Information about Orders Of Magnitude
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. The ratio most commonly used is 10.
| In words |
Decimal | Power of ten |
Order of magnitude |
|---|---|---|---|
| ten thousandths (these terms may be confusive) | 0.0001 | 10-4 | −4 |
| thousandth | 0.001 | 10-3 | −3 |
| hundredth | 0.01 | 10-2 | −2 |
| tenth | 0.1 | 10-1 | −1 |
| one | 1 | 100 | 0 |
| ten | 10 | 101 | 1 |
| hundred | 100 | 10² | 2 |
| thousand | 1,000 | 10³ | 3 |
| ten thousand | 10,000 | 104 | 4 |
| million | 1,000,000 | 106 | 6 |
| billion | 1,000,000,000 | 109 | 9 |
Orders of magnitude are generally used to make very approximate comparisons. 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. This is the reasoning behind significant figures: the amount rounded by is usually a few orders of magnitude less than the total, and therefore insignificant.
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, 4,000,000 has a logarithm of 6.602; its order of magnitude is 6. When truncating, a number of this order of magnitude is between
and 
. In a similar example, "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. In other words; when rounding its logarithm, a number of order of magnitude 10 is in between
and 
. 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.
The pages in the table at right contain lists of items that are of the same order of magnitude in various units of measurement. This is useful for getting an intuitive sense of the comparative scale of familiar objects.
Non-decimal orders of magnitude
Other orders of magnitude may be calculated using bases other than 10. 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 1000000. 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, and the suffix -illion tells that the base is 1000000. 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 000000 000000 etc.| order of magnitude | is log10 of | is log1000000 of | |
|---|---|---|---|
| 1 | 10 | 1 000000 | million |
| 2 | 100 | 1 000000 000000 | trillion |
| 3 | 1000 | 1 000000 000000 000000 | quintillion |
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 was invented for use in context of 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 super logarithm yields the categories:
-
, or
- negative numbers, 0-1, 1-10, 10-1e10, 1e10-10^1e10, 10^1e10-10^^4, 10^^4-10^^5, 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,...
- -.301, .5, 3.162, 1453, 1e1453, 10^1e1453, 10^^2@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 different otherwise).
See also
External links
- 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.
- Orders of Magnitude - Distance
- What is Order of Magnitude?
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. The ratio most commonly used is 10.
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List of orders of magnitude for area
Factor (m²) Multiple Value Item
10-70 2.61×10-70 m² the Planck area,
...
10-30 1 square femtometre (fm²)
10-28 10-28
..... Read more.
Factor (m²) Multiple Value Item
10-70 2.61×10-70 m² the Planck area,
...
10-30 1 square femtometre (fm²)
10-28 10-28
..... Read more.
List of orders of magnitude for angular velocity
Factor (rad·s−1) Value (rad·s−1) Value (rpm) Item
10−16 8.8510−16 to 7.9610−16[1] 8.4510−15 to 7.
..... Read more.
Factor (rad·s−1) Value (rad·s−1) Value (rpm) Item
10−16 8.8510−16 to 7.9610−16[1] 8.4510−15 to 7.
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worldwide view of the subject.
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Please [ improve this article] or discuss the issue on the talk page.
Orders of magnitude
(money expressed in United States dollars)
Factor ($) Long scale Short scale Money Item
10−3 one mill $0.
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This is a list of orders of magnitude for data (or information), measured in bits. This article assumes a descriptive attitude towards terminology, reflecting actual usage by the speakers of the language.
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List of orders of magnitude for density
Factor Multiple Value Item
10-27 1 yoctogram (yg)/m³ 1 × 10-27 kg/m³ very approximate density of the universe
10-24 1 zeptogram (zg)/m³
10-22 100 zg/m³ 1 × 10-22
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Factor Multiple Value Item
10-27 1 yoctogram (yg)/m³ 1 × 10-27 kg/m³ very approximate density of the universe
10-24 1 zeptogram (zg)/m³
10-22 100 zg/m³ 1 × 10-22
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joule J
101 decajoule daJ 10–1 decijoule dJ
102 hectojoule hJ 10–2 centijoule cJ
103 kilojoule kJ 10–3 millijoule mJ
106 megajoule MJ 10–6
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101 decajoule daJ 10–1 decijoule dJ
102 hectojoule hJ 10–2 centijoule cJ
103 kilojoule kJ 10–3 millijoule mJ
106 megajoule MJ 10–6
..... Read more.
Radio spectrum
ELF SLF ULF VLF LF MF HF VHF UHF SHF EHF
3 Hz 30 Hz 300 Hz 3 kHz 30 kHz 300 kHz 3 MHz 30 MHz 300 MHz 3 GHz 30 GHz
30 Hz 300 Hz 3 kHz 30 kHz 300 kHz 3 MHz 30 MHz 300 MHz 3 GHz 30 GHz 300 GHz
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ELF SLF ULF VLF LF MF HF VHF UHF SHF EHF
3 Hz 30 Hz 300 Hz 3 kHz 30 kHz 300 kHz 3 MHz 30 MHz 300 MHz 3 GHz 30 GHz
30 Hz 300 Hz 3 kHz 30 kHz 300 kHz 3 MHz 30 MHz 300 MHz 3 GHz 30 GHz 300 GHz
See also
- Hertz
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List of orders of magnitude for length
Factor (m) Multiple Value Item
10−35 1.610−35 m Planck length; size of a string; lengths smaller than this do not make any physical sense, according to current theories of physics
. . .
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Factor (m) Multiple Value Item
10−35 1.610−35 m Planck length; size of a string; lengths smaller than this do not make any physical sense, according to current theories of physics
. . .
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To help compare different orders of magnitude, the following list describes various mass levels between 10−36 kg and 1053 kg.
Factor (kg) Value Item
10−36 1.
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Factor (kg) Value Item
10−36 1.
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This list compares various sizes of positive numbers, including counts of things, dimensionless numbers and probabilities.
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Smaller than 10-36
- Computing: The number 510-324
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This page lists examples of the power in watts produced by various different sources of energy. They are grouped by orders of magnitude, and each section covers three orders of magnitude, or a factor of one thousand.
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101.325 kPa Standard atmospheric pressure for earth sea level
180 to 250 kPa Pressure in an automobile tire.
0.8 to 2 MPa Pressure used in boilers of steam locomotives.
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180 to 250 kPa Pressure in an automobile tire.
0.8 to 2 MPa Pressure used in boilers of steam locomotives.
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This is a table of specific heat capacities by magnitude. Unless otherwise noted, these values assume standard ambient temperature and pressure.
List of orders of magnitude for specific heat capacity
Factor Value J·kg −1 ·K
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List of orders of magnitude for specific heat capacity
Factor Value J·kg −1 ·K
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List of orders of magnitude for speed
Factor Value (m/s) Value (km/h) Item
10-9 1.310-9 4.6810-9 Average rate of the Moon receding from the Earth.
0.
..... Read more.
Factor Value (m/s) Value (km/h) Item
10-9 1.310-9 4.6810-9 Average rate of the Moon receding from the Earth.
0.
..... Read more.
List of orders of magnitude for temperature
Factor Multiple Item
10−∞ 0 K absolute zero: free-bodies are still, no interaction within or without a thermodynamic system
10−30
..... Read more.
Factor Multiple Item
10−∞ 0 K absolute zero: free-bodies are still, no interaction within or without a thermodynamic system
10−30
..... Read more.
Seconds
Orders of magnitude (time)Factor (s) Multiple common units orders of magnitude
10−43 Planck time, the shortest physically meaningful interval of time, and consequently the youngest the known universe can be measured. ≈ 5.
..... Read more.
List of orders of magnitude for volume
Factor (m³) Multiple Value
10−105 -- 410−105 m³ is the Planck volume
10−45 -- Volume of a proton (~1.
..... Read more.
Factor (m³) Multiple Value
10−105 -- 410−105 m³ is the Planck volume
10−45 -- Volume of a proton (~1.
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Conversion of units refers to conversion factors between different units of measurement for the same quantity.
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Techniques
The simplest way to convert from one unit to another is to carry through the units themselves in the mathematical operation...... Read more.
units of measurement have played a crucial role in human endeavour from early ages up to this day. Disparate systems of measurement used to be very common. Now there is a global standard, the International System (SI) of units, the modern form of the metric system.
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Si, si, or SI may refer to (all SI unless otherwise stated):
In language:
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In language:
- One of two Italian words:
- sì (accented) for "yes"
- si
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The international system (SI) of units defines seven SI base units: physical units defined by an operational definition.
All other physical units can be derived from these base units: these are known as SI derived units. Derivation is by dimensional analysis.
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All other physical units can be derived from these base units: these are known as SI derived units. Derivation is by dimensional analysis.
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SI derived units are part of the SI system of measurement units and are derived from the seven SI base units.
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Dimensionless derived units
The following SI units are actually dimensionless ratios, formed by dividing two identical SI units...... Read more.
An SI prefix (also known as a metric prefix) is a name or associated symbol that precedes a unit of measure (or its symbol) to form a decimal multiple or submultiple.
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In physics, Planck units are physical units of measurement defined exclusively in terms of the five universal physical constants shown in the table below in such a manner that all of these physical constants take on the numerical value of one when expressed in terms of these units.
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The concept of scale is applicable if a system is represented proportionally by another system. For example, for a scale model of an object, the ratio of corresponding lengths is a dimensionless scale, e.g. 1:25; this scale is larger than 1:50.
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For other senses of this word, see magnitude.
The magnitude of a mathematical object is its size: a property by which it can be larger or smaller than other objects of the same kind; in technical terms, an ordering of the class of objects to which
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geometric progression, also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed non-zero number called the common ratio. For example, the sequence 2, 6, 18, 54, ...
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100 (one hundred) (the Roman numeral is C for centum) is the natural number following 99 and preceding 101.
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In mathematics
One hundred is the square of 10 (in scientific notation it is written as )...... Read more.
Rounding to n significant figures is a form of rounding. Significant figures (also called significant digits) can also refer to a crude form of error representation based around significant figure rounding. For this use, see Significance arithmetic.
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