Multiples of 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 designating multiple units:

Multiplicity	Prefix		Designation		Example
Multiplicity	Russian	international	Russian	international	Example
10 1	soundboard	deca	Yes	da	dal - deciliter
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	Z	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 quantities 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, in relation to the amount of RAM, a factor of 1024 is used, and in relation to the volume of disk memory, a factor of 1000 is introduced by hard drive 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 submultiples

Submultiple units, constitute a certain proportion (part) of the established unit of measurement of a certain value. The International System of Units (SI) recommends the following prefixes for denoting submultiple units:

Length	Prefix		Designation		Example
Length	Russian	international	Russian	international	Example
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)	µm - micrometer, micron
10 −9	nano	nano	n	n	nm - nanometer
10 −12	pico	pico	n	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	yocto	yocto	And	y

Origin of consoles

Most prefixes are derived from Greek words. Deca comes from the word deca or deka (δέκα) - “ten”, hecto - from hekaton (ἑκατόν) - “hundred”, kilo - from chiloi (χίλιοι) - “thousand”, mega - from megas (μέγας), that is “ big", giga is gigantos (γίγας) - "gigantic", and tera is from teratos (τέρας), meaning "monstrous". Peta (πέντε) and exa (ἕξ) correspond to five and six places of a thousand and are translated, respectively, as “five” and “six”. The lobes 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.

The prefix milli, which goes back to the Latin mille, is also translated as “thousand”. Latin roots also have the prefixes santi - from centum ("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 comes from Danish (Norwegian) femten or Old Icelandic fimmtān and means "fifteen".

The prefix pico comes from either the French pico (“beak” or “small amount”) or the Italian piccolo, meaning “small.”

Rules for using consoles

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 micromillifarads) is not permitted.
The designation of multiples and submultiples of the original unit raised to a power is formed by adding the appropriate exponent to the designation of the multiple or submultiple unit of the original unit, the exponent meaning the exponentiation of the multiple or submultiple unit (together with the prefix). Example: 1 km² = (10³ m)² = 10 6 m² (not 10³ m²). The names of such units are formed by attaching 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 a 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”, to form multiple and submultiple units of mass, a submultiple unit of mass is used - gram (0.001 kg).

Prefixes have limited use with units of time: multiple prefixes are not combined with them at all (no one uses “kilosecond,” although this is not formally prohibited), submultiple prefixes are attached only to the second (millisecond, microsecond, etc.). In accordance with GOST 8.417-2002, the names and designations of the following SI units are not allowed to be used with prefixes: minute, hour, day (time units), degree, minute, second (plane angle units), astronomical unit, diopter and atomic mass unit.

Literature

The process of establishing a correspondence between a property and a number, so that a comparison of properties can be made by comparing numbers, is called measurement. One of the properties of bodies is their extension. The extent of a body in one direction is called the length of the body. Let's look at two lines. To compare the lengths of the rulers, let’s put them next 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 will either coincide or not. If all ends of the rulers coincide, they are equal in length. When measuring, the length of each ruler is assigned a certain number that uniquely determines its length. In this case, the number allows you to select from all the rulers uniquely those whose length is determined by this number. The property defined in this way is called a physical quantity. In this case, the process of finding a number characterizing a physical property is called measurement.

For units of length, appropriate standards have been established, when compared with which any length is determined.

Meter - a unit of measurement 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 base 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 measurement 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 measurement of length (distance), and the kilogram is a unit of measurement of mass, are called metric.

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

When making measurements and calculations, multiple and submultiple units of meters are used as units of measurement of length (distance). For example, $(10)^(-10)$m = 1A (angstrom); $(10)^(-9)$m = 1 nm (nanometer); 1 km =1000 m.

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

Units of length in non-metric systems

There are systems of units in which centimeters are units of length, for example the GHS system. The GHS system was used extensively before the International System of Units was adopted. 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 measurement 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 =201.6 m; 1 chain-20.1168 m. The Japanese system of 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 =0.03030303 cm; 1 bu=0.30303 cm.

Professional systems for measuring length and distance are used. For example, there is a typographic system, naval (used in the navy), in astronomy they use special types of units for measuring distances. Thus, in astronomy, the distance from the Earth to the Sun is an astronomical unit (AU) for measuring 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 equal to 63241.077 AU. Parsec $\approx 206264.806247\ a.u$.

Some units of length 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 solutions

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

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

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

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 are units of measurement of the length of an electromagnetic wave (as well as any other length) in the SI system.

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

Solution. According to the conditions 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 moves with acceleration $\overline(g)$, which is directed along the Y axis (Fig. 1). Let us take the following equation as the basis for solving the problem:

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

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

Let's calculate the length of the body's path:

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

1.1. Connect the names of natural phenomena and the corresponding types of physical phenomena with lines.

1.2. Check the box next to the properties that both the stone and the rubber band have.

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

1.4. Write the following numbers in standard form using the example above.

2.1. Circle the properties that the physical body may not have.

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

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

2.4. Using the arrows, “sort” the words into baskets according to their names, which reflect different physical concepts.

2.5. Write down the numbers according to the example given.

3.1. During a physics lesson, the teacher placed identical-looking magnetic arrows placed on the tips of needles on the students' desks. All the arrows turned around their axis and froze, but at the same time some of them turned out to be turned to the north with the blue end, and others with the red end. The students were surprised, but during the conversation some of them expressed their hypotheses as to why this could happen. Mark which hypothesis put forward by 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 actually occur if...”

3.3. Complete the proposal.

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. Fill in 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 submultiples and vice versa.

d) Express the length values in SI base units.

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

f) Express the following quantities in SI base units.

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 around the rod as shown in the figure. The winding width turned out to be l=9 mm. What is the diameter d of the wire? Express your answer in the indicated units.

4.6. Write down the values of length and area in the indicated units according to the example given.

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

4.8. Write the volume values in SI base units using the example given.

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. Complete the proposal. “The price of a thermometer scale division is _____.”

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

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

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

5.4. Record the readings of the clock shown in the figure.

5.5. The students measured the length of their tables using different instruments 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 circumference l of five cylindrical objects using a thread and a ruler (see figure). Write down the names of objects and measurement results in the table. Use items of different sizes. For 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, you need to construct six points on the coordinate plane according to the table data and connect them with a straight line. For example, a point with coordinates (d, l) for the vessel has already been constructed on the plane. Similarly, on the same plane, construct points for other bodies.

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

6.3. Home experiment.
1. Measure the dimensions of the 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 values of the length, width and height of the box lie within the limits:

2. Calculate within what limits the true value of the volume of the box lies.

Length and distance converter Mass converter Converter of volume measures of bulk products and food products Area converter Converter of volume and units of measurement in culinary recipes Temperature converter Converter of pressure, mechanical stress, Young's modulus Converter of energy and work Converter of power Converter of force Converter of time Linear speed converter Flat angle Converter thermal efficiency and fuel efficiency Converter of numbers in various number systems Converter of units of measurement of quantity of information Currency rates Women's clothing and shoe sizes Men's clothing and shoe sizes Angular velocity and rotational speed converter Acceleration converter Angular acceleration converter Density converter Specific volume converter Moment of inertia converter Moment of force converter Torque converter Specific heat of combustion converter (by mass) Energy density and specific heat of combustion converter (by volume) Temperature difference converter Coefficient of thermal expansion converter Thermal resistance converter Thermal conductivity converter Specific heat capacity converter Energy exposure and thermal radiation power converter Heat flux density converter Heat transfer coefficient converter Volume flow rate converter Mass flow rate converter Molar flow rate converter Mass flow density converter Molar concentration converter Mass concentration in solution converter Dynamic (absolute) viscosity converter Kinematic viscosity converter Surface tension converter Vapor permeability converter Water vapor flow density converter Sound level converter Microphone sensitivity converter Converter Sound Pressure Level (SPL) Sound Pressure Level Converter with Selectable Reference Pressure Luminance Converter Luminous Intensity Converter Illuminance Converter Computer Graphics Resolution Converter Frequency and Wavelength Converter Diopter Power and Focal Length Diopter Power and Lens Magnification (×) Converter electric charge Linear charge density converter Surface charge density converter Volume charge density converter Electric current converter Linear current density converter Surface current density converter Electric field strength converter Electrostatic potential and voltage converter Electrical resistance converter Electrical resistivity converter Electrical conductivity converter Electrical conductivity converter Electrical capacitance Inductance Converter American Wire Gauge Converter Levels in dBm (dBm or dBm), dBV (dBV), watts, etc. units Magnetomotive force converter Magnetic field strength converter Magnetic flux converter Magnetic induction converter Radiation. Ionizing radiation absorbed dose rate converter Radioactivity. Radioactive decay converter Radiation. Exposure dose converter Radiation. Absorbed dose converter Decimal prefix converter Data transfer Typography and image processing unit converter Timber volume unit converter Calculation of molar mass D. I. Mendeleev’s periodic table of chemical elements

1 gigameter [Hm] = 10000000 hectometer [Hm]

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 league naval league (UK) maritime league (international) league (statutory) mile nautical mile (UK) nautical mile (international) mile (statutory) mile (USA, geodetic) mile (Roman) 1000 yards furlong furlong (USA, geodetic) chain chain (USA, geodetic) rope (English rope) genus genus (USA, geodetic) pepper floor (English) . pole) fathom, fathom fathom (US, geodetic) cubit yard foot foot (US, geodetic) link link (US, geodetic) cubit (UK) hand span finger nail inch (US, geodetic) barley grain (eng. barleycorn) thousandth of a microinch angstrom atomic unit of length x-unit Fermi arpan soldering typographical point twip cubit (Swedish) fathom (Swedish) caliber centiinch ken arshin actus (Ancient Roman) vara de tarea vara conuquera vara castellana cubit (Greek) long reed reed long elbow 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 the Earth to the Moon cables (international) cable length (British) cable length (USA) nautical mile (USA) light minute rack unit horizontal pitch cicero pixel line inch (Russian) inch span foot fathom oblique fathom verst boundary verst

Convert feet and inches to meters and vice versa

foot inch

More about length and distance

General information

Length is the largest measurement of the body. In three-dimensional space, length is usually measured horizontally.

Distance is a quantity that determines how far two bodies are from each other.

Measuring distance and length

Units of distance and length

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

Distance in physics and biology

In biology and physics, lengths are often measured at much less than one millimeter. For this purpose, a special value has been adopted, the micrometer. One micrometer is equal to 1×10⁻⁶ meters. In biology, the size of microorganisms and cells is measured in micrometers, and in physics, the length of infrared electromagnetic radiation is measured. A micrometer is also called a micron and is sometimes, especially in English literature, 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).

Navigation distance

Shipping uses nautical miles. One nautical mile is equal to 1852 meters. It was originally measured as an arc of one minute along the meridian, that is, 1/(60x180) 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 knots. One sea knot equals a speed of one nautical mile per hour.

Distance in astronomy

In astronomy, large 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 equal to 10,000,000,000,000 or 10¹³ kilometers. This is the distance that light travels in a vacuum in one Julian year. This quantity 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 arcsecond is 1/3600 of a degree, or approximately 4.8481368 microrads in radians. Parsec can be calculated using parallax - the effect of visible changes in body position, depending on the observation point. When making measurements, lay a segment E1A2 (in the illustration) 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 laid 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 plot a segment through point S, perpendicular to E1E2, it will pass through the intersection point of segments E1A2 and E2A1, I. The distance from the Sun to point I is segment SI, it is equal to one parsec, when the angle between segments A1I and A2I is two arcseconds.

In the picture:

A1, A2: apparent star position
E1, E2: Earth position
S: Sun position
I: point of intersection
IS = 1 parsec
∠P or ∠XIA2: parallax angle
∠P = 1 arcsecond

Other units

League- an obsolete unit of length previously used 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 travels in an hour. Sea League - three nautical miles, approximately 5.6 kilometers. Lieu is a unit approximately equal to a league. In English, both leagues and leagues are called the same, league. In literature, 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 ancient 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 fabric and the length of swimming pools and sports fields and fields, such as golf and football courses.

Definition of meter

The definition of 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. The meter was later equated to the wavelength of the orange line of the electromagnetic spectrum of the krypton ⁸⁶Kr atom in a 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.

Computations

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 unitconversion.org functions.

There are multiple and submultiple units of physical quantity.

Multiple unit– a unit of physical quantity, an integer number of times larger than a systemic or non-systemic unit.

submultiple unit– a unit of physical quantity that is an integer number of times smaller than a systemic or non-systemic unit. See appendix.

The most progressive way of forming multiples and submultiples is the decimal multiplicity between major and minor units adopted in the metric system of measures. In accordance with the resolution of the XI General Conference on Weights and Measures, decimal multiples and submultiples of SI units are formed by adding prefixes.

For example, the unit of length kilometer is equal to 10 3 m, i.e. is a multiple of a meter, and the unit of length millimeter is equal to 10 -3 m, i.e. is subordinate. Factors and prefixes for the formation of multiple and submultiple SI units are given in Table 1.2.

Non-system units– units of physical quantities that are not included in the accepted system of units. They are divided:

Permitted for use on a par with SI units;

Permitted for use in special areas;

Temporarily admitted;

To obsolete (not allowed).

1.5. Systems of physical quantities and their units

Physical quantities are usually divided into basic and derivative.

Kelvin– 1/273.16 part of the thermodynamic temperature of the triple point of water;

Mole – the amount of substance of a system containing the same number of structural elements as there are atoms contained in a carbon-12 nuclide weighing 0.012 kg;

Candela– luminous intensity in a given direction of a source emitting monochromatic radiation with a frequency of 540*10 12 Hz.

Derived units of the International System of Units are formed using which are called derivatives from them. For example, in Einstein's formula E = mc 2 (m is mass, c is the speed of light), mass is the basic unit that can be measured by weighing; energy (E) is a derived unit. Basic quantities correspond to basic units of measurement, and derived quantities correspond to derived units of measurement.

Thus, system of units of physical quantities (system of units)- a set of basic and derived units of physical quantities, formed in accordance with the principles underlying this system of physical quantities.

The first system of units is the metric system.

1.5.1. Basic, additional and derived units of the system of si

The basic units of the International System of Units were chosen in 1954 by the 10th General Conference on Weights and Measures. At the same time, we proceeded from the following: 1) to cover all areas of science and technology with the system; 2) create a basis for the formation of derivative units for various physical quantities; 3) adopt practical sizes of basic units that have already become widespread; 4) choose units of such quantities that can be reproduced with the help of standards with the greatest accuracy.

The International System of Units includes two additional units - for measuring plane and solid angles.

Basic and additional SI units are given in the appendix.

Meter– the path length that light travels in a vacuum in 1/299792458 of a second;

Kilogram– a mass equal to the mass of the international prototype of the kilogram (a platinum cylindrical weight, the height and diameter of which are each 39 mm);

Second– duration of 9192631770 periods of radiation corresponding to the transition between two levels of the hyperfine structure of the ground state of the cesium-133 atom in the absence of disturbance from external fields;

Ampere- the strength of an unchanging current, which, when passing through two parallel conductors of infinite length and negligibly small circular cross-section, located at a distance of 1 m from each other in a vacuum, would create a force between these conductors equal to 2 * 10 -7 N for each meter of length ;

???????????????????????????????

the simplest equations between quantities in which the numerical coefficients are equal to unity.

For example, for linear speed, as a defining equation, you can use the expression for the speed of uniform rectilinear motion v = l/t. Then, given the length of the traveled path l (in meters) and time t (in seconds), the speed is expressed in meters per second (m/s). Therefore, the SI unit of speed – meter per second – is the speed of a rectilinearly and uniformly moving point at which it moves a distance of 1 m in 1 s.

Prefixes for multiples

Multiplicity	Prefix		Designation		Example
Multiplicity	Russian	international	Russian	international	Example
10 1	soundboard	deca	Yes	da	dal - deciliter
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	Z	Z	ZeV - zettaelectronvolt
10 24	yotta	Yotta	AND	Y	Yb - yottabyte

Binary understanding of prefixes

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 submultiples

Length	Prefix		Designation		Example
Length	Russian	international	Russian	international	Example
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)	µm - micrometer, micron
10 −9	nano	nano	n	n	nm - nanometer
10 −12	pico	pico	n	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	yocto	yocto	And	y

Origin of consoles

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

The prefix pico comes from either the French pico (“beak” or “small amount”) or the Italian piccolo, meaning “small.”

Rules for using consoles

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 micromillifarads) is not permitted.
The designation of multiples and submultiples of the original unit raised to a power is formed by adding the appropriate exponent to the designation of the multiple or submultiple unit of the original unit, the exponent meaning the exponentiation of the multiple or submultiple unit (together with the prefix). Example: 1 km² = (10³ m)² = 10 6 m² (not 10³ m²). The names of such units are formed by attaching 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 a product or to the denominator is allowed only in justified cases.

Applicability of prefixes

Literature

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

A multiple unit is a unit that is an integer number of times larger than a systemic or non-systemic unit. For example, a multiple of a unit of length - a kilometer - is 1000 times larger than the original unit of a meter; a multiple of a unit of time - a minute is 60 times larger than a second; a multiple of a unit of capacity - a hectoliter is 100 times larger than the off-system unit of a liter

A fractional unit is a unit that is an integer number of times smaller than a systemic or non-systemic unit. For example, a submultiple unit of length - a nanometer is 109 times smaller than a meter; a submultiple unit of a plane angle - a minute is 60 times smaller than a degree.

The most convenient for use are decimal multiples and submultiples, i.e., units formed by multiplying or dividing by the number 10 or a power of ten with an integer exponent. The state standard “Units of Physical Quantities” provides for the use of mainly decimal multiples and submultiples of units indicated in Table. 2.

The names of decimal multiples and submultiples are formed by adding prefixes to the names of the original units. The following rules are observed:

1) connecting two or more consoles in a row is not allowed. For example, a submultiple unit of electrical capacitance is formed with one prefix “pico” but not with two prefixes “micro”, i.e. the submultiple unit “picofarad” is used, not “micromicrofarad”;

2) when forming the name of a decimal multiple or submultiple unit from the basic SI unit - kilogram,

the name of which already contains a prefix, a new prefix is added to the simple name, i.e. to the name “gram”. For example, the multiple unit is called "megagram" rather than "kilokilogram";

3) you cannot assign proper names to submultiples and multiple units. In accordance with this rule, names such as micron or millimicron should be abandoned. Instead of the names “micron” and “millimicron”, the names “micrometer” and “nanometer” should be used, respectively;

4) if the name of the original unit consists of one word (meter, ampere, newton, etc.), then the prefix is written together with the name of the unit (millimeter, microampere, kilonewton);

5) in case of a complex name of a derived unit, a prefix is added to the name of the first unit included in the product or in the numerator of the fraction. For example, the multiple unit of moment of force is called “kilo-newton-meter”, but not “newton-kilometer”; a multiple of the unit of acoustic resistivity is called “kilopascal-second per meter”, but not “pascal-kilo-second per meter”;

6) with a complex name of a unit, formed as a combination of units with a multiple or submultiple unit of length, area or volume, it is allowed, if necessary, to use prefixes in the second factor of the numerator or in the denominator, for example, ton-kilometer, watt per square centimeter, volt per centimeter, amperes per square millimeter, etc.;

7) to form names of multiple and submultiple units from a unit raised to a power different from the first, a prefix is added to the name of the unit to the first power. For example, to form the name of a multiple or submultiple unit of a unit of area - a square meter, which is the second power of a unit of length - a meter, a prefix is added to the name of this last unit: square kilometer, square centimeter, etc.;

8) the prefixes hecto, deca, deci, centi are allowed to be used only in the names of multiple and submultiple units that are already widely used (for example, hectare, deciliter, decimeter, centimeter, etc.).

When forming multiples and submultiples, the following rules should be followed:

a) the designations of prefixes are written together with the designations of the units to which they are attached, for example mg and milligram), Mm (megameter), pF (picofarad), etc.;

b) designations of multiples and submultiples of a unit to a power different from the first are formed by raising the designation of a multiple or submultiple of this unit to the first power to the appropriate power, and the exponent refers to the entire designation (together with the prefix), for example.