Multiples of length units are in meters and vice versa. Multiples of units

Prefixes for multiples

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	Console		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 submultiple units

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	Console		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	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	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 (e.g. 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

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 ) ·

The physical phenomena you will study in 6th grade are described by quantities such as length, mass, time, and temperature. Let us recall that the basic units in which these physical quantities are measured in the International System of Units (SI) are (see § 5):

1 m - unit of length;
1 kg is a unit of mass;
1 s - unit of time interval;
1 K (K is a degree on the Kelvin scale) is a unit of temperature.

The International System of Units (SI) is metric. What does this mean? This means that through the basic units, multiples and submultiples can be obtained by multiplication or division: multiple units - by multiplying the basic unit by 10, 100, 1000, ...; submultiples - by dividing the basic unit by 10, 100, 1000, ….

The first flyleaf of the textbook presents units that are multiples and submultiples of the basic units of length, mass and time interval.

When solving problems, you will most often work with SI base units.

From multiples and submultiples it is easy to move on to the basic ones. For example, let the distance from your home to school be l = 0.500 km. Let's express it in basic units of length - meters (m). The first flyleaf shows: 1 km = 1000 m.

Then l = 0.500. 1000 m = 500 m.

Means, to move from multiple units to the base one, you need to multiply the values by 10, 100, 1000, .... One more example. The mass of cottage cheese in the package is m = 200 g. Let us express the mass of cottage cheese in basic units of mass - kilograms (kg).

1 g = 0.001 kg.

m = 200. 0.001 kg = 0.2 kg.

Therefore, in order to move from submultiple units to the fundamental one, the values of the quantities must be divided by 10, 100, 1000, ....

Think and answer

Convert the given values of quantities to SI base units:

ruler length l = 30 cm;
length of the tourist route l = 20 km;
mass of a passenger car (without passengers) m = 0.50 t;
mass of one candy m = 30 g;
time period t = 1.0 h;
the period of time from sunrise to sunset on the day of the vernal equinox.

Do it yourself at home

Draw in your notebook a straight segment of length l = 1 dm.
Divide it into 10 equal parts. What is the length of one part?
Divide the length of this part into 10 equal parts. What is the length of one part?
How many times is the length of the original straight line segment greater than the lengths of the resulting parts?

Exercises

Express the cabinet height h = 215 cm in millimeters (mm), decimeters (dm), meters (m), kilometers (km). What units are most convenient for measuring the height of a cabinet?
Express the mass of a bag of flour m = 48 kg in tons (t), centners (c), grams (g), milligrams (mg). In what units is it most convenient to measure the mass of a bag of flour?
The athlete ran a 5-kilometer distance in a period of time t = 828 s. Express this period of time in minutes (min), hours (h).
How many times do the units of length adopted in England and the USA differ: mile l 1 = 1609 m and nautical mile l 2 = 1.852 km? How many cables are there in one nautical mile?
Note. 1 cable = 185.2 m.
In the old days, to determine the mass of products made of gold and silver, units of measurement were often used: 1 share = 44.4 mg and 1 spool = 4.27 g. How many times do these units of mass differ? How many grams (g) of silver are in the 50-kopeck coin of 1896, on which it is written: “pure silver 2 spools”? How many milligrams (mg)?

International system of units(Systeme International d'Unitees), 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 developed on the basis metric system of measures, and simplifying the use of units. The advantages of the International System of Units are its universality (covers 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. Thanks to this, when calculating, if you express the values of all quantities in units of the International System of Units, you do not need to enter coefficients into 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 derivative units of the International System of Units. Russian designations are given in accordance with 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 relationship between them is given in the articles about these units.

Basic and derived units of the International System of Units

Magnitude	Unit name	Designation
Magnitude	Unit name	international	Russian
Basic units
Length	meter	m	m
Weight	kilogram	kg	kg
Time	second	s	With
Electric current strength	ampere	A	A
Thermodynamic temperature	kelvin	TO	TO
The power of light	candela	CD	cd
Quantity of substance	kilomole	kmol	kmol
Additional units
Flat angle	radian	rad	glad
Solid angle	steradian	sr	Wed
Derived units
Square	square meter	m 2	m 2
Volume, capacity	cubic meter	m 3	m 3
Frequency	hertz	Hz	Hz
Speed	meter per second	m/s	m/s
Acceleration	meters 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/m 3	kg/m 3
Force	newton	N	N
Pressure, mechanical stress	Pascal	Pa	Pa (N/m2)
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	W
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 capacity	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	Vehicle
Magnetomotive force	ampere	A	A
Entropy	joule per kelvin	J/K	J/C
Specific heat capacity	joule per kilogram kelvin	J/(kg K)	J/(kg K)
Thermal conductivity	watt per meter kelvin	W/(mK)	W/(mK)
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 derivative units for all quantities that have a mechanical nature, the rest were added to form derived units of quantities that are not reducible to mechanical ones: ampere - for electrical and magnetic quantities, kelvin - for thermal, candela - for light and mole - for quantities in the field of physical. chemistry and molecular physics. Additionally, the units of radians and steradians are used to form derived units of quantities that depend on plane or solid angles. To form the names of decimal multiples and submultiples, special units are used. SI prefixes: deci(to form units equal to 10 -1 relative 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. Multiple units, Submultiples.

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. Choose 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:

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

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, a multiple of the 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 have already been 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 to the appropriate power the designation of a multiple or submultiple of this unit to the first power, and the exponent refers to the entire designation (together with the prefix), for example:

When expressing a quantity in decimal multiples and submultiples, prefixes should be chosen so that the numerical values of the quantities are in the range from 0.1 to 1000. For example, to express a length equal to, you should choose the prefix “micro”, but not “milli”. and not "nano". With the prefix “micro” we get i.e. a number ranging from 0.1 to 1000. With the prefix “milli” we get i.e. a number less than the prefix “nano” will be obtained, i.e. a number greater than 1000.

Of the non-decimal multiples and submultiples, only time units are allowed for use - minute, hour, day and plane angle units - degree, minute, second (see Table 13, as well as § 26).

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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 (British) maritime league (international) league (statutory) mile nautical mile (British) 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 longest 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.

On the image:

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 atom ⁸⁶Kr 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 Attachment.

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 a lobe. Factors and prefixes for the formation of multiples and submultiples of 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 dimensions of basic units that have already become widespread; 4) select 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 ;

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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.