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| Orders of magnitude |
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| SI – SI base units – SI derived units – SI prefixes – conversion of units |
An order of magnitude is the class of bigness, the class of size, the class of magnitude, of any amount, where each separate class contains ten times larger amounts than the one before. It is generally used to make very approximate comparisons. If two numbers differ by one order of magnitude, one is about 10 times larger than the other. In a sense, it is one class bigger. If number A is two orders of magnitude smaller than B, it is about 100 times smaller. Three orders of magnitude would be 1000, four 10,000 etc. If A and B are of the same order of magnitude, their difference is less than ten times. The word order is used in an unusual sense, though very common in various sciences: a class or group, of similar things, here similar amounts.
The order of magnitude of a number is, intuitively speaking, the number of powers of 10 contained in the number, or a close approximation to it. More precisely, the order of magnitude of a number can be defined in terms of the logarithm of the number to the base of 10, usually as the integer part of the logarithm. Thus the order of magnitude of 4,000,000 with a logarithm of 6.602 is 6. Equivalently, this is the exponent of the power of 10 when the number is represented using scientific notation: 4.0E+06.
Alternatively, the logarithm is rounded to the nearest integer, and e.g. 500, is in the same category as 1000.
Thus, the order of magnitude is the approximate position on a logarithmic scale.
An order of magnitude estimate of a variable whose precise value is unknown is an estimate rounded in some way to the nearest power of 10. For example, an accurate order of magnitude estimate for the human population of the Earth in the year 2000 is 10
billion. An order of magnitude estimate is sometimes alsocalled a zeroth order approximation.
One way of categorising things in the physical world is by their size. The pages below contain lists of items that are of the same order of magnitude in time, length, area, volume, mass, energy or temperature. This is useful for getting an intuitive sense of the comparative size of things and the overall scale of the universe. SI units are used together with SI prefixAn SI prefix is a prefix which can be applied to any unit of the International System of Units ( SI) to give subdivisions and multiples of that unit. As part of the SI system they are officially determined by the Bureau International des Poids et Mesures.es: these were devised with orders of magnitude in mind. Each individual page also gives other units; see also conversion of unitsThis article lists conversion factors between a number of units of measurement. Key: definition exactly equal to approximatively equal to Length Area Volume Angle Mass In physics, the pound of mass is sometimes written lbm to distinguish it from the pound.
In the following table the different quantities are lined up so that the following are in the same row:
See also the separate tables for timeThe pages linked in the right-hand column contain lists of times that are of the same order of magnitude (power of ten). Rows in the table represent increasing powers of a thousand (3 orders of magnitude) Note: Planck time, the shortest physically meaning, lengthSee also SI, SI prefixes, and SI base units units length orders of magnitude orders of magnitude (area) orders of magnitude (volume) orders of magnitude (mass) orders of magnitude (time) Planck units size comparisons External links Orders of magnitude (le, areaOrders of magnitude ( surface area m² equal to. Imperial units orders of magnitude 10-8 10-8 m2 _ _ 10-7 m2 10-6 1 square millimetre 1 mm2, 10 mm2 10-4 1 square centimetre 1 cm2, 10 cm2 10-2 100 square centimetres 100 cm2, 1000 cm2 1 10 000 square centime, volumeOrders of magnitude ( volume or capacity Powers of 10³ equal to. examples orders of magnitude 10-45 cubic metres volume of a proton 10-9 cubic metres 10-9 m³ , 10-8 m³ , 10-7 m³ 10-6 cubic metres 1 millilitre(1 cubic centimetre) 1 teaspoon 3. 55 ml to 5 m, massSee also SI SI prefix SI base unit Physical unit Mass Orders of magnitude Conversion of units orders of magnitude (length) orders of magnitude (area) orders of magnitude (volume) orders of magnitude (time) List of energies in joules Planck units size comp, energy, power, temperature and dimensionless numbers.
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