Order of magnitude

The magnitude is at number systems and scientific computing the factor that is necessary in the particular number representation to increase a value to be in or out, while maintaining the single digits, and their order.

  • Particular order is the power (mathematics) the factors 10 ( decimal scale ) or 2 ( binary scale ).
  • As an order of magnitude of a physical quantity by explicitly refers to the orders of magnitude with respect to its base unit.
  • In addition, a general description of " order " then value ranges or scales which are applied over these powers of a base.

Shown she is in exponential notation ( floating point).

  • 4.1 Basic sizes
  • 4.2 Derived quantities
  • 4.3 Thematic compilations

Decimal order of magnitude

Often assumes a decimal, so called " a scale " usually a factor ( or divisor) of 10. For example, different to the sizes " 2 meters " and " 200 meters " to two orders of magnitude, ie by a factor of 102 = 100 So general rule is that an additive change in the magnitude indicates an exponential change in actual size, or that one of the actual size on the order of magnitude (multiplied by a constant factor ) reached by taking the logarithm.

The emerging context dependent magnitudes are drastically different. A scientific calculator for one, estimates to 1099, but it is estimated the magnitude of the number of elementary particles in the universe "just" in 1087, and the universe is old as on the order of 1018 seconds. In contrast is the order of the number of different possible paths between 100 cities in the problem of the traveling salesman already 10158th

Binary magnitude

A binary magnitude corresponds to a doubling halving respectively. It depends in particular in computer engineering from the data type.

Magnitude and unit

In scientific practice, however, an order of magnitude is often used as a rather imprecise concept of proportions, and generally meant the power of the floating point number. The purpose of this application is derived from the context and is usually in the name of large or very large differences in numbers. For example, the nearest star to five orders of magnitude farther away from Earth than the sun. What is meant here are thus decimal orders of magnitude and that rounded to an integer. Magnitude in this sense is a millimeter ( one thousandth of a meter ) → centimeter ( a hundredth ) → decimeter ( one tenth of a meter ) → meter. For example, one says, one size would be " in the centimeter range ."

In the SI unit system are the main purpose for units that determine the decimal order of magnitude to the base unit, precisely controlled. In the areas of engineering, the technical notation is used with a factor of 1000 as magnitude, ie limited to the nanometer micrometer → → → meter → millimeter kilometer, and so on.

Examples of units with orders of magnitude

  • Mass: gram (g), kilograms (kg), tonne ( t)
  • Energy: electron volts (eV ), mega electron volts ( MeV), giga ( GeV ), joule ( J), kilowatt-hour ( kWh), terawatt-hour (TWh )
  • Power: milliwatts (mW ), watts ( W), kilowatts ( kW), megawatts ( MW)
  • Time: femtosecond (fs), picosecond (ps ), nanosecond (ns), microsecond ( microseconds ), millisecond ( ms), second ( s ), minute (min), hour ( h), day ( d), year (a )
  • Frequency: hertz ( Hz), kilohertz ( kHz), megahertz ( MHz)
  • Length: nanometer ( nm), micrometers ( microns ), millimeters ( mm), centimeters (cm), meters (m), kilometers (km), Astronomical unit ( AE) Light Year ( ly ) parsec (pc)
  • Area: square meters (sqm ), Ar ( a), hectare (ha), square kilometer (km ²)
  • Volume: milliliter ( ml), centilitres ( cl ), liter ( l ) cubic meter ( m³)
  • Temperature: nanokelvin ( nK ), micro- Kelvin ( μK ), millikelvin (mK), Kelvin ( K)
  • Pressure: kilopascals (kPa ), hPa (hPa ), Pascal (Pa)

Magnitude scales different elementary sizes

The relevant range of values ​​of physical quantities in nature and technology often sweeps over many orders of magnitude. Therefore, a logarithmic scale - the order of magnitude the linear - suitable for representing such scales.

The following articles provide the basis of exemplary phenomena occurring an overview of the magnitude of the main sizes:

Base sizes

  • Orders of magnitude of the mass
  • Orders of magnitude of length
  • Orders of magnitude of time
  • Orders of magnitude of the current
  • Orders of magnitude of the temperature
  • Orders of magnitude of light intensity

Derived quantities

  • Orders of magnitude of the energy
  • Orders of magnitude of the surface
  • Orders of magnitude of frequency
  • Orders of magnitude of the velocity
  • Orders of magnitude of the acceleration
  • Orders of magnitude of performance
  • Orders of magnitude of the electric voltage
  • Orders of magnitude of the force
  • Orders of magnitude of the volume

Thematic compilations

  • Magnitudes of the data rates
Numeral system Multiplication 10 (number) Fundamental unit Light-year
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