Value is something that can be measured. Concepts such as length, area, volume, mass, time, speed, etc. are called quantities. The value is measurement result, it is determined by a number expressed in certain units. The units in which a quantity is measured are called units of measurement.
To designate a quantity, a number is written, and next to it is the name of the unit in which it was measured. For example, 5 cm, 10 kg, 12 km, 5 min. Each value has an infinite number of values, for example, the length can be equal to: 1 cm, 2 cm, 3 cm, etc.
The same value can be expressed in different units, for example, kilogram, gram, and ton are units of weight. The same quantity expressed in different units different numbers. For example, 5 cm = 50 mm (length), 1 hour = 60 minutes (time), 2 kg = 2000 g (weight).
To measure a quantity means to find out how many times it contains another quantity of the same kind, taken as a unit of measurement.
For example, we want to know exact length some room. So we need to measure this length using another length that is well known to us, for example, using a meter. To do this, set aside a meter along the length of the room as many times as possible. If he fits exactly 7 times along the length of the room, then its length is 7 meters.
As a result of measuring the quantity, one obtains or named number, for example 12 meters, or several named numbers, for example 5 meters 7 centimeters, the totality of which is called composite named number.
Measures
In each state, the government has established certain units of measurement for various quantities. A precisely calculated unit of measurement, taken as a model, is called standard or exemplary unit. Model units of the meter, kilogram, centimeter, etc., were made, according to which units for everyday use are made. Units that have come into use and approved by the state are called measures.
The measures are called homogeneous if they serve to measure quantities of the same kind. So, grams and kilograms are homogeneous measures, since they serve to measure weight.
Units
The following are units of measurement for various quantities that are often found in math problems:
Measures of weight/mass
- 1 ton = 10 centners
- 1 centner = 100 kilograms
- 1 kilogram = 1000 grams
- 1 gram = 1000 milligrams
- 1 kilometer = 1000 meters
- 1 meter = 10 decimeters
- 1 decimeter = 10 centimeters
- 1 centimeter = 10 millimeters
- 1 sq. kilometer = 100 hectares
- 1 hectare = 10000 sq. meters
- 1 sq. meter = 10000 sq. centimeters
- 1 sq. centimeter = 100 sq. millimeters
- 1 cu. meter = 1000 cubic meters decimeters
- 1 cu. decimeter = 1000 cu. centimeters
- 1 cu. centimeter = 1000 cu. millimeters
Let's consider another value like liter. A liter is used to measure the capacity of vessels. A liter is a volume that is equal to one cubic decimeter (1 liter = 1 cubic decimeter).
Measures of time
- 1 century (century) = 100 years
- 1 year = 12 months
- 1 month = 30 days
- 1 week = 7 days
- 1 day = 24 hours
- 1 hour = 60 minutes
- 1 minute = 60 seconds
- 1 second = 1000 milliseconds
In addition, time units such as quarter and decade are used.
- quarter - 3 months
- decade - 10 days
The month is taken as 30 days, unless it is required to specify the day and name of the month. January, March, May, July, August, October and December - 31 days. February in a simple year - 28 days, February in leap year- 29 days. April, June, September, November - 30 days.
A year is (approximately) the time during which the Earth makes full turn around the sun. It is customary to count every three consecutive years for 365 days, and the fourth following them - for 366 days. A year with 366 days is called leap year, and years containing 365 days - simple. By the fourth year, one extra day is added next reason. The time of revolution of the Earth around the Sun does not contain exactly 365 days, but 365 days and 6 hours (approximately). Thus, a simple year is shorter than a true year by 6 hours, and 4 simple years shorter than 4 true years for 24 hours, i.e. for one day. Therefore, one day (February 29) is added to every fourth year.
You will learn about other types of quantities as you further study various sciences.
Measure abbreviations
Abbreviated names of measures are usually written without a dot:
|
Measures of weight/mass
|
Area measures (square measures)
|
|
Measures of time
|
A measure of the capacity of vessels
|
Measuring instruments
To measure various quantities, special measuring instruments are used. Some of them are very simple and are intended for simple measurements. Such devices include a measuring ruler, tape measure, measuring cylinder, etc. Other measuring devices are more complex. Such devices include stopwatches, thermometers, electronic scales, etc.
Measuring instruments, as a rule, have a measuring scale (or short scale). This means that dash divisions are marked on the device, and the corresponding value of the quantity is written next to each dash division. The distance between two strokes, next to which the value of the value is written, can be further divided into several more smaller divisions, these divisions are most often not indicated by numbers.
It is not difficult to determine which value of the value corresponds to each smallest division. So, for example, the figure below shows a measuring ruler:
The numbers 1, 2, 3, 4, etc. indicate the distances between the strokes, which are divided by 10 identical divisions. Therefore, each division (the distance between the nearest strokes) corresponds to 1 mm. This value is called scale division measuring instrument.
Before proceeding with the measurement of a quantity, it is necessary to determine the value of the division of the scale of the instrument used.
In order to determine the division price, you must:
- Find the two nearest strokes of the scale, next to which the magnitude values are written.
- subtract from greater value divide the smaller and the resulting number by the number of divisions in between.
As an example, let's determine the scale division value of the thermometer shown in the figure on the left.
Let's take two strokes, near which the numerical values of the measured quantity (temperature) are plotted.
For example, strokes with symbols 20 °С and 30 °С. The distance between these strokes is divided into 10 divisions. Thus, the price of each division will be equal to:
(30 °C - 20 °C) : 10 = 1 °C
Therefore, the thermometer shows 47 °C.
Measure various quantities in Everyday life each and every one of us has to do. For example, to come to school or work on time, you have to measure the time that will be spent on the road. Meteorologists measure temperature to predict the weather. Atmosphere pressure, wind speed, etc.
Fixed size, which is conditionally assigned by agreement numerical value equal to 1 (\displaystyle 1). Any other quantity of the same kind can be compared with a unit of a physical quantity and their ratio can be expressed as a number. It is used for the quantitative expression of physical quantities homogeneous with it. Units of measurement have names and designations assigned to them by agreement.
A number with an indication of the unit of measure is called named.
Distinguish between basic and derived units. Basic units in this system of units are set for those physical quantities that are chosen as the main ones in the corresponding system of physical quantities . So, the International System of Units (SI) is based on the International System of Units (eng. International System of Quantities, ISQ), in which seven quantities are the main ones: length, mass, time, electric current, thermodynamic temperature, amount of substance and luminous intensity. Accordingly, in SI, the basic units are the units of the indicated quantities.
The sizes of the basic units are established by agreement within the framework of the corresponding system of units and are fixed either using standards (prototypes) or by fixing numerical values fundamental physical constants.
Derived units are determined through the main ones by using those relationships between physical quantities that are established in the system of physical quantities.
Exist a large number of various systems units that differ both in the systems of quantities on which they are based and in the choice of base units.
The rules for writing unit designations in the production of scientific literature, textbooks and other printed products are defined by GOST 8.417-2002 "State system for ensuring the uniformity of measurements". In printed publications, it is allowed to use either international or Russian designations of units. The simultaneous use of both types of designations in the same publication is not allowed, with the exception of publications on units of physical quantities.
Story
Units of measurement were among the earliest tools invented by humans. primitive societies needed elementary measures to solve everyday problems: building dwellings of a certain size and shape, creating clothes, exchanging food or raw materials.
The earliest known unified systems measurements, apparently, were created in the 4th and 3rd millennium BC. e. the ancient peoples of Mesopotamia, Egypt, the Indus Valley, and possibly also Persia.
There are mentions of weight and measure in the Bible (Leviticus 19:35-36) - this is a commandment to be honest and have fair measures.
In 1875, an agreement on the Meter Convention was signed between 17 countries. With the signing of this treaty, the International Bureau of Weights and Measures and the International Committee of Weights and Measures were established and the General Conferences on Weights and Measures (CGPM) were established, usually meeting every four years. These international bodies created the current SI system, which was adopted in 1954 by the 10th CGPM and approved by the 11th CGPM in 1960.
On November 16, 2018, the session of the 26th CGPM was held in Versailles at the Palais des Congrès. iridium prototype of the kilogram (since 1889), which will be officially replaced new implementation as physical experiment value based
GOVERNMENT OF THE RUSSIAN FEDERATION
ON THE APPROVAL OF THE REGULATION
IN RUSSIAN FEDERATION
Article 6 federal law"On Ensuring the Uniformity of Measurements" Government Russian Federation decides:
Approve the attached Regulations on units of quantities allowed for use in the Russian Federation.
Prime Minister
Russian Federation
V. PUTIN
Approved
Government Decree
Russian Federation
dated October 31, 2009 N 879
POSITION
ON UNITS OF VALUES ALLOWED FOR USE
IN RUSSIAN FEDERATION
I. General provisions
1. This Regulation establishes the units of quantities allowed for use in the Russian Federation, their names and designations, as well as the rules for their application and spelling.
2. In the Russian Federation, units of the International System of Units (SI) are used, adopted by the General Conference on Weights and Measures and recommended for use international organization legal metrology.
3. The concepts used in this Regulation mean the following:
"value" - a property of an object, phenomenon or process that can be distinguished qualitatively and quantified;
"off-system unit of quantity" - a unit of quantity that is not included in accepted system units;
"unit of quantity" - a fixed value of a quantity, which is taken as a unit of such a quantity and is used for the quantitative expression of quantities homogeneous with it;
"coherent unit of quantity" - a derived unit of quantity, which is the product of basic units raised to a power, with a proportionality factor equal to 1;
"logarithmic unit of a quantity" - the logarithm of the dimensionless ratio of a quantity to the quantity of the same name taken as the initial one;
"International System of Units (SI)" - a system of units based on the International System of Units;
"basic quantity" - a quantity conditionally accepted as independent of other quantities of the International System of Quantities;
"SI base unit" - a unit of base quantity in the International System of Units (SI);
"relative value" - the dimensionless ratio of the value to the value of the same name, taken as the original;
"derived value" - a value determined through the basic values of the system;
"SI derived unit" - a unit of a derived quantity of the International System of Units (SI);
"SI system of units" - a set of basic and derived SI units, their decimal multiples and submultiples, as well as the rules for their use.
II. Units of quantities allowed for use,
their names and designations
4. In the Russian Federation, the basic SI units, derived SI units and individual off-system units of quantities are allowed to be used.
5. The basic units of the International System of Units (SI) are given in Appendix N 1.
6. SI derived units are formed through SI base units according to mathematical rules and are defined as the product of the base SI units to the appropriate powers. Separate derived SI units have special names and symbols.
Derived units of the International System of Units SI are given in Appendix No. 2.
7. Non-system units of quantities are given in Appendix N 3. Relative and logarithmic units of quantities are given in Appendix N 4.
III. Rules for the use of units of quantities
8. In the Russian Federation, multiples and submultiples of basic SI units, derived SI units and individual non-systemic units of quantities, formed with the help of decimal factors and prefixes, are allowed to be used.
Decimal factors, prefixes and designations of prefixes for the formation of multiple and submultiple units of quantities are given in Appendix No. 5.
9. In the legal acts of the Russian Federation, when establishing mandatory requirements for quantities, measurements and indicators of compliance with accuracy, the designation of units of quantities using the letters of the Russian alphabet (hereinafter - Russian designation units).
10. In technical documentation(design, technological and program documentation, specifications, standardization documents, instructions, manuals, guidelines and regulations), in methodological, scientific, technical and other product documentation various kinds, as well as in scientific and technical publications (including textbooks and study guides) international is applied (using letters of Latin or Greek alphabet) or the Russian designation of units of quantities.
The simultaneous use of Russian and international designations of units of quantities is not allowed, except for cases related to the explanation of the use of such units.
11. When indicating units of quantities on technical means, devices and measuring instruments, it is allowed to use the international designation of units of quantities along with the Russian designation of units of quantities.
IV. Rules for writing units of quantities
12. When writing the values of quantities, the designations of units of quantities are used by letters or special characters(°), ("), ("). At the same time, 2 types of letter designations are established - the international designation of units of quantities and the Russian designation of units of quantities.
13. Letter designations of units of sizes are printed by a direct font. In the notation of units of quantities, the dot is not put.
14. Designations of units of quantities are placed after the numerical values of quantities in the same line with them (without transfer to the next line). The numeric value, which is a fraction with a slash, in front of the designation of the unit of magnitude, is enclosed in brackets. A space is placed between the numerical value and the designation of the unit of magnitude.
The exceptions are the designations of units of quantities in the form of a sign placed above the line, before which there is no space.
15. Subject to availability decimal fraction in the numerical value of a quantity, the designation of the unit of quantity is indicated after the last digit. A space is placed between the numerical value and the letter designation of the unit of magnitude.
16. When specifying values of quantities with limiting deviations, the value of quantities and their limiting deviations are enclosed in brackets, and the designations of units of quantities are placed outside the brackets or the designations of units of quantities are placed both behind the numerical value of the quantity and behind its limiting deviation.
17. When designating units of quantities in explanations of the designations of quantities to formulas, it is not allowed to designate units of quantities in one line with formulas expressing dependencies between quantities or between their numerical values presented in alphabetic form.
18. Letter designations of units of quantities included in the product of units of quantities are separated by a dot on middle line("·"). It is not allowed to use the symbol "x" to denote the product of units of magnitude.
It is allowed to separate the letter designations of the units of quantities included in the product with spaces.
19. In the alphabetic designations of ratios of units of quantities, only one slash or horizontal line is used as a division sign. It is allowed to use the letter designation of a unit of quantity in the form of a product of the designations of units of quantities raised to a power (positive or negative).
If for one of the units of quantities included in the ratio, a letter designation is set in the form negative degree, slash, or horizontal bar does not apply.
20. When using a slash, the letter designation of units of quantities in the numerator and denominator is placed in a line, and the product of the designations of units of quantities in the denominator is enclosed in brackets.
21. When specifying a derived SI unit, consisting of 2 or more units of quantities, it is not allowed to combine the letter designation and the name of the units of quantities (for some units of quantities, indicate the designations, and for others - the names).
22. It is allowed to use a combination of signs (°), ("), ("), (%) and (promille) with letter designations of units of quantities.
23. Designations of derived SI units that do not have special names must contain a minimum number of designations for units of quantities with special names and basic SI units with the lowest possible exponents.
24. When specifying a range of numerical values of a quantity, expressed in the same units of quantities, the designation of the unit of quantity is indicated after the last numerical value of the range.
Appendix No. 1
allowed for use
In Russian federation
BASIC UNITS OF THE INTERNATIONAL SYSTEM OF UNITS (SI)
| Value name | Unit of magnitude | |||
|---|---|---|---|---|
| Name | designation | definition | ||
| international | Russian | |||
| 1. Length | meter | m | m | meter - the length of the path traveled by light in a vacuum in a time interval of 1/299 792 458 seconds (XVII General Conference on Weights and Measures (CGPM), 1983, Resolution 1) |
| 2. Weight | kilogram | kg | kg | kilogram is a unit of mass, equal to the mass international prototype of the kilogram (I CGPM, 1889, and III CGPM, 1901) |
| 3. Time | second | s | with | second - time equal to 9 192 631 770 periods of radiation corresponding to the transition between two hyperfine levels of the ground state of the cesium-133 atom (XIII CGPM, 1967, Resolution 1) |
| 4. Electric current, power electric current | ampere | A | A | ampere - the strength of an unchanging current, which, when passing through two parallel straight conductors infinite length and negligible area of the circular cross section, located in vacuum at a distance of 1 meter from each other, would cause on each section of a conductor 1 meter long an interaction force equal to 2 10 -7 newtons (International Committee for Weights and Measures, 1946, Resolution 2, approved by IX CGPM, 1948 ) |
| 5. Amount of substance | mole | mol | mole | mole - the amount of substance of a system containing as many structural elements as there are atoms in carbon-12 weighing 0.012 kilograms. When using a mole structural elements must be specified and may be atoms, molecules, ions, electrons and other particles or specified groups of particles (XIV CGPM, 1971, Resolution 3) |
| 6. Thermodynamic temperature | kelvin | K | K | kelvin - a unit of thermodynamic temperature equal to 1/273.16 of the thermodynamic temperature of the triple point of water (XIII CGPM, 1967, Resolution 4) |
| 7. Power of light | candela | cd | cd | candela - the power of light in given direction a source emitting monochromatic radiation with a frequency of 540 10 12 hertz, energy force of light in that direction is 1/683 watt per steradian (XVI CGPM, 1979, Resolution 3) |
Appendix No. 2
to the Regulations on units of quantities,
allowed for use
In Russian federation
DERIVATIVE UNITS OF THE INTERNATIONAL SYSTEM OF UNITS (SI)
| Value name | Unit of magnitude | |||
|---|---|---|---|---|
| Name | designation | expression in terms of base and derived SI units | ||
| international | Russian | |||
| 1. Flat corner | radian | rad | glad | m m -1 = 1 |
| 2. Solid angle | steradian | sr | Wed | m 2 m -2 \u003d 1 |
| 3. Square | square meter | m2 | m 2 | m 2 |
| 4. Volume | cubic meter | m 3 | m 3 | m 3 |
| 5. Speed | meters per second | m/s | m/s | m s -1 |
| 6. Acceleration | meters per second squared | m/s 2 | m/s 2 | m s -2 |
| 7. Frequency | hertz | Hz | Hz | s s -1 |
| 8. Strength | newton | N | H | m kg s -2 |
| 9. Density | kilogram per cubic meter | kg/m3 | kg / m 3 | kg m -3 |
| 10. Pressure | pascal | Ra | Pa | m -1 kg s -2 |
| 11. Energy, work, amount of heat | joule | J | J | m 2 kg s -2 |
| 12. Heat capacity | joule per kelvin | J/K | J/K | m 2 kg s -2 K -1 |
| 13. Power | watt | W | Tue | m 2 kg s -3 |
| 14. Electric charge, quantity of electricity | pendant | C | Cl | c A |
| 15. electrical voltage, electric potential, difference electrical potentials, electromotive force | volt | V | AT | m 2 kg s -3 A -1 |
| 16. Electrical capacitance | farad | F | F | m -2 kg -1 s 4 A 2 |
| 17. Electrical resistance | ohm | Omega | Ohm | m 2 kg s -3 A -2 |
| 18. electrical conductivity | Siemens | S | Cm | m -2 kg -1 s 3 A 2 |
| 19. Flux of magnetic induction, magnetic flux | weber | wb | wb | m 2 kg s -2 A -1 |
| 20. Density magnetic flux, magnetic induction | tesla | T | Tl | kg s -2 A -1 |
| 21. Inductance, mutual inductance | Henry | H | gn | m 2 kg s -2 A -2 |
| 22. Temperature Celsius | degree Celsius | °C | °C | To |
| 23. Luminous flux | lumen | lm | lm | cd sr |
| 24. Illumination | luxury | lx | OK | m -2 cd sr |
| 25. Nuclide activity in a radioactive source (radionuclide activity) | becquerel | bq | Bq | from -1 |
| 26. Absorbed dose ionizing radiation, kerma | gray | Gy | Gr | m 2 s -2 |
| 27. Equivalent dose of ionizing radiation effective dose of ionizing radiation | sievert | Sv | Sv | m 2 s -2 |
| 28. Catalyst activity | rolled | kat | cat | mol s -1 |
| 29. Moment of force | newton meter | N m | N m | m 2 kg s -2 |
| 30. Electric field strength | volt per meter | V/m | V/m | m kg s -3 A -1 |
| 31. Magnetic field strength | ampere per meter | A/m | A/m | m -1 A |
| 32. Electrical conductivity | siemens per meter | S/m | cm/m | m -3 kg -1 s 3 A 2 |
Note. SI derived units with special names and symbols may be used to form other SI derived units. It is allowed to use derived SI units formed through the basic SI units according to the rules for the formation of coherent units of quantities and defined as the product of the basic SI units in the appropriate powers.
Coherent units of quantities are formed on the basis of the simplest equations of connection between quantities, in which the numerical coefficients are equal to 1. In this case, the designations of quantities in the equations of connection between quantities are replaced by the designations of the basic SI units.
If the relation equation between quantities contains a numerical coefficient other than 1, to form a coherent unit of quantity in right side The equations are substituted with the values of quantities in basic SI units, which, after multiplication by a coefficient, give a total numerical value equal to 1.
Appendix No. 3
to the Regulations on units of quantities,
allowed for use
In Russian federation
OUTSIDE UNITS OF VALUES
| Value name | Unit of magnitude | ||||
|---|---|---|---|---|---|
| Name | designation | ratio with SI unit | scope (validity period) | ||
| international | Russian | ||||
| 1. Mass | ton | t | T | 1 10 3 kg | all areas |
| atomic unit masses | u | a.u.m. | 1.6605402 10 -27 kg (approximately) |
atomic physics | |
| carat | - | car | 2 10 -4 | for precious stones and pearls | |
| 2. Time | minute | min | min | 60 s | all areas |
| hour | h | h | 3600 s | ||
| day | d | day | 86400 s | ||
| 3. Volume, capacity | liter | l | l | 1 10 -3 m 3 | all areas |
| 4. Flat corner | degree | ° | ° | (Pi/180) rad = 1.745329... 10 -2 rad | all areas |
| minute | " | " | (Pi/10800) rad = 2.908882... 10 -4 rad | ||
| second | " | " | (Pi/648000) rad = 4.848137... 10 -6 rad | ||
| hail (gon) | gon | hail | (Pi/200) rad = 1.57080... 10 -2 rad | ||
| 5. Length | astronomical unit | ua | a.u. | 1.49598 10 11 m (approximately) |
astronomy |
| light year | ly | holy year | 9.4607 10 15 m (approximately) |
||
| parsec | pc | PC | 3.0857 10 16 m (approximately) |
||
| angstrom | ° BUT |
° BUT |
10 -10 m | physics, optics | |
| nautical mile | n mile | mile | 1852 m | maritime and aviation navigation | |
| foot | ft | foot | 0.3048 m | aviation navigation | |
| inch | inch | inch | 0.0254 m | industry | |
| 6. Square | hectare | ha | ha | 1 10 4 m 2 | agriculture and forestry |
| ar | a | a | 1 10 2 m 2 | ||
| 7. Strength | gram-force | gf | gs | 9.80665 10 -3 N | |
| kilogram-force | kgf | kgf | 9.80665 N | ||
| ton-force | tf | ts | 9806.65 N | ||
| 8. Pressure | bar | bar | bar | 1 10 5 Pa | industry |
| kilogram-force per square centimeter | kgf/cm2 | kgf / cm 2 | 98066.5 Pa | all regions (valid until 2016) | |
| millimeter of water column | mmH2O | mm water column | 9.80665 Pa | all regions (valid until 2016) | |
| meter of water column | mH2O | m w.c. | 9806.65 Pa | all regions (valid until 2016) | |
| technical atmosphere | - | at | 9.80665 10 4 Pa | all regions (valid until 2016) | |
| millimeter of mercury | mm Hg | mmHg. | 133.3224 Pa | medicine, meteorology, aviation navigation | |
| 9. Optical power | diopter | - | diopter | 1 m -1 | optics |
| 10. Line density | tex | tex | tex | 1 10 -6 kg/m | textile industry |
| 11. Speed | knot | kn | bonds | 0.514 m/s (approximately) |
maritime navigation |
| 12. Acceleration | gal | Gal | Gal | 0.01 m/s 2 | maritime navigation |
| 13. RPM | revolution per second | r/s | r/s | 1 s -1 | electrical engineering, industry |
| revolution per minute | r/min | rpm | 1/60 s -1 = 0.016 s -1 (approximately) |
||
| 14. Energy | electron-volt | eV | eV | 1.60218 10 -19 J (approximately) |
physics |
| kilowatt-hour | kW h | kWh | 3.6 10 6 J | electrical engineering | |
| 15. Full power | volt-ampere | VA | V A | - | electrical engineering |
| 16. Reactive power | var | var | var | - | electrical engineering |
| 17. Electric charge, amount of electricity | ampere-hour | A h | Ah | 3.6 10 3 C | electrical engineering |
| 18. Amount of information | bit | bit | bit | - | |
| byte | B(byte) | byte | - | ||
| 19. Information transfer rate | bits per second | bit/s | bps | - | information technology, communications |
| bytes per second | B/s (byte/s) | bytes/s | - | ||
| 20. Exposure dose photon radiation(exposure dose of gamma radiation and X-ray radiation) | x-ray | R | R | 2.57976 10 -4 C/kg (approximately) |
nuclear physics, medicine |
| 21. Equivalent dose of ionizing radiation, effective dose of ionizing radiation) | rem | rem | rem | 0.01 Sv | nuclear physics, medicine |
| 22. Absorbed dose | glad | rad | glad | 0.01 J/kg | nuclear physics, medicine |
| 23. Exposure dose rate | roentgen per second | R/s | R/s | - | nuclear physics, medicine |
| 24. Radionuclide activity | curie | Ci | Key | 3.7 10 10 Bq | nuclear physics, medicine |
| 25. Kinematic viscosity | stokes | St | St | 10 -4 m 2 / s | industry |
| 26. The amount of heat, thermodynamic potential | calorie (international) | cal | feces | 4.1868 J | industry |
| thermochemical calorie | calth | cal TX | 4.1840 J (approximately) |
industry | |
| calorie 15 degree | cal 15 | cal 15 | 4.1855 J (approximately) |
industry | |
| Heat flow (heat output) | calorie per second | cal/s | cal/s | 4.1868 W | industry |
| kilocalorie per hour | kcal/h | kcal/h | 1.163 W | ||
| gigacalories per hour | Gcal/h | Gcal/h | 1.163 10 6 W | ||
Notes: 1. Non-system units of quantities are used only in cases where quantitative values quantities it is impossible or impractical to express in SI units;
2. Names and designations of units of mass (atomic mass unit, carat), time, flat angle, length, area, pressure, optical power, linear density, speed, acceleration, rotational speed are not used with prefixes.
3. For the value of time, it is allowed to use other units that have become widespread, for example, a week, a month, a year, a century, a millennium, the names and designations of which are not used with prefixes.
4. For the unit of capacity "litre" (letter designation 1 "el"), the designation L is allowed.
5. Designations of units of a flat angle "degree", "minute", "second" are written above the line.
6. The name and designation of the unit of information quantity "byte" (1 byte = 8 bits) are used with binary prefixes "Kilo", "Mega", "Giga", which correspond to the multipliers "2 10", "2 20" and "2 30 " (1 KB = 1024 bytes, 1 MB = 1024 KB, 1 GB = 1024 MB). Prefix data is written with capital letter. It is allowed to use the international designation of the unit of information with the prefixes "K" "M" "G", recommended international standard International Electrotechnical Commission IEC 60027-2 (KB, MB, GB, Kbyte, Mbyte, Gbyte).
7. It is allowed to use other off-system units of quantities. In this case, the names of non-systemic units of quantities are used together with an indication of their relationship with the basic and derived SI units.
Appendix No. 4
to the Regulations on units of quantities,
allowed for use
In Russian federation
RELATIVE AND LOG UNITS
| Value name | Unit of magnitude | |||
|---|---|---|---|---|
| Name | designation | meaning | ||
| international | Russian | |||
| 1. Relative value: efficiency; relative extension; relative density; deformation; relative dielectric and magnetic permeability; magnetic susceptibility; mass fraction component; mole fraction of a component; and the like. | unit | 1 | 1 | 1 |
| percent | % | % | 1 10 -2 | |
| ppm | ppm | ppm | 1 10 -3 | |
| ppm | ppm | ppm | 1 10 -6 | |
| 2. Logarithmic value: sound pressure level; gain, attenuation, etc. | white | B | B | 1 B \u003d lg (P 2 / P 1) at P \u003d 10P 1 1 B \u003d 2 lg (F 2 / F 1 at F 2 \u003d √10F 1, where P 1, P 2 are such similar quantities as power, energy, energy density, etc.; F 1, F 2 are such identical quantities such as voltage, current, field strength, etc. |
| decibel | dB | dB | 0.1 B | |
| 3. Logarithmic value - volume level | background | phon | background | 1 background is equal to the sound volume level for which the sound pressure level equal to it in terms of the volume level of a sound with a frequency of 1000 Hz is 1 dB |
| 4. Logarithmic value - frequency interval | octave | - | oct | 1 octave is equal to log 2 (f 2 / f 1) with f 2 / f 1 = 2, where f 1, f 2 - frequencies |
| decade | - | dec | 1 decade is equal to lg(f 2 /f 1) at f 2 /f 1 = 10, where f 1 , f 2 - frequencies | |
| 5. Logarithmic value: voltage attenuation, current attenuation, field strength attenuation, etc. | neper | Np | Np | 1 Np \u003d ln (F 2 / F 1) at F 2 / F 1 \u003d e \u003d 2.718 ..., where F 1, F 2 are such quantities of the same name as voltage, current, field strength, etc., e - base natural logarithms. 1 Np = 0.8686 B = 8.686 dB |
Appendix No. 5
to the Regulations on units of quantities,
allowed for use
In Russian federation
DECIMAL MULTIPLIERS, PREFACES AND DESIGNATIONS OF PREFACES
FOR FORMATION OF MULTIPLE AND PARTITIONAL UNITS OF VALUES
| Decimal multiplier | Prefix | Prefix designation | Decimal multiplier | Prefix | Prefix designation | ||
|---|---|---|---|---|---|---|---|
| international | Russian | international | Russian | ||||
| 10 24 | yotta | Y | And | 10 -1 | deci | d | d |
| 10 21 | zetta | Z | W | 10 -2 | centi | with | with |
| 10 18 | exa | E | E | 10 -3 | Milli | m | m |
| 10 15 | peta | R | P | 10 -6 | micro | mu | mk |
| 10 12 | tera | T | T | 10 -9 | nano | n | n |
| 10 9 | giga | G | G | 10 -12 | pico | R | P |
| 10 6 | mega | M | M | 10 -15 | femto | f | f |
| 10 3 | kilo | k | to | 10 -18 | atto | a | a |
| 10 2 | hecto | h | G | 10 -21 | zepto | z | h |
| 10 1 | soundboard | da | Yes | 10 -24 | yokto | y | and |
Note. For the formation of multiple and submultiple units of mass, instead of the unit of mass - kilogram, a submultiple unit of mass - gram is used and the prefix is \u200b\u200battached to the word "gram". The fractional unit of mass - gram is used without attaching a prefix.
When writing the names and symbols of decimal multiples and submultiples of SI units formed with the help of prefixes, the prefix or its designation is written together with the name or designation of the unit.
It is allowed to attach a prefix to the second factor of the product or to the denominator in cases where such units are widely used.
2 or more prefixes are not attached to the name and designation of the original unit at the same time.
The names of decimal multiples and submultiples of the original unit raised to a power are formed by adding a prefix to the name of the original unit.
The notation for decimal multiples and submultiples of the original unit raised to a power is formed by adding the appropriate exponent to the notation for the decimal multiple or fractional unit original unit. In this case, the exponent means raising to the power of a decimal multiple or submultiple unit together with a prefix.
Physical quantity called physical property material object, process, physical phenomenon, quantified.
The value of a physical quantity expressed by one or more numbers characterizing this physical quantity, indicating the unit of measure.
The size of a physical quantity are the values of the numbers appearing in the meaning of the physical quantity.
Units of measurement of physical quantities.
The unit of measurement of a physical quantity is a fixed size value that is assigned a numeric value, equal to one. It is used for the quantitative expression of physical quantities homogeneous with it. A system of units of physical quantities is a set of basic and derived units based on a certain system of quantities.
Only a few systems of units have become widespread. In most cases, many countries use the metric system.
Basic units.
Measure physical quantity - means to compare it with another similar physical quantity, taken as a unit.
The length of an object is compared with a unit of length, body weight - with a unit of weight, etc. But if one researcher measures the length in sazhens, and another in feet, it will be difficult for them to compare these two values. Therefore, all physical quantities around the world are usually measured in the same units. In 1963, the International System of Units SI (System international - SI) was adopted.
For each physical quantity in the system of units, an appropriate unit of measurement must be provided. Standard units is its physical realization.
The length standard is meter- the distance between two strokes applied on a specially shaped rod made of an alloy of platinum and iridium.
Standard time is the duration of any correctly repeating process, which is chosen as the movement of the Earth around the Sun: the Earth makes one revolution per year. But the unit of time is not a year, but give me a sec.
For a unit speed take the speed of such a uniform rectilinear motion, at which the body moves 1 m in 1 s.
A separate unit of measurement is used for area, volume, length, etc. Each unit is determined when choosing one or another standard. But the system of units is much more convenient if only a few units are chosen as the main ones, and the rest are determined through the main ones. For example, if the unit of length is a meter, then the unit of area is a square meter, volume is a cubic meter, speed is a meter per second, and so on.
Basic units The physical quantities in the International System of Units (SI) are: meter (m), kilogram (kg), second (s), ampere (A), kelvin (K), candela (cd) and mole (mol).
|
Basic SI units |
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|
Value |
Unit |
Designation |
|
|
Name |
Russian |
international |
|
|
The strength of the electric current |
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Thermodynamic temperature |
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The power of light |
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Amount of substance |
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There are also SI derived units that have own names:
|
SI derived units with their own names |
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Unit |
Derived unit expression |
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Value |
Name |
Designation |
Via other SI units |
Through the main and additional units SI |
|
Pressure |
m -1 ChkgChs -2 |
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Energy, work, amount of heat |
m 2 ChkgChs -2 |
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|
Power, energy flow |
m 2 ChkgChs -3 |
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Quantity of electricity, electric charge |
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Electrical voltage, electrical potential |
m 2 ChkgChs -3 CHA -1 |
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Electrical capacitance |
m -2 Chkg -1 Hs 4 CHA 2 |
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Electrical resistance |
m 2 ChkgChs -3 CHA -2 |
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|
electrical conductivity |
m -2 Chkg -1 Hs 3 CHA 2 |
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Flux of magnetic induction |
m 2 ChkgChs -2 CHA -1 |
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Magnetic induction |
kghs -2 CHA -1 |
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Inductance |
m 2 ChkgChs -2 CHA -2 |
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Light flow |
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illumination |
m 2 ChkdChsr |
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|
Activity radioactive source |
becquerel |
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|
Absorbed radiation dose |
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Andmeasurements. To obtain an accurate, objective and easily reproducible description of a physical quantity, measurements are used. Without measurements, a physical quantity cannot be quantified. Definitions such as "low" or "high" pressure, "low" or "high" temperature reflect only subjective opinions and do not contain comparisons with reference values. When measuring a physical quantity, it is assigned a certain numerical value.
Measurements are made using measuring instruments. There is a fairly large number of measuring instruments and fixtures, from the simplest to the most complex. For example, length is measured with a ruler or tape measure, temperature with a thermometer, width with calipers.
Measuring instruments are classified: according to the method of presenting information (indicating or recording), according to the measurement method ( direct action and comparison), according to the form of presentation of indications (analogue and digital), etc.
The measuring instruments are characterized by the following parameters:
Measuring range- the range of values of the measured quantity, on which the device is designed during its normal operation (with a given measurement accuracy).
Sensitivity threshold- the minimum (threshold) value of the measured value, distinguished by the device.
Sensitivity- relates the value of the measured parameter and the corresponding change in instrument readings.
Accuracy- the ability of the device to indicate true value measured indicator.
Stability- the ability of the device to maintain given accuracy measurements within a certain time after calibration.
This lesson will not be new for beginners. We all heard from school such things as a centimeter, a meter, a kilometer. And when it came to mass, they usually said grams, kilograms, tons.
Centimeters, meters and kilometers; grams, kilograms and tons are one common name — units of measurement of physical quantities.
AT this lesson we will look at the most popular units of measurement, but we will not go deep into this topic, since units of measurement go into the realm of physics. We are forced to study part of the physics, as we need it for the further study of mathematics.
Lesson contentLength units
The following units of measurement are used to measure length:
- millimeters
- centimeters
- decimeters
- meters
- kilometers
millimeter(mm). You can even see millimeters with your own eyes if you take the ruler that we used at school every day.
Small lines that follow each other in a row are millimeters. More precisely, the distance between these lines is one millimeter (1 mm):
centimeter(cm). On the ruler, each centimeter is indicated by a number. For example, our ruler, which was in the first figure, had a length of 15 centimeters. The last centimeter on this ruler is marked with the number 15.
There are 10 millimeters in one centimeter. You can put an equal sign between one centimeter and ten millimeters, since they denote the same length
1cm=10mm
You can see for yourself if you count the number of millimeters in the previous figure. You will find that the number of millimeters (distance between lines) is 10.
The next unit of length is decimeter(dm). There are ten centimeters in one decimeter. Between one decimeter and ten centimeters, you can put an equal sign, since they denote the same length:
1 dm = 10 cm
You can verify this if you count the number of centimeters in the following figure:
You will find that the number of centimeters is 10.
The next unit of measure is meter(m). There are ten decimeters in one meter. You can put an equal sign between one meter and ten decimeters, because they denote the same length:
1 m = 10 dm
Unfortunately, the meter cannot be illustrated in the figure, because it is rather large. If you want to see the meter live, take a tape measure. Everyone has it in the house. On a tape measure, one meter will be designated as 100 cm. This is because there are ten decimeters in one meter, and one hundred centimeters in ten decimeters:
1 m = 10 dm = 100 cm
100 is obtained by converting one meter to centimeters. This is separate topic, which we will look at a little later. In the meantime, let's move on to the next unit of length, which is called a kilometer.
A kilometer is considered the most big unit length measurements. Of course, there are other older units, such as a megameter, a gigameter, a terameter, but we will not consider them, since a kilometer is enough for us to further study mathematics.
There are a thousand meters in one kilometer. You can put an equal sign between one kilometer and a thousand meters, since they denote the same length:
1 km = 1000 m
Distances between cities and countries are measured in kilometers. For example, the distance from Moscow to St. Petersburg is about 714 kilometers.
International system of units SI
The international system of units SI is a certain set of generally accepted physical quantities.
The main purpose of the international system of SI units is to reach agreements between countries.
We know that the languages and traditions of the countries of the world are different. There's nothing to be done about it. But the laws of mathematics and physics work the same everywhere. If in one country “twice two is four”, then in another country “twice two is four”.
The main problem was that for each physical quantity there are several units of measurement. For example, we have just learned that there are millimeters, centimeters, decimeters, meters and kilometers for measuring length. If several scholars speaking different languages, will gather in one place to solve a particular problem, then such a large variety of units of measurement of length can give rise to contradictions between these scientists.
One scientist will claim that in their country length is measured in meters. The second might say that in their country, length is measured in kilometers. The third one can offer his own unit of measurement.
Therefore, the international system of units SI was created. SI is an abbreviation for the French phrase Le Système International d'Unités, SI (which in Russian means - the international system of units SI).
The SI lists the most popular physical quantities and each of them has its own generally accepted unit of measurement. For example, in all countries, when solving problems, it was agreed that the length would be measured in meters. Therefore, when solving problems, if the length is given in another unit of measurement (for example, in kilometers), then it must be converted to meters. We will talk about how to convert one unit of measure to another a little later. And while we draw our international system SI units.
Our drawing will be a table of physical quantities. We will include each studied physical quantity in our table and indicate the unit of measurement that is accepted in all countries. Now we have studied the units of measurement of length and learned that meters are defined in the SI system for measuring length. So our table will look like this:
Mass units
Mass is a measure of the amount of matter in a body. In the people, body weight is called weight. Usually, when something is weighed, they say "it weighs so many kilograms" , although we are not talking about weight, but about the mass of this body.
However, mass and weight are different concepts. Weight is the force with which a body acts on a horizontal support. Weight is measured in newtons. And mass is a quantity that shows the amount of matter in this body.
But there is nothing wrong with calling the mass of the body weight. Even in medicine they say "human weight" , although we are talking about the mass of a person. The main thing is to be aware that these are different concepts.
The following units of measure are used to measure mass:
- milligrams
- grams
- kilograms
- centners
- tons
The smallest unit of measure is milligram(mg). Milligram most likely you will never put into practice. They are used by chemists and other scientists who work with small substances. It is enough for you to know that such a unit of mass measurement exists.
The next unit of measure is gram(G). In grams, it is customary to measure the amount of a product when compiling a recipe.
There are a thousand milligrams in one gram. You can put an equal sign between one gram and a thousand milligrams, because they denote the same mass:
1 g = 1000 mg
The next unit of measure is kilogram(kg). The kilogram is a common unit of measure. It measures everything. The kilogram is included in the SI system. Let's also include one more physical quantity in our SI table. We will call it "mass":
There are a thousand grams in one kilogram. You can put an equal sign between one kilogram and a thousand grams, because they denote the same mass:
1 kg = 1000 g
The next unit of measure is centner(c). In centners, it is convenient to measure the mass of a crop harvested from a small area or the mass of some kind of cargo.
There are one hundred kilograms in one centner. Between one centner and one hundred kilograms you can put an equal sign, because they denote the same mass:
1 q = 100 kg
The next unit of measure is ton(t). In tons, large loads and masses are usually measured. big bodies. For example, mass spaceship or car.
There are a thousand kilograms in one ton. You can put an equal sign between one ton and a thousand kilograms, because they denote the same mass:
1 t = 1000 kg
Time units
We don't need to explain what time is. Everyone knows what time is and why it is needed. If we open the discussion to what time is and try to define it, then we will begin to delve into philosophy, and this is not what we need now. Let's start with time units.
The following units of measurement are used to measure time:
- seconds
- minutes
- day
The smallest unit of measure is second(with). Of course, there are also smaller units such as milliseconds, microseconds, nanoseconds, but we will not consider them, since this moment it makes no sense.
Measured in seconds various indicators. For example, how many seconds does it take an athlete to run 100 meters. The second is included in the international SI system of units for measuring time and is denoted as "s". Let's also include one more physical quantity in our SI table. We will call it "time":
minute(m). There are 60 seconds in one minute. You can put an equal sign between one minute and sixty seconds, since they represent the same time:
1 m = 60 s
The next unit of measure is hour(h). There are 60 minutes in one hour. You can put an equal sign between one hour and sixty minutes, since they represent the same time:
1 h = 60 m
For example, if we studied this lesson for one hour and we are asked how much time we spent studying it, we can answer in two ways: "we studied the lesson for one hour" or so "we studied the lesson for sixty minutes" . In both cases, we will answer correctly.
The next unit of time is day. There are 24 hours in a day. Between one day and twenty-four hours you can put an equal sign, since they denote the same time:
1 day = 24 hours
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