Draft measures of measurement in different countries. Units of measurement from antiquity to the present day. Everything we don't think about seems simple to us. For example, here are the numbers
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 value in different units is expressed by 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 the exact length of a 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 has 28 days, February in a leap year has 29 days. April, June, September, November - 30 days.
A year is (approximately) the time it takes for the Earth to complete one revolution 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. One extra day is added to the fourth year for the following 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 are shorter than 4 true years by 24 hours, that is, by 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:
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Measures of weight/mass
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Area measures (square measures)
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Measures of time
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A measure of the capacity of vessels
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Measuring instruments
To measure various quantities, special measuring instruments are used. Some of them are very simple and are designed 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 into 10 equal divisions. Therefore, each division (the distance between the nearest strokes) corresponds to 1 mm. This value is called scale division measuring instrument.
Before you start measuring a quantity, you should 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 the smaller value from the larger value and divide 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.
Each of us constantly has to measure various quantities in everyday life. 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, atmospheric pressure, wind speed, etc. to predict the weather.
What measures of length existed in antiquity? Every country in the world has its own way of measuring distance. But this is very inconvenient, because in different countries these systems of measures do not coincide. Units of measurement have come down to us from time immemorial. The English king once, many, many years ago, stretched out his right hand and declared: “The distance from the tip of my nose to the thumb of my hand will serve as a measure of length for all my people and be called “YARD”. His subjects immediately prepared a bronze rod “from the royal nose to the finger”, and for a long time the yard became a unit of length for all Englishmen. The length of a yard is 91.44 cm. Units of measurement have come down to us from time immemorial. The English king once, many, many years ago, stretched out his right hand and declared: “The distance from the tip of my nose to the thumb of my hand will serve as a measure of length for all my people and be called “YARD”. His subjects immediately prepared a bronze rod “from the royal nose to the finger”, and for a long time the yard became a unit of length for all Englishmen. Yard length 91.44 cm.
In the Middle Ages in Europe, another unit of length was invented - FUT. A foot is the average length of an adult male foot. In English it means "foot", "leg". One foot is equal to 30.48 cm. Long distances were measured in ancient Rome in steps: 2000 steps later became equal to one mile, or 1.609 km.
In ancient times, the Indians used their unit of measure for the territory when buying land. The area that a person runs in a day was such a unit of measurement. Therefore, in order to buy more land, the buyer hired the fastest "measurer" - a runner, for example, there were their own measures of length - a vershok, span, cubit. Long distances were measured by the flight of an arrow. However, these were approximate, imprecise measures. After all, different people could have different inches, spans, elbows. Yes, and the bow shot at different distances. Therefore, with the development of trade, exact measures of length were required. So that the seller and the buyer do not deceive each other ... ARSHIN became such a measure in Russia. Three arshins made up a FATCH, 500 fathoms - a VERST. In ancient times, the Indians used their unit of measurement of the territory when buying land. The area that a person runs in a day was such a unit of measurement. Therefore, in order to buy more land, the buyer hired the fastest "meter" - a runner. And in Ancient Russia, for example, there were their own measures of length - a vershok, a span, an elbow. Long distances were measured by the flight of an arrow. However, these were approximate, imprecise measures. After all, different people could have different inches, spans, elbows. Yes, and the bow shot at different distances. Therefore, with the development of trade, exact measures of length were required. So that the seller and the buyer do not deceive each other ... ARSHIN became such a measure in Russia. Three arshins made a FATCH, 500 fathoms - a MILESTONE..
In the 18th century, Russia got two copies: N 11 and N 28 ... In the 18th century, French scientists proposed a metric system of measures for all times and for all peoples. The meter was chosen as a unit of length - one forty-millionth part of the earth's meridian passing through Paris. Scientists have made a standard (sample) of the meter in the form of a ruler of platinum. It's such a metal. True, everyone was afraid that this standard would be lost, and just in case, they made 31 copies of the meter and distributed them to different countries. Russia - got two copies: N 11 and N Now most countries use this metric system
Name- translation Ancient Greece Ancient Rome Linear value in the SI system (often approximate) SI Other variants of linear values \u200b\u200b"finger" dactyl (ancient Greek δάκτυλος) other Greek. digit (lat. digitus) lat. 1.85cm 1.85cm approx. 1 inch 1.997 cm "1/12 whole" ounce (lat. un cia) lat. OK. 7 cm 7.39 cm 22.18 cm \u003d 3 palm "foot" pus (other Greek πούς) other Greek. dog (lat. pes) lat. dog monetalis (lat. pes monetalis) lat. dog naturalis (lat. pes naturalis) lat. dog drusianus (lat. pes drusianus) lat. 29.62 cm dog \u003d 1 Roman foot \u003d 12 ounces 29.62 cm 25.00 cm 33.27 cm 30.80 cm 29.57 cm; 29.6352 cm
Measures of area GreeceGreece (Athens) Athens Roman Empire What was the measure based on? πλεθρ ον square feet 876 m² arura arura (50 square feet) 43.8 m²
Ancient Egypt Measures of length 1 Parasang is equal to 1/9 shem = 6.98 km Parasang 1 shem = 62.82 km Egyptian system (from the 5th to the 1st centuries BC inclusive): Athur usual = 3 miles = 5.235 km. Athur royal = 1 1/2 parasangam = 10.47 km. Parasang = 1 1/9 shema = 6.98 km. Shem \u003d 1 1/5 atura of the usual \u003d 6.282 km. Mile = 10 furlongs = 1.745 km. Stadion = 3 1/3 khet = 174.5 m. Xylon \u003d 3 royal cubits \u003d 1.57 m. Royal cubit \u003d 1 1/6 cubits small \u003d 1 1/5 pigeons \u003d 52.35 cm. Zeretz (feet) = 1 1/3 spitam = 2 dihasam = 34.9 cm Spitam = 1 1/2 dihas = 26.175 cm Dihas = 2 shespam = 17.45 cm Shesp = 4 tebam = 8.725 cm Teb (finger) \u003d 2.18 cm. Canna \u003d 5 steps \u003d 11 2/3 grains \u003d 4.07 m. Step \u003d 2 1/3 grains \u003d 81.44 cm.
English system of measures The English system of measures is used in Great Britain, the USA and other countries. Some of these measures in a number of countries vary somewhat in size, so the following are mainly rounded metric equivalents of English measures, convenient for practical calculations.
Measures of length 1 nautical mile (nautical mile, UK) = 10 cable cables = 1.8532 km nautical mile 1 nautical mile (nautical mile, USA, from July 1, 1954) = 1.852 km 1 cable (cable, UK) = 185.3182 mcablets 1 cables (cable, USA) = 185.3249 m 1 statute mile (statute mile) = 8 furlongs = feet = 1609.344 mustard mile 1 furlong (furlong) = 10 chains = 201.168 mfarlong 1 chain (chain) = 4 rods = 100 links = 20.1168 mchain 1 rod (rod, pole, perch, field, perch) = 5.5 yards = 5.0292 mrodpolperch 1 yard (yard) = 3 feet = 0.9144 yard 1 foot (foot) = 3 handam = 12 inches = 0.3048 mft 1 hand (hand) = 4 inches = 10.16 cmhand 1 inch (inch) = 12 lines = 72 dots = 1000 mils = 2.54 cm 1 line (line) = 6 dots = 2 .1167 mm line 1 point (point) = 0.353 mm point 1 mil (mil) = 0.0254 mmmil
Area measures 1 mile² (square mile) \u003d 640 acres \u003d 2.59 km² 1 acre (acre) \u003d 4 ores \u003d 4046.86 m2 , perch²) = 30.25 yards² = 25.293 m² 1 yard² (square yard) = 9 feet² = 0.83613 m² 1 ft² (square foot) = 144 inches² = 929.03 cm² ft² 1 inch² (square inch) = 6.4516 cm²
For a long time, people have been faced with the need to determine distances, lengths of objects, time, areas, volumes, etc.
Measurements were needed in construction, and in trade, and in astronomy, in fact, in any sphere of life. Very high measurement accuracy was needed during the construction of the Egyptian pyramids.
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The importance of measurements increased as society developed and, in particular, as science developed. And in order to measure, it was necessary to come up with units of various physical quantities. Let's remember how it is written in the textbook: "To measure some quantity means to compare it with a homogeneous quantity taken as a unit of this quantity."
The purpose of my work was to find out: what units of length and mass existed and exist now, what is their origin?
Vershok, cubit and other units ...
Measure what is measurable and make what is not measurable accessible.”
G. Galileo
The most ancient units were subjective units. So, for example, sailors measured the path with pipes, that is, the distance that the ship traveled during the time until the sailor smoked his pipe. In Spain, a similar unit was a cigar, in Japan - a horse shoe, that is, the path that a horse traveled until the straw sole tied to its hooves, which replaced the horseshoe, was worn out.
In the program of the Olympic Games of Ancient Hellas there was a stadion race. It has been established that the Greek stage (or stages) is the length of the stadium in Olympia - 192.27 m. horizon. This time is approximately two minutes...
The stages, as a unit of measurement of distances, were also among the Romans (185 cm), and among the Babylonians (about 195 cm), and among the Egyptians (195 cm).
In Siberia, in ancient times, a measure of distance was used - beech. This is the distance at which a person ceases to see separately the horns of a bull.
For many peoples, the length of the arrow was used to determine the distance - the range of the arrow. Our expressions “keep out of a gun shot”, later “on a cannon shot” are reminiscent of such units of length.
The ancient Romans measured distances in steps or double steps (left foot step, right foot step). A thousand double steps equaled a mile (Latin "mille" - a thousand).
The length of a rope or fabric is inconvenient to measure in steps or stages. For this, the units found among many peoples, identified with the names of parts of the human body, turned out to be suitable. Elbow - the distance from the end of the fingers to the elbow joint.
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A measure of length for fabrics, ropes, etc. winding materials, many peoples had a double cubit. We still use this measure for a rough estimate of the length ...
In Russia, for a long time, the arshin (about 71 cm) was used as a unit of length. This measure arose during trade with eastern countries (Persian, “arsh” - cubit). Numerous expressions: “It’s like swallowing a yardstick”, “Measure on your own yardstick” and others testify to its spread.
To measure smaller lengths, a span was used - the distance between the ends of the spaced thumb and forefinger.
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A span or, as it was also called, a quarter (18 cm) was 1/4 of an arshin, and 1/16 of an arshin was equal to a vershok (4.4 cm).
A very common unit of length was the fathom. The first mention of it occurs in the XI century. Since 1554, the sazhen was set equal to 3 arshins (2.13 m) and it was called royal (or eagle, printed) in contrast to arbitrary ones - flyweight and oblique. The fly fathom - the span of the arms - is approximately 2.5 arshins. The fisherman, who shows us what a big fish he missed, shows us the flywheel.
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Oblique sazhen - the distance from the end of the right arm extended upward to the toe of the left leg, it is approximately equal to 3.25 arshins.
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Let's remember, as in fairy tales about giants: "A slanting sazhen in the shoulders." Surprisingly, the coincidence of the ancient Roman measure of length - the "architectural cane" and the ancient Russian oblique fathom: 248 cm. This means the fathom "oblique from foot to hand, from earth to earth." This fathom was determined by the length of the rope, one end of which was pressed with the foot to the ground, and the other was thrown over the arm of a standing person bent at the elbow and lowered again to the ground.
When adding the oblique sazhen mentioned above four times, we get a "Lithuanian cubit" (62 cm).
In the countries of Western Europe, an inch (2.54 cm) has long been used as units - the length of the joint of the thumb (from the Dutch "inch" - thumb) and a foot (30 cm) - the average length of the human foot (from the English "foot" - sole).
Rice. 6 Fig. 7
A cubit, a vershok, a span, a sazhen, an inch, a foot, etc. are very convenient for measurements, since they are always “at hand”. But the units of length corresponding to the parts of the human body have a great disadvantage: different people have fingers, feet, etc. have different lengths. To get rid of arbitrariness, in the XIV century. subjective units begin to be replaced by a set of objective units. So, for example, in 1324 in England a legal inch was established, equal to the length of three barley grains attached to each other, stretched out from the middle part of the ear. The foot was defined as the average length of the feet of sixteen people leaving the church, i.e., by measuring random people, they sought to obtain a more constant value of the unit - the average length of the foot.
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What value do we determine by weighing the body on a balance scale?
What people and when invented the lever scales is unknown. It is possible that this was done by many peoples independently of each other, and the ease of use was the reason for their wide distribution.
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When weighing on a balance scale, the body to be weighed is placed on one cup, and the weights are placed on the other. Weights are selected so as to establish balance. In this case, the masses of the weighed body and weights are balanced. If the balanced scales are transferred, for example, to the Moon, where the weight of the body is 6 times less than on Earth, the balance will not be disturbed, since the weight of both the body and the weights on the Moon has decreased by the same number of times, but the mass has remained the same.
Therefore, when weighing a body on a balance scale, we determine its mass, not its weight.
Units of mass, like units of length, were first established according to natural patterns. Most often by the mass of a seed. So, for example, the mass of precious stones was determined and is still determined in carats (0.2 g) - this is the mass of the seed of one of the types of beans.
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Later, the unit of mass was taken to be the mass of water filling a vessel of a certain capacity. For example, in ancient Babylon, talent was taken as a unit of mass - the mass of water that fills such a vessel, from which water flows evenly through a hole of a certain size for one hour.
According to the mass of grains or water, metal weights of various masses were made. They were used for weighing.
Weights that served as a standard (sample) were kept in temples or government offices.
In Russia, the oldest unit of mass was the hryvnia (409.5 g). There is an assumption that this unit was brought to us from the East. Subsequently, she received the name of the pound. To determine large masses, a pood (16.38 kg) was used, and small ones - a spool (12.8 g).
In 1791, in France, it was decided to create a decimal metric system of measures. The main quantities in this system were chosen to be length and mass.
The commission, which included the largest French scientists, proposed to take as a unit of length 1/40,000,000 of the length of the earth's meridian passing through Paris . The astronomers Méchain and Delambert were commissioned to measure the length of the meridian. The work continued for six years. The scientists measured the length of the meridian located between the cities of Dunkirk and Barcelona, and then calculated the total length of a quarter of the meridian from the pole to the equator.
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Based on their data, a standard of a new unit was made from platinum. . This unit was called meter - from the Greek word "metron", which means "measure".
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The mass of one cubic decimeter of distilled water at the temperature of its highest density of 4°C, determined by weighing in vacuum, was taken as a mass unit. The standard of this unit, called the kilogram, was made in the form of a platinum cylinder.
In 1869, the St. Petersburg Academy of Sciences appealed to scientific institutions around the world with a call to make the decimal metric system proposed by French scientists international. This appeal also said that “the achievements of science have led to the need to abandon the previous definition of the meter as 1/40,000,000 of a quarter of the length of the Parisian meridian, since later, more accurate measurements of the meridian gave different results.” In addition, it became known that the length of the meridian changes over time. But since it was unthinkable after each measurement of the meridian to change the length of the meter, the St. Petersburg Academy of Sciences proposed to take the meter stored in the French archive (archival meter) as a prototype - the first sample and make from it the most accurate and stable copies for different countries, making it metric system of international measures.
When was the metric system of measures introduced in our country? Advanced Russian scientists, who did a lot to ensure that the metric system of measures became international, could not overcome the resistance of the tsarist government to the introduction of the metric system of measures in our country. It was only possible to achieve that in 1899 a law was adopted, prepared by D. I. Mendeleev, according to which, along with Russian measures, “it was allowed to use the international meter and kilogram in Russia”, as well as multiple units of them - gram, centimeter, etc.
The issue of using the metric system of measures in Russia was finally resolved after the Great October Socialist Revolution. On September 14, 1918, the Council of People's Commissars of the RSFSR issued a resolution stating: "To base all measurements on the international metric system of measures and weights with decimal divisions and derivatives."
Units of measurement of different countries. Each country in the world uses its own methods of measuring volume, weight and quantity, that is, it has a special system of measures. It is essential for the successful trading and exchange of goods. But the most difficult thing is that in different countries these systems of measures do not coincide. So, for example, the United States borrowed from the British a special, "English" system of measures. Today, the US is practically the only country that uses it.
Slide 10 from the presentation "Measurements". The size of the archive with the presentation is 315 KB.Mathematics Grade 2
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