Prefixes for multiple units

Multiple units- units that are an integer number of times greater than the basic unit of measurement of some physical quantity. The International System of Units (SI) recommends the following prefixes for denoting multiple units:

multiplicity	Console		Designation		Example
	Russian	international	Russian	international
10 1	soundboard	Deca	Yes	da	dal - decalitre
10 2	hecto	hecto	G	h	hPa - hectopascal
10 3	kilo	kilo	To	k	kN - kilonewton
10 6	mega	Mega	M	M	MPa - megapascal
10 9	giga	Giga	G	G	GHz - gigahertz
10 12	tera	Tera	T	T	TV - teravolt
10 15	peta	Peta	P	P	Pflop -	10 18	exa	Hexa	E	E	EB - exabyte
10 21	zetta	Zetta	W	Z	ZeV - zettaelectronvolt
10 24	yotta	Yotta	AND	Y	Yb - yottabyte

Binary understanding of prefixes

In programming and the computer-related industry, the same prefixes kilo-, mega-, giga-, tera-, etc., when applied to values ​​that are multiples of powers of two (for example, bytes), can mean a multiple of not 1000 , and 1024=2 10 . Which system is used should be clear from the context (for example, for the amount of RAM, the multiplicity of 1024 is used, and for the amount of disk memory, the multiplicity of 1000 is introduced by hard disk manufacturers).

1 kilobyte	= 1024 1	= 2 10	= 1024 bytes
1 megabyte	= 1024 2	= 2 20	= 1,048,576 bytes
1 gigabyte	= 1024 3	= 2 30	= 1,073,741,824 bytes
1 terabyte	= 1024 4	= 2 40	= 1,099,511,627,776 bytes
1 petabyte	= 1024 5	= 2 50	= 1,125,899,906,842,624 bytes
1 exabyte	= 1024 6	= 2 60	= 1,152,921,504,606,846,976 bytes
1 zettabyte	= 1024 7	= 2 70	= 1 180 591 620 717 411 303 424 bytes
1 yottabyte	= 1024 8	= 2 80	= 1 208 925 819 614 629 174 706 176 bytes

To avoid confusion, in April 1999 the International Electrotechnical Commission introduced a new standard for naming binary numbers (see Binary prefixes).

Prefixes for submultiple units

submultiple units, make up a certain proportion (part) of the established unit of measurement of a certain quantity. The International System of Units (SI) recommends the following prefixes for submultiple units:

Dolnost	Console		Designation		Example
	Russian	international	Russian	international
10 −1	deci	deci	d	d	dm - decimeter
10 −2	centi	centi	With	c	cm - centimeter
10 −3	Milli	milli	m	m	mm - millimeter
10 −6	micro	micro	mk	(u)	micron - micrometer, micron
10 −9	nano	nano	n	n	nm - nanometer
10 −12	pico	pico	P	p	pF - picofarad
10 −15	femto	femto	f	f	fs - femtosecond
10 −18	atto	atto	A	a	ac - attosecond
10 −21	zepto	zepto	h	z
10 −24	yokto	yocto	And	y

Origin of prefixes

Most prefixes are derived from Greek words. Deca comes from the word deca or deka (δέκα) - "ten", hecto - from hekaton (ἑκατόν) - "one hundred", kilo - from chiloi (χίλιοι) - "thousand", mega - from megas (μέγας), that is, " big", giga is gigantos (γίγας) - "giant", and tera is from teratos (τέρας), which means "monstrous". Peta (πέντε) and exa (ἕξ) correspond to five and six thousand digits and are translated as "five" and "six" respectively. Longitudinal micro (from micros, μικρός) and nano (from nanos, νᾶνος) are translated as "small" and "dwarf". From one word ὀκτώ (októ), meaning "eight", the prefixes yotta (1000 8) and yokto (1/1000 8) are formed.

As "thousand" the prefix milli, which goes back to the Latin mille, is also translated. Latin roots also have the prefixes santi - from centum ("one hundred") and deci - from decimus ("tenth"), zetta - from septem ("seven"). Zepto ("seven") comes from the Latin word septem or from the French sept.

The prefix atto is derived from the Danish atten ("eighteen"). Femto is derived from Danish (Norwegian) femten or Old Norse fimmtān and means "fifteen".

The prefix pico comes either from the French pico ("beak" or "small number"), or from the Italian piccolo, meaning "small".

Rules for using prefixes

• Prefixes should be written together with the name of the unit or, accordingly, with its designation.
• The use of two or more prefixes in a row (eg micromillifarad) is not permitted.
• The symbols for multiples and submultiples of the original unit raised to a power are formed by adding the corresponding exponent to the designation of a multiple or submultiple of the original unit, and the exponent means raising the multiple or submultiple to the power (together with the prefix). Example: 1 km² = (10³ m)² = 10 6 m² (not 10³ m²). The names of such units are formed by adding a prefix to the name of the original unit: square kilometer (not kilo-square meter).
• If the unit is a product or ratio of units, the prefix, or its designation, is usually attached to the name or designation of the first unit: kPa s / m (kilopascal second per meter). Attaching a prefix to the second factor of the product or to the denominator is allowed only in justified cases.

Applicability of prefixes

Due to the fact that the name of the unit of mass in SI - kilogram - contains the prefix "kilo", for the formation of multiple and submultiple units of mass, a submultiple unit of mass is used - grams (0.001 kg).

Prefixes have limited use with units of time: multiple prefixes don't go with them at all (nobody uses "kilosecond", although it's not formally forbidden), prefixes are only attached to the second (millisecond, microsecond, etc.). In accordance with GOST 8.417-2002, the name and designations of the following SI units are not allowed to be used with prefixes: minute, hour, day (time units), degree, minute, second (flat angle units), astronomical unit, diopter and atomic mass unit.

see also

• Non-SI unit prefix (English Wikipedia)
• IEEE standard for prefixes

Literature

SI prefixes
Multiples prefixes	deca-( 10 1 ) hecto- ( 10²) kilo- ( 10³) mega- ( 10 6 ) giga- ( 10 9 ) tera- ( 10 12 ) peta- ( 10 15 ) exa- ( 10 18 ) ·

The process of establishing a correspondence between a property and a number, and so that the comparison of properties could be done using a comparison of numbers, is called measurement. One of the properties of bodies is their length. The length of the body in one direction is called the length of the body. Let's look at two lines. To compare the lengths of the rulers, we will attach them to each other so that one of the ends of the first ruler coincides with the end of the second ruler. The second ends of the rulers either match or they don't. If all ends of the rulers coincide, they are equal in length. When measuring the length of each ruler, a certain number is assigned, which uniquely determines its length. In this case, the number allows you to choose from all the rulers uniquely those whose length is determined by this number. A property defined in this way is called a physical quantity. The process of finding a number that characterizes a physical property is called measurement.

For units of length, the corresponding standards are established, by comparison with which any length is determined.

Meter - a unit of length (distance) in metric systems

Length and distance in the International System of Units (SI) are measured in meters (m). The meter is the basic unit of the SI system. In addition to the SI system, the meter serves as the basic unit and is used to measure distance in some other systems. For example, the meter is a unit of length in the ISS (a system in which three units were considered basic: meter, kilogram, second). Currently, the ISS is not considered an independent system. Systems in which the meter is a unit of length (distance) and the kilogram is a unit of mass are called metric.

By definition, 1 meter is the length of the path that light travels in vacuum in $\frac(1)(299792458)$ seconds.

In measurements and calculations, multiples and submultiples of a meter are used as units of measurement for length (distance). For example, $(10)^(-10)$m = 1A (angstrom); $(10)^(-9)$m = 1 nm (nano meter); 1 km = 1000 m.

Currently, in our country, the International System of Units of Measurement (SI) is most often used.

Length units in non-metric systems

There are systems of units in which centimeters are units of length, such as the CGS system. The CGS system was used extensively before the adoption of the International System of Units. Otherwise, it is called the absolute physical system of units. Within its framework, 3 units of measurement are considered basic: centimeter, gram, second.

There are national systems of units for measuring length and distance. For example, the British system is not metric. The units of length and distance in this system are: mile, furlong, chain, rod, yard, foot and other units that are unusual for us. $1\mile=1.609\km;;$1 furlong=201.6m; 1 chain-20.1168 m. The Japanese system for measuring length and distance, also differs from the metric one. It uses, for example, such units of length as: mo, rin, bu, shaku and others. 1 mo=0.003030303 cm; 1 rin \u003d 0.03030303 cm; 1 bu \u003d 0.30303 cm.

Professional systems for measuring length and distance are used. For example, there is a typographic system, nautical (used in the navy), and astronomy uses special kinds of distance units. So, in astronomy, the distance from the Earth to the Sun is an astronomical unit (AU) of measurement of length (distance).

1 AU = 149 ~ 597 870.7 km, which is equal to the distance from the Sun to the Earth. A light year is 63241.077 AU. Parsec $\approx 206264.806247\ au$.

Some length units that were previously used in our country are no longer used. So, in the old Russian system there were: span, foot, elbow, arshin, measure, verst and other units. 1 span = 17.78 cm; 1 foot = 35.56 cm; 1 measure = 106.68 cm; 1 verst = 1066.8 meters.

Examples of problems with a solution

Example 1

Exercise. What is the electromagnetic wave length ($\lambda $) if the photon energy is $\varepsilon =(10)^(-18)J$? What are the units for measuring the length of an electromagnetic wave?

Solution. As a basis for solving the problem, we use the formula for determining the photon energy in the form:

\[\varepsilon =h\nu \ \left(1.1\right),\]

where $h=6.62\cdot (10)^(-34)$J$\cdot c$; $\nu $ is the frequency of oscillations in an electromagnetic wave, it is related to the wavelength of light as:

\[\nu =\frac(c)(\lambda )\ \left(1.2\right),\]

where $c=3\cdot (10)^8\frac(m)(c)$ is the speed of light in vacuum. Taking into account formula (1.2), we express from (1.1) the wavelength:

\[\varepsilon =h\nu =\frac(hc)(\lambda )\to \lambda =\frac(hc)(\varepsilon )\left(1.3\right).\]

Let's calculate the wavelength:

\[\lambda =\frac(6,62\cdot (10)^(-34)\cdot 3\cdot (10)^8)((10)^(-18))=1.99\cdot (10 )^(-7\ )\left(m\right).\]

Answer.$\lambda =1.99\cdot (10)^(-7\ )$m=199 nm. Meters - units of measurement of the length of an electromagnetic wave (as well as any other length) in the SI system.

Example 2

Exercise. The body fell from a height equal to $h=1\ $km. What is the length of the path ($S$) that the body will cover in the first second of fall if its initial velocity is zero? \textit()

Solution. By the condition of the problem, we have:

In this problem, we are dealing with uniformly accelerated motion of a body in the Earth's gravitational field. This means that the body is moving with an acceleration $\overline(g)$, which is directed along the Y axis (Fig. 1). As a basis for solving the problem, we take the equation:

\[\overline(s)=(\overline(s))_0+(\overline(v))_0t+\frac(\overline(g)t^2)(2)\ \left(2.1\right).\]

We place the reference point at the point where the body begins to move, take into account that the initial velocity of the body is zero, then in the projection onto the Y axis we write expression (2.1) as:

Let's calculate the path length of the body:

Answer.$h_1=4.9\ $m, the distance that the body will cover in the first second of its movement does not depend on the height from which it fell.

International system of units(Systeme International d "Unitees), a system of units of physical quantities adopted by the 11th General Conference on Weights and Measures(1960). The abbreviated designation of the system is SI (in Russian transcription - SI). The international system of units was developed to replace the complex set of systems of units and individual non-systemic units that has developed on the basis of metric system, and simplifying the use of units. The advantages of the International System of Units are its universality (covering all branches of science and technology) and coherence, i.e., the consistency of derived units that are formed according to equations that do not contain proportionality coefficients. Due to this, when calculating, if the values ​​of all quantities are expressed in units of the International System of Units, it is not required to enter coefficients in the formulas that depend on the choice of units.

The table below shows the names and designations (international and Russian) of the main, additional and some derived units of the International System of Units. Russian designations are given in accordance with the current GOSTs; the designations provided for by the draft new GOST "Units of physical quantities" are also given. The definition of basic and additional units and quantities, the ratios between them are given in the articles about these units.

Basic and derived units of the International System of Units

Value	Unit name	Designation
		international	Russian
Basic units
Length	meter	m	m
Weight	kilogram	kg	kg
Time	second	s	With
The strength of the electric current	ampere	A	A
Thermodynamic temperature	kelvin	TO	TO
The power of light	candela	cd	cd
Amount of substance	kilomole	kmol	kmol
Additional units
flat corner	radian	rad	glad
Solid angle	steradian	sr	Wed
Derived units
Square	square meter	m2	m 2
Volume, capacity	cubic meter	m 3	m 3
Frequency	hertz	Hz	Hz
Speed	meters per second	m/s	m/s
Acceleration	meter per second squared	m/s 2	m/s 2
Angular velocity	radians per second	rad/s	rad/s
Angular acceleration	radian per second squared	rad/s 2	rad/s 2
Density	kilogram per cubic meter	kg/m3	kg / m 3
Force	newton	N	H
Pressure, mechanical stress	Pascal	Pa	Pa (N / m 2)
Kinematic viscosity	square meter per second	m2/s	m 2 /s
Dynamic viscosity	pascal second	Pa s	Pass
Work, energy, amount of heat	joule	J	J
Power	watt	W	Tue
The amount of electricity	pendant	WITH	cl
Electrical voltage, electromotive force	volt	V	IN
Electric field strength	volt per meter	V/m	V/m
Electrical resistance	ohm	w	Ohm
electrical conductivity	Siemens	S	Cm
Electrical capacitance	farad	F	F
magnetic flux	weber	wb	wb
Inductance	Henry	H	gn
Magnetic induction	tesla	T	Tl
Magnetic field strength	ampere per meter	A/m	A/m
Magnetomotive force	ampere	A	A
Entropy	joule per kelvin	J/K	J/K
Specific heat capacity	joule per kilogram kelvin	J/(kg K)	J/(kg K)
Thermal conductivity	watt per meter kelvin	W/(m K)	W/(m K)
Radiation intensity	watt per steradian	w/sr	Tue/Wed
wave number	unit per meter	m-1	m -1
Light flow	lumen	lm	lm
Brightness	candela per square meter	cd/m2	cd/m2
illumination	luxury	lx	OK

The first three basic units (meter, kilogram, second) allow the formation of coherent derived units for all quantities that have a mechanical. nature; chemistry and molecular physics. In addition, the units of radians and steradians serve to form derived units of quantities that depend on flat or solid angles. To form the names of decimal multiples and submultiples, special ones are used. SI prefixes: deci(for the formation of units equal to 10 -1 in relation to the original), centi (10 -2), Milli (10 -3), micro (10 -6), nano (10 -9), pico(10 -12), femto (10 -15), atto (10 -18), soundboard (10 1), hecto (10 2), kilo (10 3), mega (10 6), giga (10 9), tera(10 12); cm. Multiples, Sub-multiples.

1.1. Draw lines to connect the names of natural phenomena and their corresponding types of physical phenomena.

1.2. Tick ​​the properties that both the stone and the rubber band have.

1.3. Fill in the gaps in the text so that you get the names of the sciences that study various phenomena at the intersection of physics and astronomy, biology, geology.

1.4. Write the following numbers in standard form according to the above pattern.

2.1. Circle those properties that a physical body might not have.

2.2. The figure shows bodies consisting of the same substance. Write down the name of this substance.

2.3. Choose from the suggested words two words denoting the substances from which the corresponding parts of a simple pencil are made, and write them down in the empty boxes.

2.4. Use the arrows to "sort" the words into baskets according to their names, reflecting different physical concepts.

2.5. Write down the numbers as shown.

3.1. At a physics lesson, the teacher placed the students on the tables identical-looking magnetic arrows placed on the tips of the needles. All the arrows turned around their axis and froze, but at the same time, some of them turned to the north with a blue end, while others turned red. The students were surprised, but during the conversation, some of them expressed their hypotheses why this could happen. Mark which hypothesis put forward by the students can be refuted and which cannot by crossing out the unnecessary word in the right column of the table.

3.2. Choose the correct continuation of the phrase “In physics, a phenomenon is considered to be really occurring if ...”

3.3. Add an offer.

3.4. Choose the correct continuation of the phrase.

3.5. Even in ancient times, people observed that:

4.1. Finish the sentence.

4.2. Insert the missing words and letters into the text.
In the International System of Units (SI):

4.3. a) Express multiple units of length in meters and vice versa.

b) Express the meter in submultiples and vice versa.

c) Express the second in submultiple units and vice versa.

d) Express in basic SI units the values ​​of length.

e) Express in basic SI units the values ​​of time intervals.

f) Express in basic SI units the values ​​of the following quantities.

4.4. Measure the width l of the textbook page with a ruler. Express the result in centimeters, millimeters and meters.

4.5. A wire was wound on the rod as shown in the figure. The winding width was equal to l=9 mm. What is the diameter d of the wire? Express your answer in the given units.

4.6. Write down the length and area values ​​in the indicated units according to the given sample.

4.7. Determine the area of ​​triangle S1 and trapezoid S2 in the specified units.

4.8. Write down the volume values ​​in basic SI units according to the given sample.

4.9. First, hot water with a volume of 0.2 m3 was poured into the bath, then cold water with a volume of 2 liters was added. What is the volume of water in the bath?

4.10. Add an offer. "The price of division of the thermometer scale is _____."

5.1. Use the picture and fill in the gaps in the text.

5.2. Write down the values ​​of the volume of water in the vessels, taking into account the measurement error.

5.3. Write down the lengths of the table, measured with different rulers, taking into account the measurement error.

5.4. Record the clock shown in the figure.

5.5. The students measured the length of their tables with different devices and recorded the results in a table.

6.1. Underline the names of devices that use an electric motor.

6.2. Home experiment.
1. Measure the diameter d and the circumference l of five cylindrical objects using a thread and a ruler (see figure). Write down the names of objects and the results of measurements in the table. Use objects of different sizes. As an example, the first column of the table already contains the values ​​obtained for a vessel with a diameter d = 11 cm and a circumference l = 35 cm.

2. Using the table, plot the dependence of the circumference l of an object on its diameter d. To do this, on the coordinate plane, you need to build six points according to the data in the table and connect them with a straight line. For example, a point with coordinates (d, l) for the vessel has already been built on the plane. Similarly, on the same plane, construct points for other bodies.

3. Using the resulting graph, determine what is the diameter d of the cylindrical part of the plastic bottle if its circumference is l = 19cm.
d= 6 cm

6.3. Home experiment.
1. Measure the dimensions of a matchbox using a ruler with millimeter divisions and write down these values, taking into account the measurement error.

The previous entry means that the true length, width, and height of the box lie within:

2. Calculate the limits of the true value of the volume of the box.

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1 gigameter [gm] = 10000000 hectometer [gm]

Initial value

Converted value

meter exameter petameter terameter gigameter megameter kilometer hectometer decameter decimeter centimeter millimeter micrometer micron nanometer picometer femtometer attometer megaparsec kiloparsec parsec light year astronomical unit (international) mile (statute) mile (US, geodetic) mile (Roman) 1000 yards furlong furlong (US, geodetic) chain chain (US, geodetic) rope (English rope) genus genus (US, geodetic) perch field (eng. . pole) fathom fathom (US, geodetic) cubit yard foot foot (US, geodetic) link link (US, geodetic) cubit (Brit.) hand span finger nail inch inch (US, geodetic) barleycorn (eng. barleycorn) thousandth of a microinch angstrom atomic unit of length x-unit fermi arpan ration typographic point twip cubit (Swedish) fathom (Swedish) caliber centiinch ken arshin actus (O.R.) vara de tarea vara conuquera vara castellana cubit (Greek) long reed reed long cubit palm "finger" Planck length classical electron radius Bohr radius equatorial radius of the Earth polar radius of the Earth distance from the Earth to the Sun radius of the Sun light nanosecond light microsecond light millisecond light second light hour light day light week Billion light years Distance from Earth to the Moon cables (international) cable (British) cable (US) nautical mile (US) light minute rack unit horizontal pitch cicero pixel line inch (Russian) vershok span foot fathom oblique fathom verst boundary verst

Converter feet and inches to meters and vice versa

foot inch

m

More about length and distance

General information

Length is the largest measurement of the body. In three dimensions, length is usually measured horizontally.

Distance is a measure of how far two bodies are from each other.

Distance and length measurement

Distance and length units

In the SI system, length is measured in meters. Derived quantities such as kilometer (1000 meters) and centimeter (1/100 meter) are also widely used in the metric system. In countries that do not use the metric system, such as the US and the UK, units such as inches, feet, and miles are used.

Distance in physics and biology

In biology and physics, lengths are often measured much less than one millimeter. For this, a special value, a micrometer, has been adopted. One micrometer is equal to 1×10⁻⁶ meters. In biology, micrometers measure the size of microorganisms and cells, and in physics, the length of infrared electromagnetic radiation. A micrometer is also called a micron and sometimes, especially in English literature, is denoted by the Greek letter µ. Other derivatives of the meter are also widely used: nanometers (1×10⁻⁹ meters), picometers (1×10⁻¹² meters), femtometers (1×10⁻¹⁵ meters), and attometers (1×10⁻¹⁸ meters).

Distance in navigation

Shipping uses nautical miles. One nautical mile is equal to 1852 meters. Initially, it was measured as an arc of one minute along the meridian, that is, 1/(60 × 180) of the meridian. This made latitude calculations easier, since 60 nautical miles equaled one degree of latitude. When distance is measured in nautical miles, speed is often measured in nautical knots. One knot is equal to one nautical mile per hour.

distance in astronomy

In astronomy, long distances are measured, so special quantities are adopted to facilitate calculations.

astronomical unit(au, au) is equal to 149,597,870,700 meters. The value of one astronomical unit is a constant, that is, a constant value. It is generally accepted that the Earth is located at a distance of one astronomical unit from the Sun.

Light year equals 10,000,000,000,000 or 10¹³ kilometers. This is the distance that light travels in a vacuum in one Julian year. This value is used in popular science literature more often than in physics and astronomy.

Parsec approximately equal to 30,856,775,814,671,900 meters or approximately 3.09 × 10¹³ kilometers. One parsec is the distance from the Sun to another astronomical object, such as a planet, star, moon, or asteroid, with an angle of one arcsecond. One arc second is 1/3600 of a degree, or about 4.8481368 mrad in radians. Parsec can be calculated using parallax - the effect of a visible change in the position of the body, depending on the point of observation. During measurements, a segment E1A2 (in the illustration) is laid from the Earth (point E1) to a star or other astronomical object (point A2). Six months later, when the Sun is on the other side of the Earth, a new segment E2A1 is drawn from the new position of the Earth (point E2) to the new position in space of the same astronomical object (point A1). In this case, the Sun will be at the intersection of these two segments, at point S. The length of each of the segments E1S and E2S is equal to one astronomical unit. If we postpone the segment through the point S, perpendicular to E1E2, it will pass through the intersection point of the segments E1A2 and E2A1, I. The distance from the Sun to point I is the SI segment, it is equal to one parsec when the angle between the segments A1I and A2I is two arcseconds.

On the image:

• A1, A2: apparent star position
• E1, E2: Earth position
• S: position of the sun
• I: point of intersection
• IS = 1 parsec
• ∠P or ∠XIA2: parallax angle
• ∠P = 1 arc second

Other units

League- an obsolete unit of length used earlier in many countries. It is still used in some places, such as the Yucatan Peninsula and rural areas of Mexico. This is the distance a person walks in an hour. Marine League - three nautical miles, approximately 5.6 kilometers. Lie - a unit approximately equal to the league. In English, both leagues and leagues are called the same, league. In literature, the league is sometimes found in the title of books, such as "20,000 Leagues Under the Sea" - the famous novel by Jules Verne.

Elbow- an old value equal to the distance from the tip of the middle finger to the elbow. This value was widespread in the ancient world, in the Middle Ages, and until modern times.

Yard used in the British imperial system and is equal to three feet or 0.9144 meters. In some countries, such as Canada, where the metric system is adopted, yards are used to measure the fabric and length of swimming pools and sports fields and grounds, such as golf and football courses.

Meter Definition

The definition of the meter has changed several times. The meter was originally defined as 1/10,000,000 of the distance from the North Pole to the equator. Later, the meter was equal to the length of the platinum-iridium standard. Later, the meter was equated to the wavelength of the orange line of the electromagnetic spectrum of the krypton atom ⁸⁶Kr in vacuum, multiplied by 1,650,763.73. Today, a meter is defined as the distance traveled by light in a vacuum in 1/299,792,458 of a second.

Computing

In geometry, the distance between two points, A and B, with coordinates A(x₁, y₁) and B(x₂, y₂) is calculated by the formula:

and within a few minutes you will receive an answer.

Calculations for converting units in the converter " Length and distance converter' are performed using the functions of unitconversion.org .