Hecto decimal multiplier. Abbreviated notation of numerical values

Multiples of units- units that are an integer number of times greater than the basic unit of measurement of some physical quantity. International system units (SI) recommends the following decimal prefixes to denote multiple units:

Application of decimal prefixes to units of measurement in binary notation

Main article: Binary prefixes

In programming and the computer-related industry, the same prefixes kilo-, mega-, giga-, tera-, etc., when applied to powers of two (e.g. byte), may mean the multiplicity is not 1000, but 1024 = 2 10. Which system is used should be clear from the context (e.g. in relation to the volume RAM a multiplicity of 1024 is used, and in relation to volume disk memory introduced by manufacturers hard drives- multiplicity 1000).

To avoid confusion in April 1999 International Electrotechnical Commission introduced a new naming standard binary numbers(cm. 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:

Origin of consoles

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

How “thousand” is translated is the prefix milli, which goes back to lat. mille. Latin roots also have the prefixes centi - from centum(“one hundred”) and deci - from decimus(“tenth”), zetta - from septem("seven"). Zepto ("seven") comes from lat. words septem or from fr. sept.

The prefix atto is derived from date atten("eighteen"). Femto goes back to date And norwegian femten or to other-nor. fimmtan and means "fifteen".

The prefix pico comes from either fr. pico(“beak” or “small amount”), either from Italian piccolo, that is, “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 designations of multiples and submultiples of the original unit raised to a power are formed by adding the appropriate exponent to the designation of the multiple or submultiple unit of the original unit, where the exponent means 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 - a gram (0.001 kg).

Prefixes are used to a limited extent with units of time: multiple prefixes are not combined with them at all - no one uses “kilosecond”, although this is not formally prohibited, however, there is an exception to this rule: in cosmology the unit used is " gigayears"(billion years); sub-multiple prefixes are attached only to second(millisecond, microsecond, etc.). According to 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(flat angle units), astronomical unit, diopter And atomic mass unit.

WITH meters of the multiple prefixes, in practice only kilo- is used: instead of megameters (Mm), gigameters (Gm), etc. they write “thousands of kilometers,” “millions of kilometers,” etc.; instead of square megameters (Mm²) they write “millions of square kilometers”.

Capacity capacitors traditionally measured in microfarads and picofarads, but not millifarads or nanofarads [ source not specified 221 days ] (they write 60,000 pF, not 60 nF; 2000 µF, not 2 mF). However, in radio engineering the use of the nanofarad unit is allowed.

Prefixes corresponding to exponents not divisible by 3 (hecto-, deca-, deci-, centi-) are not recommended. Widely used only centimeter(being the basic unit in the system GHS) And decibel, to a lesser extent - decimeter and hectopascal (in weather reports), and also hectare. In some countries the volume guilt measured in decalitres.

Length and distance converter Mass converter Bulk and food volume converter Area converter Volume and units converter in culinary recipes Temperature converter Pressure converter, mechanical stress, Young's modulus Energy and work converter Power converter Force converter Time converter Converter linear speed Flat angle Thermal efficiency and fuel efficiency converter Number converter 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 Torque 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 Converter heat flux density heat transfer coefficient converter volumetric 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 vapor permeability and vapor transfer velocity converter sound level converter Microphone sensitivity converter Sound pressure level (SPL) converter Sound pressure level converter with selectable reference pressure Brightness converter Luminous intensity converter Illuminance converter Resolution converter computer graphics 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 Converter electric current Linear current density converter Surface current density converter Electric field strength converter Electrostatic potential and voltage converter Converter electrical resistance Electrical resistivity converter Electrical conductivity converter Electrical conductivity converter Electrical capacitance Inductance converter American wire gauge converter Levels in dBm (dBm or dBmW), dBV (dBV), watts and other units Magnetomotive force converter Voltage converter magnetic field 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 Imaging Converter Timber Volume Unit Converter Molar Mass Calculation Periodic table chemical elements D. I. Mendeleev

1 milli [m] = 1000 micro [μ]

Initial value

Converted value

without prefix yotta zetta exa peta tera giga mega kilo hecto deca deci santi milli micro nano pico femto atto zepto yocto

Optical power in diopters and lens magnification

Metric system and International System of Units (SI)

Introduction

In this article we will talk about the metric system and its history. We will see how and why it began and how it gradually evolved into what we have today. We will also look at the SI system, which was developed from the metric system of measures.

For our ancestors, who lived in a world full of dangers, the ability to measure various quantities in their natural habitat made it possible to get closer to understanding the essence of natural phenomena, knowledge of their environment and the ability to somehow influence what surrounded them. That is why people tried to invent and improve various measurement systems. At the dawn of human development, having a measurement system was no less important than it is now. Fulfill different measurements was necessary when building housing, sewing clothes different sizes, cooking and, of course, trade and exchange could not do without measurement! Many believe that the creation and adoption of the International System of SI Units is the most serious achievement not only of science and technology, but also of human development in general.

Early measurement systems

IN early systems In all measures and number systems, people used traditional objects to measure and compare. For example, it is believed that decimal system appeared due to the fact that we have ten fingers and toes. Our hands are always with us - that's why since ancient times people have used (and still use) fingers for counting. And yet we did not always use the base 10 system for counting, and indeed metric system is a relatively new invention. Each region developed its own systems of units and, although these systems have much in common, most systems are still so different that converting units of measurement from one system to another has always been a problem. This problem became more and more serious as trade between different peoples developed.

The accuracy of the first systems of weights and measures directly depended on the size of the objects that surrounded the people who developed these systems. It is clear that the measurements were inaccurate, since “ measuring devices"didn't have exact dimensions. For example, parts of the body were commonly used as a measure of length; mass and volume were measured using the volume and mass of seeds and other small objects whose dimensions were more or less the same. Below we will take a closer look at such units.

Length measures

In ancient Egypt, length was first measured simply elbows, and later with royal elbows. The length of the elbow was determined as the distance from the bend of the elbow to the end of the extended middle finger. Thus, the royal cubit was defined as the cubit of the reigning pharaoh. A model cubit was created and made available to the general public so that everyone could make their own length measures. This, of course, was an arbitrary unit that changed when a new reigning person took the throne. Ancient Babylon used a similar system, but with minor differences.

The elbow was divided into smaller units: palm, hand, zerets(ft), and you(finger), which were represented by the widths of the palm, hand (with thumb), foot and finger, respectively. At the same time, they decided to agree on how many fingers there were in the palm (4), in the hand (5) and in the elbow (28 in Egypt and 30 in Babylon). It was more convenient and more accurate than measuring ratios every time.

Measures of mass and weight

Weight measures were also based on the parameters of various objects. Seeds, grains, beans and similar items were used as weight measures. A classic example of a unit of mass that is still used today is carat. Carats are now used to measure mass. precious stones and pearls, and once upon a time the weight of carob seeds, otherwise called carob, was determined as a carat. The tree is cultivated in the Mediterranean, and its seeds are distinguished by their constant mass, so they were convenient to use as a measure of weight and mass. IN different places different seeds were used as small units of weight, and larger units were usually multiples of smaller units. Archaeologists often find similar large weights, usually made of stone. They consisted of 60, 100 and other numbers of small units. Since there was no uniform standard for the number of small units, as well as for their weight, this led to conflicts when sellers and buyers who lived in different places met.

Volume measures

Initially, volume was also measured using small objects. For example, the volume of a pot or jug ​​was determined by filling it to the top with small objects relative to the standard volume - like seeds. However, the lack of standardization led to the same problems when measuring volume as when measuring mass.

Evolution of various systems of measures

The ancient Greek system of measures was based on the ancient Egyptian and Babylonian ones, and the Romans created their system based on the ancient Greek one. Then, by fire and sword and, of course, as a result of trade, these systems spread throughout Europe. It should be noted that here we are talking only about the most common systems. But there were many other systems of weights and measures, because exchange and trade were necessary for absolutely everyone. If there was no writing in the area or it was not customary to record the results of the exchange, then we can only guess how these people measured volume and weight.

There are many regional variations in systems of measures and weights. This is due to their independent development and the influence of other systems on them as a result of trade and conquest. Various systems were not only in different countries, but often within the same country, where each trading city had its own, because local rulers did not want unification in order to maintain their power. As travel, trade, industry, and science developed, many countries sought to unify systems of weights and measures, at least within their own countries.

Already in the 13th century, and possibly earlier, scientists and philosophers discussed the creation unified system measurements. However, it was only after the French Revolution and the subsequent colonization of various regions of the world by France and other European countries, which already had their own systems of weights and measures, that a new system was developed, adopted in most countries of the world. This new system was decimal metric system. It was based on the base 10, that is, for any physical quantity there was one basic unit, and all other units could be formed in a standard way using decimal prefixes. Each such fractional or multiple unit could be divided into ten smaller units, and these smaller units, in turn, could be divided into 10 even smaller units, and so on.

As we know, most early measurement systems were not based on base 10. The convenience of the base 10 system is that the number system we are familiar with has the same base, which allows us to quickly and conveniently, using simple and familiar rules, convert from smaller units to big and vice versa. Many scientists believe that the choice of ten as the base of the number system is arbitrary and is connected only with the fact that we have ten fingers and if we had a different number of fingers, then we would probably use a different number system.

Metric system

In the early days of the metric system, man-made prototypes were used as measures of length and weight, as in previous systems. The metric system has evolved from a system based on material standards and dependence on their accuracy to a system based on natural phenomena and fundamental physical constants. For example, the time unit second was initially defined as a fraction of the tropical year 1900. The disadvantage of this definition was the impossibility of experimental verification of this constant in subsequent years. Therefore, the second was redefined as a certain number of periods of radiation corresponding to the transition between two hyperfine levels of the ground state of the radioactive atom of cesium-133, which is at rest at 0 K. The unit of distance, the meter, was related to the wavelength of the line of the radiation spectrum of the isotope krypton-86, but later The meter was redefined as the distance that light travels in a vacuum in a period of time equal to 1/299,792,458 of a second.

The International System of Units (SI) was created based on the metric system. It should be noted that traditionally the metric system includes units of mass, length and time, but in the SI system the number of base units has been expanded to seven. We will discuss them below.

International System of Units (SI)

The International System of Units (SI) has seven basic units for measuring basic quantities (mass, time, length, luminous intensity, amount of matter, electric current, thermodynamic temperature). This kilogram(kg) to measure mass, second(c) to measure time, meter(m) to measure distance, candela(cd) to measure luminous intensity, mole(abbreviation mole) to measure the amount of a substance, ampere(A) to measure electric current, and kelvin(K) to measure temperature.

Currently, only the kilogram still has a man-made standard, while the remaining units are based on universal physical constants or natural phenomena. This is convenient because the physical constants or natural phenomena on which the units of measurement are based can be easily verified at any time; In addition, there is no danger of loss or damage to standards. There is also no need to create copies of the standards to ensure their availability in different points planets. This eliminates errors associated with the accuracy of making copies of physical objects, and thus provides greater accuracy.

Decimal prefixes

To form multiples and submultiples that differ from the base units of the SI system by a certain integer number of times, which is a power of ten, it uses prefixes attached to the name of the base unit. The following is a list of all currently used prefixes and the decimal factors they represent:

For example, 5 gigameters is equal to 5,000,000,000 meters, while 3 microcandelas is equal to 0.000003 candelas. It is interesting to note that, despite the presence of a prefix in the unit kilogram, it is the base unit of the SI. Therefore, the above prefixes are applied with the gram as if it were a base unit.

At the time of writing this article, there are only three countries that have not adopted the SI system: the United States, Liberia and Myanmar. In Canada and the UK, traditional units are still widely used, although the SI system in these countries is official system units. It’s enough to go into a store and see price tags per pound of goods (it turns out cheaper!), or try to buy building materials measured in meters and kilograms. It won't work! Not to mention the packaging of goods, where everything is labeled in grams, kilograms and liters, but not in whole numbers, but converted from pounds, ounces, pints and quarts. Milk space in refrigerators is also calculated per half-gallon or gallon, not per liter milk carton.

Do you find it difficult to translate units of measurement from one language to another? Colleagues are ready to help you. Post a question in TCTerms and within a few minutes you will receive an answer.

Calculations for converting units in the converter " Decimal prefix converter" are performed using unitconversion.org functions.

Abbreviations for electrical quantities

During assembly electronic circuits willy-nilly you have to recalculate the resistance values ​​of resistors, capacitor capacities, and inductance of coils.

So, for example, there is a need to convert microfarads into picofarads, kilo-ohms into ohms, millihenry into microhenry.

How not to get confused in calculations?

If a mistake is made and an element with the wrong rating is selected, the assembled device will not work correctly or have other characteristics.

This situation is not uncommon in practice, since sometimes on the housings of radio elements the capacitance value is indicated in nano farads (nF), and on schematic diagram capacitor capacities are usually indicated in micro farads (µF) and pico farads (pF). This misleads many novice radio amateurs and, as a result, slows down the assembly of the electronic device.

To prevent this situation from happening, you need to learn simple calculations.

In order not to get confused in microfarads, nanofarads, picofarads, you need to familiarize yourself with the dimension table. I'm sure you will find it useful more than once.

This table includes decimal multiples and fractional (multiple) prefixes. International system of units, which goes by the abbreviated name SI, includes six multiples (deca, hecto, kilo, mega, giga, tera) and eight submultiples (deci, santi, milli, micro, nano, pico, femto, atto). Many of these attachments have been used in electronics for a long time.

How to use the table?

As we can see from the table, the difference between many prefixes is exactly 1000. So, for example, this rule applies between multiples, starting with the prefix kilo-.

• Mega - 1,000,000

  Giga – 1,000,000,000

  Tera – 1,000,000,000,000

So, if next to the resistor designation it says 1 MΩ (1 Mega Ohm), then its resistance will be 1,000,000 (1 million) Ohm. If there is a resistor with a nominal resistance of 1 kOhm (1 kilo ohm), then in Ohms it will be 1000 (1 thousand) Ohms.

For submultiple or otherwise fractional values, the situation is similar, only the numerical value does not increase, but decreases.

In order not to get confused in microfarads, nanofarads, picofarads, you need to remember one simple rule. You need to understand that milli, micro, nano and pico are all different exactly 1000. That is, if they tell you 47 microfarads, then this means that in nanofarads it will be 1000 times more - 47,000 nanofarads. In picofarads this will already be another 1000 times more - 47,000,000 picofarads. As you can see, the difference between 1 microfarad and 1 picofarad is 1,000,000 times.

Also, in practice, sometimes it is necessary to know the value in microfarads, but the value of the capacitance is indicated in nanofarads. So if the capacitance of the capacitor is 1 nanofarad, then in microfarads it will be 0.001 microfarads. If the capacitance is 0.01 microfarads, then in picofarads it will be 10,000 pF, and in nanofarads, respectively, 10 nF.

Prefixes denoting the dimension of a quantity are used for abbreviated notation. Agree it’s easier to write 1mA, than 0.001 Ampere or, for example, 400 µH, than 0.0004 Henry.

The table shown earlier also contains an abbreviated designation for the prefix. So as not to write Mega, write only the letter M. The prefix is ​​usually followed by an abbreviation for the electrical quantity. For example, the word Ampere do not write, but indicate only the letter A. The same applies when abbreviating the unit of measurement of capacity. Farad. In this case, only the letter is written F.

Along with the abbreviated notation in Russian, which is often used in old radio-electronic literature, there is also an international abbreviated notation of prefixes. It is also indicated in the table.

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 rotation frequency 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 Vapor permeability and vapor transfer rate converter Sound level converter Microphone sensitivity converter Sound Pressure Level (SPL) Converter 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 (×) Electric charge converter 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 mega [M] = 0.001 giga [G]

Initial value

Converted value

without prefix yotta zetta exa peta tera giga mega kilo hecto deca deci santi milli micro nano pico femto atto zepto yocto

Metric system and International System of Units (SI)

Introduction

In this article we will talk about the metric system and its history. We will see how and why it began and how it gradually evolved into what we have today. We will also look at the SI system, which was developed from the metric system of measures.

For our ancestors, who lived in a world full of dangers, the ability to measure various quantities in their natural habitat made it possible to get closer to understanding the essence of natural phenomena, knowledge of their environment and the ability to somehow influence what surrounded them. That is why people tried to invent and improve various measurement systems. At the dawn of human development, having a measurement system was no less important than it is now. It was necessary to carry out various measurements when building housing, sewing clothes of different sizes, preparing food and, of course, trade and exchange could not do without measurement! Many believe that the creation and adoption of the International System of SI Units is the most serious achievement not only of science and technology, but also of human development in general.

Early measurement systems

In early measurement and number systems, people used traditional objects to measure and compare. For example, it is believed that the decimal system appeared due to the fact that we have ten fingers and toes. Our hands are always with us - that's why since ancient times people have used (and still use) fingers for counting. Still, we haven't always used the base 10 system for counting, and the metric system is a relatively new invention. Each region developed its own systems of units and, although these systems have much in common, most systems are still so different that converting units of measurement from one system to another has always been a problem. This problem became more and more serious as trade between different peoples developed.

The accuracy of the first systems of weights and measures directly depended on the size of the objects that surrounded the people who developed these systems. It is clear that the measurements were inaccurate, since the “measuring devices” did not have exact dimensions. For example, parts of the body were commonly used as a measure of length; mass and volume were measured using the volume and mass of seeds and other small objects whose dimensions were more or less the same. Below we will take a closer look at such units.

Length measures

In ancient Egypt, length was first measured simply elbows, and later with royal elbows. The length of the elbow was determined as the distance from the bend of the elbow to the end of the extended middle finger. Thus, the royal cubit was defined as the cubit of the reigning pharaoh. A model cubit was created and made available to the general public so that everyone could make their own length measures. This, of course, was an arbitrary unit that changed when a new reigning person took the throne. Ancient Babylon used a similar system, but with minor differences.

The elbow was divided into smaller units: palm, hand, zerets(ft), and you(finger), which were represented by the widths of the palm, hand (with thumb), foot and finger, respectively. At the same time, they decided to agree on how many fingers there were in the palm (4), in the hand (5) and in the elbow (28 in Egypt and 30 in Babylon). It was more convenient and more accurate than measuring ratios every time.

Measures of mass and weight

Weight measures were also based on the parameters of various objects. Seeds, grains, beans and similar items were used as weight measures. A classic example of a unit of mass that is still used today is carat. Nowadays, the weight of precious stones and pearls is measured in carats, and once upon a time the weight of carob seeds, otherwise called carob, was determined as a carat. The tree is cultivated in the Mediterranean, and its seeds are distinguished by their constant mass, so they were convenient to use as a measure of weight and mass. Different places used different seeds as small units of weight, and larger units were usually multiples of smaller units. Archaeologists often find similar large weights, usually made of stone. They consisted of 60, 100 and other numbers of small units. Since there was no uniform standard for the number of small units, as well as for their weight, this led to conflicts when sellers and buyers who lived in different places met.

Volume measures

Initially, volume was also measured using small objects. For example, the volume of a pot or jug ​​was determined by filling it to the top with small objects relative to the standard volume - like seeds. However, the lack of standardization led to the same problems when measuring volume as when measuring mass.

Evolution of various systems of measures

The ancient Greek system of measures was based on the ancient Egyptian and Babylonian ones, and the Romans created their system based on the ancient Greek one. Then, by fire and sword and, of course, as a result of trade, these systems spread throughout Europe. It should be noted that here we are talking only about the most common systems. But there were many other systems of weights and measures, because exchange and trade were necessary for absolutely everyone. If there was no writing in the area or it was not customary to record the results of the exchange, then we can only guess how these people measured volume and weight.

There are many regional variations in systems of measures and weights. This is due to their independent development and the influence of other systems on them as a result of trade and conquest. There were different systems not only in different countries, but often within the same country, where each trading city had its own, because local rulers did not want unification in order to maintain their power. As travel, trade, industry, and science developed, many countries sought to unify systems of weights and measures, at least within their own countries.

Already in the 13th century, and possibly earlier, scientists and philosophers discussed the creation of a unified measurement system. However, it was only after the French Revolution and the subsequent colonization of various regions of the world by France and other European countries, which already had their own systems of weights and measures, that a new system was developed, adopted in most countries of the world. This new system was decimal metric system. It was based on the base 10, that is, for any physical quantity there was one basic unit, and all other units could be formed in a standard way using decimal prefixes. Each such fractional or multiple unit could be divided into ten smaller units, and these smaller units, in turn, could be divided into 10 even smaller units, and so on.

As we know, most early measurement systems were not based on base 10. The convenience of the base 10 system is that the number system we are familiar with has the same base, which allows us to quickly and conveniently, using simple and familiar rules, convert from smaller units to big and vice versa. Many scientists believe that the choice of ten as the base of the number system is arbitrary and is connected only with the fact that we have ten fingers and if we had a different number of fingers, then we would probably use a different number system.

Metric system

In the early days of the metric system, man-made prototypes were used as measures of length and weight, as in previous systems. The metric system has evolved from a system based on material standards and dependence on their accuracy to a system based on natural phenomena and fundamental physical constants. For example, the time unit second was initially defined as a fraction of the tropical year 1900. The disadvantage of this definition was the impossibility of experimental verification of this constant in subsequent years. Therefore, the second was redefined as a certain number of periods of radiation corresponding to the transition between two hyperfine levels of the ground state of the radioactive atom of cesium-133, which is at rest at 0 K. The unit of distance, the meter, was related to the wavelength of the line of the radiation spectrum of the isotope krypton-86, but later The meter was redefined as the distance that light travels in a vacuum in a period of time equal to 1/299,792,458 of a second.

The International System of Units (SI) was created based on the metric system. It should be noted that traditionally the metric system includes units of mass, length and time, but in the SI system the number of base units has been expanded to seven. We will discuss them below.

International System of Units (SI)

The International System of Units (SI) has seven basic units for measuring basic quantities (mass, time, length, luminous intensity, amount of matter, electric current, thermodynamic temperature). This kilogram(kg) to measure mass, second(c) to measure time, meter(m) to measure distance, candela(cd) to measure luminous intensity, mole(abbreviation mole) to measure the amount of a substance, ampere(A) to measure electric current, and kelvin(K) to measure temperature.

Currently, only the kilogram still has a man-made standard, while the remaining units are based on universal physical constants or natural phenomena. This is convenient because the physical constants or natural phenomena on which the units of measurement are based can be easily verified at any time; In addition, there is no danger of loss or damage to standards. There is also no need to create copies of standards to ensure their availability in different parts of the world. This eliminates errors associated with the accuracy of making copies of physical objects, and thus provides greater accuracy.

Decimal prefixes

To form multiples and submultiples that differ from the base units of the SI system by a certain integer number of times, which is a power of ten, it uses prefixes attached to the name of the base unit. The following is a list of all currently used prefixes and the decimal factors they represent:

For example, 5 gigameters is equal to 5,000,000,000 meters, while 3 microcandelas is equal to 0.000003 candelas. It is interesting to note that, despite the presence of a prefix in the unit kilogram, it is the base unit of the SI. Therefore, the above prefixes are applied with the gram as if it were a base unit.

At the time of writing this article, there are only three countries that have not adopted the SI system: the United States, Liberia and Myanmar. In Canada and the UK, traditional units are still widely used, even though the SI system is the official unit system in these countries. It’s enough to go into a store and see price tags per pound of goods (it turns out cheaper!), or try to buy building materials measured in meters and kilograms. It won't work! Not to mention the packaging of goods, where everything is labeled in grams, kilograms and liters, but not in whole numbers, but converted from pounds, ounces, pints and quarts. Milk space in refrigerators is also calculated per half-gallon or gallon, not per liter milk carton.

Do you find it difficult to translate units of measurement from one language to another? Colleagues are ready to help you. Post a question in TCTerms and within a few minutes you will receive an answer.

Calculations for converting units in the converter " Decimal prefix converter" are performed using unitconversion.org functions.

Material from Wikipedia - the free encyclopedia

With the exception of specially specified cases, the “Regulations on units of quantities allowed for use in Russian Federation"allows the use of both Russian and international designations of units, but prohibits, however, their simultaneous use.

Prefixes for multiples

Multiples of units- units that are an integer number of times (10 to some degree) greater than the basic unit of measurement of some physical quantity. The International System of Units (SI) recommends the following decimal prefixes to represent multiple units:

Applying decimal prefixes to binary units

The Regulations on units of quantities allowed for use in the Russian Federation establish that the name and designation of the unit of information quantity “byte” (1 byte = 8 bits) are used with the binary prefixes “Kilo”, “Mega”, “Giga”, which correspond multipliers 2 10, 2 20 and 2 30 (1 KB = 1024 bytes, 1 MB = 1024 KB, 1 GB = 1024 MB).

The same Regulations also allow the use of an international designation for a unit of information with the prefixes “K” “M” “G” (KB, MB, GB, Kbyte, Mbyte, Gbyte).

In programming and the computer industry, the same prefixes "kilo", "mega", "giga", "tera", etc., when applied to powers of two (e.g. bytes), can mean both a multiple of 1000 and 1024 = 2 10. Which system is used is sometimes clear from the context (for example, in relation to the amount of RAM, a factor of 1024 is used, and in relation to the total volume of disk memory of hard drives, a factor of 1000 is used).

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:

Origin of consoles

Prefixes were introduced into SI gradually. In 1960, the XI General Conference on Weights and Measures (GCPM) adopted a number of prefix names and corresponding symbols for factors ranging from 10 −12 to 10 12. Prefixes for 10 −15 and 10 −18 were added by the XII CGPM in 1964, and for 10 15 and 10 18 by the XV CGPM in 1975. The most recent addition to the list of prefixes took place at the XIX CGPM in 1991, when they were adopted prefixes for factors 10 −24, 10 −21, 10 21 and 10 24.

Most prefixes are derived from words in ancient Greek. Deca - from ancient Greek. δέκα “ten”, hecto- from ancient Greek. ἑκατόν “one hundred”, kilo- from ancient Greek. χίλιοι “thousand”, mega- from ancient Greek. μέγας , that is, “big”, giga- - this is ancient Greek. γίγας - “giant”, and tera - from ancient Greek. τέρας , which means "monster". Peta- (ancient Greek. πέντε ) and exa- (ancient Greek. ἕξ ) correspond to five and six digits of a thousand and are translated, respectively, as “five” and “six”. Lobed micro- (from ancient Greek. μικρός ) and nano- (from ancient Greek. νᾶνος ) are translated as “small” and “dwarf”. From one word in ancient Greek. ὀκτώ (okto), meaning “eight”, the prefixes iotta (1000 8) and iocto (1/1000 8) are formed.

The prefix milli, which goes back to Lat., is also translated as “thousand”. mille. Latin roots also have the prefixes centi - from centum(“one hundred”) and deci - from decimus(“tenth”), zetta - from septem("seven"). Zepto ("seven") comes from the Latin. septem or from fr. sept.

The prefix atto is derived from dates. atten (“eighteen”). Femto dates back to dates. and norwegian femten or to other Scand. fimmtān and means "fifteen".

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

Rules for using consoles

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). On the other hand, a submultiple unit of mass - a gram - can be used without attaching a prefix.

Prefixes are used to a limited extent with units of time: multiple prefixes are rarely combined with them, although this is not formally prohibited - “kilosecond” is used only in astronomy, and in cosmology and geochronology the units “gigayear” (billion years) and “megayear” (million) are used. years); beat prefixes are attached only to the second (millisecond, microsecond, etc.).

In accordance with the “Regulations on units of quantities allowed for use in the Russian Federation”, the names and designations of non-system units of mass, time, plane angle, length, area, pressure, optical force, linear density, speed, acceleration and rotation frequency are not used with prefixes .

With meters from multiple prefixes, in practice, only kilo- is used: instead of megameters (Mm), gigameters (Gm), etc. they write “thousands of kilometers,” “millions of kilometers,” etc.; instead of square megameters (Mm²) they write “millions of square kilometers”.

Prefixes corresponding to exponents not divisible by 3 (hecto-, deca-, deci-, centi-) are not recommended. Only the centimeter (which is the basic unit in the GHS system) and the decibel are widely used, and to a lesser extent the decimeter and hectopascal (in meteorological reports), as well as the hectare. In some countries, the volume of wine and other drinks is measured in deciliters and hectoliters (with retail sales also centiliters). Sometimes a unit of hectograms (in Italy its colloquial name is etto) are used when measuring the mass of food products.

See also

• Non-SI unit prefix

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Notes

Literature

Excerpt characterizing SI Prefixes

In October 1805, Russian troops occupied villages and towns of the Archduchy of Austria, and more new regiments came from Russia and, burdening the residents with billeting, were stationed at the Braunau fortress. The main apartment of Commander-in-Chief Kutuzov was in Braunau.
On October 11, 1805, one of the infantry regiments that had just arrived at Braunau, awaiting inspection by the commander-in-chief, stood half a mile from the city. Despite the non-Russian terrain and situation (orchards, stone fences, tiled roofs, mountains visible in the distance), despite the non-Russian people looking at the soldiers with curiosity, the regiment had exactly the same appearance as any Russian regiment had when preparing for a review somewhere in the middle of Russia.
In the evening, on the last march, an order was received that the commander-in-chief would inspect the regiment on the march. Although the words of the order seemed unclear to the regimental commander, and the question arose how to understand the words of the order: in marching uniform or not? In the council of battalion commanders, it was decided to present the regiment in full dress uniform on the basis that it is always better to bow than not to bow. And the soldiers, after a thirty-mile march, did not sleep a wink, they repaired and cleaned themselves all night; adjutants and company commanders counted and expelled; and by morning the regiment, instead of the sprawling, disorderly crowd that it had been the day before during the last march, represented an orderly mass of 2,000 people, each of whom knew his place, his job, and of whom, on each of them, every button and strap was in its place and sparkled with cleanliness . Not only was the outer part in good order, but if the commander-in-chief had wanted to look under the uniforms, he would have seen an equally clean shirt on each one and in each knapsack he would have found the legal number of things, “stuff and soap,” as the soldiers say. There was only one circumstance about which no one could be calm. It was shoes. More than half the people's boots were broken. But this deficiency was not due to the fault of the regimental commander, since, despite repeated demands, the goods were not released to him from the Austrian department, and the regiment marched a thousand miles.
The regimental commander was an elderly, sanguine general with graying eyebrows and sideburns, thick-set and wider from chest to back than from one shoulder to the other. He was wearing a new, brand new uniform with wrinkled folds and thick golden epaulettes, which seemed to lift his fat shoulders upward rather than downwards. The regimental commander had the appearance of a man happily performing one of the most solemn affairs of life. He walked in front of the front and, as he walked, trembled at every step, slightly arching his back. It was clear that the regimental commander was admiring his regiment, happy with it, that all his mental strength was occupied only with the regiment; but, despite the fact that his trembling gait seemed to say that, in addition to military interests, the interests of social life and the female sex occupied a significant place in his soul.
“Well, Father Mikhailo Mitrich,” he turned to one battalion commander (the battalion commander leaned forward smiling; it was clear that they were happy), “it was a lot of trouble this night.” However, it seems that nothing is wrong, the regiment is not bad... Eh?
The battalion commander understood the funny irony and laughed.
- And in Tsaritsyn Meadow they wouldn’t have driven you away from the field.
- What? - said the commander.
At this time, along the road from the city, along which the makhalnye were placed, two horsemen appeared. These were the adjutant and the Cossack riding behind.
The adjutant was sent from the main headquarters to confirm to the regimental commander what was said unclearly in yesterday's order, namely, that the commander-in-chief wanted to see the regiment exactly in the position in which it was marching - in overcoats, in covers and without any preparations.
A member of the Gofkriegsrat from Vienna arrived to Kutuzov the day before, with proposals and demands to join the army of Archduke Ferdinand and Mack as soon as possible, and Kutuzov, not considering this connection beneficial, among other evidence in favor of his opinion, intended to show the Austrian general that sad situation , in which troops came from Russia. For this purpose, he wanted to go out to meet the regiment, so the worse the situation of the regiment, the more pleasant it would be for the commander-in-chief. Although the adjutant did not know these details, he conveyed to the regimental commander the commander-in-chief’s indispensable requirement that the people wear overcoats and covers, and that otherwise the commander-in-chief would be dissatisfied. Having heard these words, the regimental commander lowered his head, silently raised his shoulders and spread his hands with a sanguine gesture.
- We've done things! - he said. “I told you, Mikhailo Mitrich, that on a campaign, we wear greatcoats,” he turned reproachfully to the battalion commander. - Oh, my God! - he added and decisively stepped forward. - Gentlemen, company commanders! – he shouted in a voice familiar to the command. - Sergeants major!... Will they be here soon? - he turned to the arriving adjutant with an expression of respectful courtesy, apparently referring to the person about whom he was speaking.
- In an hour, I think.
- Will we have time to change clothes?
- I don’t know, General...
The regimental commander, himself approaching the ranks, ordered that they change into their overcoats again. The company commanders scattered to their companies, the sergeants began to fuss (their overcoats were not entirely in good working order) and at the same moment the previously regular, silent quadrangles swayed, stretched out, and hummed with conversation. Soldiers ran and ran up from all sides, threw them from behind with their shoulders, dragged backpacks over their heads, took off their greatcoats and, raising their arms high, pulled them into their sleeves.
Half an hour later everything returned to its previous order, only the quadrangles turned gray from black. The regimental commander, again with a trembling gait, stepped forward of the regiment and looked at it from afar.
- What else is this? What is this! – he shouted, stopping. - Commander of the 3rd company!..
- Commander of the 3rd company to the general! commander to the general, 3rd company to the commander!... - voices were heard along the ranks, and the adjutant ran to look for the hesitant officer.
When the sounds of zealous voices, misinterpreting, shouting “general to the 3rd company”, reached their destination, the required officer appeared from behind the company and, although the man was already elderly and did not have the habit of running, awkwardly clinging to his toes, trotted towards the general. The captain's face expressed the anxiety of a schoolboy who is told to tell a lesson he has not learned. There were spots on his red (obviously from intemperance) nose, and his mouth could not find a position. The regimental commander examined the captain from head to toe as he approached breathlessly, slowing his pace as he approached.
– You’ll soon dress people up in sundresses! What is this? - shouted the regimental commander, protruding his lower jaw and pointing in the ranks of the 3rd company to a soldier in an overcoat the color of factory cloth, different from other overcoats. – Where were you? The commander-in-chief is expected, and you are moving away from your place? Huh?... I'll teach you how to dress people in Cossacks for a parade!... Huh?...
The company commander, without taking his eyes off his superior, pressed his two fingers more and more to the visor, as if in this one pressing he now saw his salvation.
- Well, why are you silent? Who's dressed up as a Hungarian? – the regimental commander joked sternly.
- Your Excellency...
- Well, what about “your excellency”? Your Excellency! Your Excellency! And what about Your Excellency, no one knows.
“Your Excellency, this is Dolokhov, demoted...” the captain said quietly.
– Was he demoted to field marshal or something, or to soldier? And a soldier must be dressed like everyone else, in uniform.
“Your Excellency, you yourself allowed him to go.”
- Allowed? Allowed? “You’re always like this, young people,” said the regimental commander, cooling down somewhat. - Allowed? I’ll tell you something, and you and...” The regimental commander paused. - I’ll tell you something, and you and... - What? - he said, getting irritated again. - Please dress people decently...
And the regimental commander, looking back at the adjutant, walked towards the regiment with his trembling gait. It was clear that he himself liked his irritation, and that, having walked around the regiment, he wanted to find another pretext for his anger. Having cut off one officer for not cleaning his badge, another for being out of line, he approached the 3rd company.
- How are you standing? Where's the leg? Where's the leg? - the regimental commander shouted with an expression of suffering in his voice, still about five people short of Dolokhov, dressed in a bluish overcoat.
Dolokhov slowly straightened his bent leg and looked straight into the general’s face with his bright and insolent gaze.
- Why the blue overcoat? Down with... Sergeant Major! Changing his clothes... rubbish... - He didn’t have time to finish.
“General, I am obliged to carry out orders, but I am not obliged to endure...” Dolokhov said hastily.