative numbers, 0–1, 1–10, 10–1e10, 1e10–10^1e10, 10^1e10–⁴10, ⁴10–⁵10, etc. (see tetration)

The "midpoints" which determine which round number is nearer are in the first case:

1.076, 2.071, 1453, 4.20e31, 1.69e316,...

and, depending on the interpolation method, in the second case

−.301, .5, 3.162, 1453, 1e1453, , ,... (see notation of extremely large numbers)

For extremely small numbers (in the sense of close to zero) neither method is suitable directly, but of course the generalized order of magnitude of the reciprocal can be considered.

Similar to the logarithmic scale one can have a double logarithmic scale (example provided here) and super-logarithmic scale. The intervals above all have the same length on them, with the "midpoints" actually midway. More generally, a point midway between two points corresponds to the generalised f-mean with f(x) the corresponding function log log x or slog x. In the case of log log x, this mean of two numbers (e.g. 2 and 16 giving 4) does not depend on the base of the logarithm, just like in the case of log x (geometric mean, 2 and 8 giving 4), but unlike in the case of log log log x (4 and 65536 giving 16 if the base is 2, but, otherwise).

See also

• Orders of approximation
• Big O notation
• Decibel
• Number sense
• Names of large numbers
• Names of small numbers

Further reading

• Asimov, Isaac The Measure of the Universe (1988)

External links

• The Scale of the Universe 2 Interactive tool from Planck length 10⁻³⁵ meters to universe size 10²⁷
• Cosmos – an Illustrated Dimensional Journey from microcosmos to macrocosmos – from Digital Nature Agency
• Powers of 10, a graphic animated illustration that starts with a view of the Milky Way at 10²³ meters and ends with subatomic particles at 10⁻¹⁶ meters.
• What is Order of Magnitude?

References

UpToDate Contents

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• Iron oxide nanoparticle agglomeration influences dose rates and modulates oxidative stress-mediated dose-response profiles in vitro.

• Sharma G, Kodali V, Gaffrey M, Wang W, Minard KR, Karin NJ, Teeguarden JG, Thrall BD.Author information Battelle Memorial Institute , Columbus, OH , USA.AbstractAbstract Spontaneous agglomeration of engineered nanoparticles (ENPs) is a common problem in cell culture media which can confound interpretation of in vitro nanotoxicity studies. The authors created stable agglomerates of iron oxide nanoparticles (IONPs) in conventional culture medium, which varied in hydrodynamic size (276 nm-1.5 μm) but were composed of identical primary particles with similar surface potentials and protein coatings. Studies using C10 lung epithelial cells show that the dose rate effects of agglomeration can be substantial, varying by over an order of magnitude difference in cellular dose in some cases. Quantification by magnetic particle detection showed that small agglomerates of carboxylated IONPs induced greater cytotoxicity and redox-regulated gene expression when compared with large agglomerates on an equivalent total cellular IONP mass dose basis, whereas agglomerates of amine-modified IONPs failed to induce cytotoxicity or redox-regulated gene expression despite delivery of similar cellular doses. Dosimetry modelling and experimental measurements reveal that on a delivered surface area basis, large and small agglomerates of carboxylated IONPs have similar inherent potency for the generation of ROS, induction of stress-related genes and eventual cytotoxicity. The results suggest that reactive moieties on the agglomerate surface are more efficient in catalysing cellular ROS production than molecules buried within the agglomerate core. Because of the dynamic, size and density-dependent nature of ENP delivery to cells in vitro, the biological consequences of agglomeration are not discernible from static measures of exposure concentration (μg/ml) alone, highlighting the central importance of integrated physical characterisation and quantitative dosimetry for in vitro studies. The combined experimental and computational approach provides a quantitative framework for evaluating relationships between the biocompatibility of nanoparticles and their physical and chemical characteristics.
• Nanotoxicology.Nanotoxicology.2014 Sep;8:663-75. doi: 10.3109/17435390.2013.822115. Epub 2013 Jul 31.
• Abstract Spontaneous agglomeration of engineered nanoparticles (ENPs) is a common problem in cell culture media which can confound interpretation of in vitro nanotoxicity studies. The authors created stable agglomerates of iron oxide nanoparticles (IONPs) in conventional culture medium, which varied
• PMID 23837572

• Effect of pulsed electric field treatment on enzyme kinetics and thermostability of endogenous ascorbic acid oxidase in carrots (Daucus carota cv. Nantes).

• Leong SY, Oey I.Author information Department of Food Science, University of Otago, Dunedin, New Zealand.AbstractThe objective of this research was to study the enzyme kinetics and thermostability of endogenous ascorbic acid oxidase (AAO) in carrot purée (Daucus carota cv. Nantes) after being treated with pulsed electric field (PEF) processing. Various PEF treatments using electric field strength between 0.2 and 1.2kV/cm and pulsed electrical energy between 1 and 520kJ/kg were conducted. The enzyme kinetics and the kinetics of AAO thermal inactivation (55-70°C) were described using Michaelis-Menten model and first order reaction model, respectively. Overall, the estimated Vmax and KM values were situated in the same order of magnitude as the untreated carrot purée after being exposed to pulsed electrical energy between 1 and 400kJ/kg, but slightly changed at pulsed electrical energy above 500kJ/kg. However, AAO presented different thermostability depending on the electric field strength applied. After PEF treatment at the electric field strength between 0.2 and 0.5kV/cm, AAO became thermolabile (i.e. increase in inactivation rate (k value) at reference temperature) but the temperature dependence of k value (Ea value) for AAO inactivation in carrot purée decreased, indicating that the changes in k values were less temperature dependent. It is obvious that PEF treatment affects the temperature stability of endogenous AAO. The changes in enzyme kinetics and thermostability of AAO in carrot purée could be related to the resulting carrot purée composition, alteration in intracellular environment and the effective concentration of AAO released after being subjected to PEF treatment.
• Food chemistry.Food Chem.2014 Mar 1;146:538-47. doi: 10.1016/j.foodchem.2013.09.096. Epub 2013 Sep 25.
• The objective of this research was to study the enzyme kinetics and thermostability of endogenous ascorbic acid oxidase (AAO) in carrot purée (Daucus carota cv. Nantes) after being treated with pulsed electric field (PEF) processing. Various PEF treatments using electric field strength between 0.2
• PMID 24176379

• Antimicrobial activity of antihypertensive food-derived peptides and selected alanine analogues.

• McClean S, Beggs LB, Welch RW.Author information Biomedical Sciences Research Institute, University of Ulster, Coleraine BT52 1SA, UK. Electronic address: s.mcclean@ulster.ac.uk.AbstractThis study evaluated four food-derived peptides with known antihypertensive activities for antimicrobial activity against pathogenic microorganisms, and assessed structure-function relationships using alanine analogues. The peptides (EVSLNSGYY, barley; PGTAVFK, soybean; TTMPLW, α-casein; VHLPP, α-zein) and the six alanine substitution peptides of PGTAVFK were synthesised, characterised and evaluated for antimicrobial activity using the bacteria, Escherichia coli, Staphylococcus aureus, and Micrococcus luteus and the yeast, Candida albicans. The peptides TTMPLW and PGTAVFK inhibited growth of all four microorganisms tested, with activities of a similar order of magnitude to ampicillin and ethanol controls. EVSLNSGYY inhibited the growth of the bacteria, but VHLPP showed no antimicrobial activity. The alanine analogue, PGAAVFK showed the highest overall antimicrobial activity and PGTAVFA showed no activity; overall, the activities of the analogues were consistent with their structures. Some peptides with antihypertensive activity also show antimicrobial activity, suggesting that food-derived peptides may exert beneficial effects via a number of mechanisms.
• Food chemistry.Food Chem.2014 Mar 1;146:443-7. doi: 10.1016/j.foodchem.2013.09.094. Epub 2013 Sep 25.
• This study evaluated four food-derived peptides with known antihypertensive activities for antimicrobial activity against pathogenic microorganisms, and assessed structure-function relationships using alanine analogues. The peptides (EVSLNSGYY, barley; PGTAVFK, soybean; TTMPLW, α-casein; VHLPP, α-
• PMID 24176365

Japanese Journal

• Formation of Elastic Gels from Deacetylated Chitin Nanofibers Reinforced with Sulfobutyl Ether β-Cyclodextrin

• Anraku Makoto,Iohara Daisuke,Hiraga Ayumu,Uekama Kaneto,Ifuku Shinsuke,Pipkin James D.,Hirayama Fumitoshi
• Chemistry Letters, 2015
• … Among the various CyDs tested and their derivatives, SBE-β-CyD formed a stiff, non-fluid elastic gel that can be easily formed into a variety of shapes, whereas other gels prepared from neutral CyDs formed a weak, rather fluid gels. … The viscosity of the deacetylated chitin nanofiber/SBE-β-CyD gel was higher by about one order of magnitude at a 1.0%w/v concentration of SBE-β-CyD. …
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• InGaAs axial-junction nanowire-array solar cells

• Nakai Eiji,Chen Muyi,Yoshimura Masatoshi,Tomioka Katsuhiro,Fukui Takashi
• Jpn. J. Appl. Phys. 54(1), 015201, 2014-12-15
• … The measured electron-beam-induced current (EBIC) signals showed the formation of an axial p–i–n junction, which confirms power generation under sunlight illumination. … The series resistance of the NW SCs is much higher than that of conventional planar SCs based on Si or other III–V compound semiconductors. …
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• Measurement of energy flux to a substrate by thermal and Langmuir probes during inductively coupled plasma assisted DC magnetron sputtering

• Matsuda Yoshinobu,Mine Kenji,Wakiyama Shintaro,Shinohara Masanori
• Jpn. J. Appl. Phys. 54(1S), 01AB02, 2014-11-06
• … To understand the deposition mechanism during the inductively coupled plasma (ICP) assisted DC magnetron sputter-deposition of transparent conductive Al-doped ZnO (AZO) films, energy flux to a substrate was investigated. …
• NAID 150000110060

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• order of magnitudeの意味 - 英和辞書 - 英語辞書 - goo辞書

order of magnitudeとは。意味や和訳。1 大規模.2 ある単位からその10倍までの範囲，桁. - goo英和辞書は14万項目以上を収録し、発音、音声、慣用句、例文が分かる英和辞書です。

Related Pictures

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★リンクテーブル★

リンク元	「桁」「digit」
関連記事	「order」「magnitude」

「桁」

　　[★]

英

digit、order、order of magnitude

関

オーダー、指令、順序、順番、要求、目、数字、指、次数、命令、秩序

「digit」

　　[★]

• n.

• 数字、桁、指

関

digitus、finger、numeral、order、order of magnitude

　 　 　

「order」

　　[★]

• n.

• (生物)目

• of the order of ～: ほぼ～程度の

Body stores are of the order of 2-4mg, sufficient for 3-4 years if supplies are completely cut off.

　 　 　 　 　 　 　 　 　 　 　 　 　 　 　 　

「magnitude」

　　[★]

• n.

• 大きさ、規模、振幅

関

amplitude、scale、size