Physical quantity called the physical property of a material object, process, physical phenomenon, characterized quantitatively.
The value of a physical quantity expressed by one or more numbers characterizing this physical quantity, indicating the unit of measurement.
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 uniform rectilinear motion, at which the body makes a movement of 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).
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Basic SI units |
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Value |
Unit |
Designation |
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Name |
Russian |
international |
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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 derived SI units, which have their own names:
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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 basic and additional SI units |
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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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Radioactive source activity |
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 comparison with reference values. When measuring a physical quantity, it is assigned a certain numerical value.
Measurements are made using measuring devices. 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 method of measurement (direct action and comparison), according to the form of presentation of indications (analog 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 the true value of the measured indicator.
Stability- the ability of the device to maintain a given measurement accuracy for a certain time after calibration.
Since the earliest times, people have been seriously interested in the question of how it is most convenient to compare quantities expressed in different values. And it's not just natural curiosity. The man of the most ancient terrestrial civilizations attached purely applied significance to this rather difficult matter. Correctly measuring the land, determining the weight of the product on the market, calculating the required ratio of goods in barter, determining the correct rate of grapes when harvesting wine - these are just a few of the tasks that often surfaced in the already difficult life of our ancestors. Therefore, poorly educated and illiterate people, if necessary, to compare the values, went for advice to their more experienced comrades, and they often took an appropriate bribe for such a service, and quite a good one, by the way.
What can be compared
Nowadays, this lesson also plays a significant role in the process of studying the exact sciences. Of course, everyone knows that it is necessary to compare homogeneous values, that is, apples with apples, and beets with beets. It would never occur to anyone to try to express degrees Celsius in kilometers or kilograms in decibels, but we have known the length of the boa constrictor in parrots since childhood (for those who do not remember: there are 38 parrots in one boa constrictor). Although parrots are also different, and in fact the length of the boa constrictor will vary depending on the subspecies of the parrot, but these are the details that we will try to figure out.
Dimensions
When the task says: "Compare the values of the quantities", it is necessary to bring these same quantities to the same denominator, that is, to express them in the same values for ease of comparison. It is clear that it will not be difficult for many of us to compare the value expressed in kilograms with the value expressed in centners or in tons. However, there are homogeneous quantities that can be expressed in different dimensions and, moreover, in different measurement systems. Try, for example, comparing kinematic viscosities and determining which fluid is more viscous in centistokes and square meters per second. Does not work? And it won't work. To do this, you need to reflect both values in the same values, and already by the numerical value to determine which of them is superior to the opponent.
Measurement system
In order to understand what quantities can be compared, let's try to recall the existing measurement systems. To optimize and speed up settlement processes in 1875, seventeen countries (including Russia, the USA, Germany, etc.) signed a metric convention and defined the metric system of measures. To develop and consolidate the standards of the meter and kilogram, the International Committee for Weights and Measures was founded, and the International Bureau of Weights and Measures was set up in Paris. This system eventually evolved into the International System of Units, SI. At present, this system is adopted by most countries in the field of technical calculations, including those countries where national ones are traditionally used in everyday life (for example, the USA and England).
GHS
However, in parallel with the generally accepted standard of standards, another, less convenient CGS system (centimeter-gram-second) developed. It was proposed in 1832 by the German physicist Gauss, and in 1874 modernized by Maxwell and Thompson, mainly in the field of electrodynamics. In 1889, a more convenient ISS (meter-kilogram-second) system was proposed. Comparing objects by the size of the reference values of the meter and kilogram is much more convenient for engineers than using their derivatives (centi-, milli-, deci-, etc.). However, this concept also did not find a mass response in the hearts of those for whom it was intended. All over the world, it was actively developed and used, therefore, calculations in the CGS were carried out less and less, and after 1960, with the introduction of the SI system, the CGS practically fell into disuse. At present, the CGS is actually used in practice only in calculations in theoretical mechanics and astrophysics, and then because of the simpler form of writing the laws of electromagnetism.
Step-by-step instruction
Let's analyze an example in detail. Suppose the problem is: "Compare the values of 25 tons and 19570 kg. Which of the values is greater?" The first thing to do is to determine in what quantities we have given values. So, the first value is given in tons, and the second - in kilograms. At the second step, we check whether the compilers of the problem are trying to mislead us by trying to force us to compare heterogeneous quantities. There are also such trap tasks, especially in quick tests, where 20-30 seconds are given to answer each question. As we can see, the values are homogeneous: both in kilograms and in tons, we measure the mass and weight of the body, so the second test was passed with a positive result. The third step, we translate kilograms into tons or, conversely, tons into kilograms for ease of comparison. In the first version, 25 and 19.57 tons are obtained, and in the second: 25,000 and 19,570 kilograms. And now you can compare the magnitudes of these values with peace of mind. As can be clearly seen, the first value (25 tons) in both cases is greater than the second (19,570 kg).
Traps
As mentioned above, modern tests contain a lot of deception tasks. These are not necessarily tasks that we have analyzed, a rather harmless-looking question can turn out to be a trap, especially one where a completely logical answer suggests itself. However, the deceit, as a rule, lies in the details or in a small nuance that the compilers of the task are trying to disguise in every possible way. For example, instead of the question already familiar to you from the analyzed problems with the formulation of the question: "Compare values where possible" - the compilers of the test can simply ask you to compare the indicated values, and choose the values themselves strikingly similar to each other. For example, kg * m / s 2 and m / s 2. In the first case, this is the force acting on the object (newtons), and in the second - the acceleration of the body, or m / s 2 and m / s, where you are asked to compare the acceleration with the speed of the body, that is, absolutely heterogeneous quantities.
Complex comparisons
However, very often two values are given in tasks, expressed not only in different units of measurement and in different systems of calculation, but also different from each other in the specifics of the physical meaning. For example, the statement of the problem says: "Compare the values of the dynamic and kinematic viscosities and determine which liquid is more viscous." In this case, the values are indicated in SI units, that is, in m 2 / s, and dynamic - in CGS, that is, in poise. How to proceed in this case?
To solve such problems, you can use the instructions presented above with a small addition to it. We decide in which of the systems we will work: let it be generally accepted among engineers. In the second step, we also check if this is a trap? But in this example, too, everything is clean. We compare two fluids in terms of internal friction (viscosity), so both values are homogeneous. The third step is to convert from poise to pascal second, that is, to the generally accepted units of the SI system. Next, we translate the kinematic viscosity into dynamic, multiplying it by the corresponding value of the density of the liquid (table value), and compare the results obtained.
Out of the system
There are also non-systemic units of measurement, that is, units that are not included in the SI, but according to the results of the decisions of the convening of the General Conference on Weights and Measures (GCVM), acceptable for sharing with the SI. It is possible to compare such quantities with each other only when they are reduced to a general form in the SI standard. Non-systemic units include such units as minute, hour, day, liter, electron volt, knot, hectare, bar, angstrom and many others.
Natural number as a measure of magnitude
It is known that numbers arose from the need for counting and measuring, but if natural numbers are sufficient for counting, then other numbers are needed to measure quantities. However, as a result of measuring quantities, we will consider only natural numbers. Having defined the meaning of a natural number as a measure of magnitude, we will find out what is the meaning of arithmetic operations on such numbers. This knowledge is necessary for a primary school teacher not only to justify the choice of actions when solving problems with quantities, but also to understand another approach to the interpretation of a natural number that exists in elementary mathematics.
We will consider a natural number in connection with the measurement of positive scalar quantities - lengths, areas, masses, time, etc., therefore, before talking about the relationship between quantities and natural numbers, we recall some facts related to the magnitude and its measurement, especially since the concept magnitudes, along with numbers, is a core element in an elementary course in mathematics.
The concept of a positive scalar quantity and its measurement
Consider two statements that use the word "length":
1) Many objects around us have length.
2) The table has a length.
The first sentence states that objects of some class have length. In the second, we are talking about the fact that a specific object from this class has a length. Summarizing, we can say that the term "length" is used to refer to properties, or a class of objects (objects have a length), or a specific object from this class (a table has a length).
But how does this property differ from other properties of objects of this class? So, for example, a table can have not only a length, but also be made of wood or metal; tables can be of different shapes. It can be said about the length that different tables have this property to varying degrees (one table can be longer or shorter than the other), which cannot be said about the shape - one table cannot be “more rectangular” than the other.
Thus, the property "to have length" is a special property of objects, it appears when objects are compared according to their length (length). The comparison process establishes that either two objects have the same length, or the length of one is less than the length of the other.
Other known quantities can be considered similarly: area, mass, time, etc. They are special properties of the objects and phenomena around us and appear when objects and phenomena are compared according to this property, and each value is associated with a certain method of comparison.
Quantities that express the same property of objects are called quantities of the same kind or homogeneous quantities . For example, the length of a table and the length of a room are quantities of the same kind.
Let us recall the main provisions related to homogeneous quantities.
1. Any two quantities of the same kind are comparable: they are either equal or one is less than the other. In other words, for quantities of the same kind, the relations "is equal to", "less than" and "greater than", and for any quantities A and B, one and only one of the relations is true: A<В, А = В, А>IN.
For example, we say that the length of the hypotenuse of a right triangle is greater than the length of any leg of this triangle, the mass of an apple is less than the mass of a watermelon, and the lengths of opposite sides of the rectangle are equal.
2. The relation "less than" for homogeneous quantities is transitive: if A< В и В < С, то А < С.
So, if the area of triangle F 1 is less than the area of triangle F 2, and the area of triangle F 2 is less than the area of triangle F 3, then the area of triangle F 1 is less than the area of triangle F 3.
3. Values of the same kind can be added, as a result of addition, a value of the same kind is obtained. In other words, for any two quantities A and B, the value C \u003d A + B is uniquely determined, which is called the sum of the quantities A and B.
The addition of quantities is commutative and associative.
For example, if A is the mass of the watermelon and B is the mass of the melon, then C = A + B is the mass of the watermelon and melon. Obviously, A + B = B + A and (A + B) + C = A + (B + C).
The difference between A and B is the value
C \u003d A - B, that A \u003d B + C.
The difference between A and B exists if and only if A>B.
For example, if A is the length of segment a, B is the length of segment b, then C \u003d A-B is the length of segment c (Fig. 1).
5. A quantity can be multiplied by a positive real number, resulting in a quantity of the same kind. More precisely, for any value A and any positive real number x, there is a single value B =
X. A, which is called the product of the quantity A and the number x.
For example, if A is the time allotted for one lesson, then multiplying A by the number x \u003d 3, we get the value B \u003d 3·A - the time for which 3 lessons will pass.
6. Values of the same kind can be divided, resulting in a number. Division is determined by multiplying a value by a number.
Partial quantities A and B is such a positive real number x = A: B, that A = x·B.
So, if A is the length of segment a, B is the length of segment b (Fig. 2) and segment A consists of 4 segments equal to b, then A: B \u003d 4, since A \u003d 4 B.
Quantities, as properties of objects, have one more feature - they can be quantified. To do this, the value must be measured. To carry out a measurement from this kind of quantities, a value is chosen, which is called a unit of measurement. We will refer to it as E.
If the quantity A is given and the unit of quantity E (of the same kind) is chosen, then to measure the value of A - this means to find such a positive real number x that A \u003d x E.
The number x is called numerical value of A with a unit of E. It shows how many times the value of A is greater (or less) than the value of E, taken as a unit of measurement.
If A \u003d x E, then the number x is also called a measure of the value of A at unity E and write x \u003d m E (A).
For example, if A is the length of segment a, E is the length of segment b (Fig. 2), then A=a·E. The number 4 is the numerical value of the length A with a unit of length E, or, in other words, the number 4 is the measure of the length of A with a unit of length E.
In practice, when measuring quantities, people use standard units of quantities: for example, length is measured in meters, centimeters, etc. The measurement result is recorded in this form: 2.7 kg; 13 cm; 16 p. Based on the concept of measurement given above, these records can be considered as the product of a number and a unit of magnitude. For example, 2.7 kg = 2.7 kg; 13 cm = 13 cm; 16 s = 16 s.
Using this representation, it is possible to substantiate the process of transition from one unit of quantity to another. For example, suppose you want to express h in minutes. Since h = h and hour = 60 min, then h = 60 min = ( 60) min = 25 min.
A quantity that is determined by a single numerical value is called scalar value .
If, with the chosen unit of measurement, a scalar value takes only positive numerical values, then it is called a positive scalar.
Positive scalar values are length, area, volume, mass, time, cost and quantity of goods, etc.
Measuring quantities allows you to move from comparing quantities to comparing numbers, from operations on quantities to corresponding operations on numbers, and vice versa.
1. If the quantities A and B are measured using the unit of the quantity E, then the relationship between the quantities A and B will be the same as the relationship between their numerical values, and vice versa:
A+B<=>m(A) + m(B);
A<В <=>m (A) A>B<=>m (A) > m (B). For example, if the masses of two bodies are such that A \u003d 5 kg, B \u003d 3 kg, then it can be argued that A> B, since 5> 3. 2. If the quantities A and B are measured using the unit of the quantity E, then to find the numerical value of the sum A + B, it is enough to add the numerical values of the quantities A and B: A + B = C<=>m (A + B) \u003d m (A) + m (B). For example, if A = 5 kg, B = 3 kg, then A + B = 5 kg + 3 kg = = (5 + 3) kg = 8 kg. 3. If the values \u200b\u200bof A and B are such that B \u003d x A, where x is a positive real number, and the value A is measured using the unit of E, then to find the numerical value of B at units E, it is enough to multiply the number x by number m (A): B = x A<=>m (B) \u003d x m (A). For example, if the mass B is 3 times the mass A and A = 2 kg, then B = 3A = 3 (2 kg) = (3 2) kg = 6 kg. In mathematics, when writing the product of the value A and the number x, it is customary to write the number before the value, i.e. Ha. But it is allowed to write like this: Ah. Then the numerical value of the quantity A is multiplied by x, if the value of the quantity A x is found. The considered concepts - an object (object, phenomenon, process), its magnitude, the numerical value of a magnitude, a unit of magnitude - must be able to isolate in texts and tasks. For example, the mathematical content of the sentence “We bought 3 kilograms of apples” can be described as follows: the sentence considers such an object as apples, and its property is mass; to measure the mass used the unit of mass -kilogram; as a result of the measurement, the number 3 was obtained - the numerical value of the mass of apples with a unit of mass - kilogram. The same object can have several properties, which are quantities. For example, for a person, this is height, mass, age, etc. The process of uniform movement is characterized by three quantities: distance, speed and time, between which there is a relationship expressed by the formula s = v t. If quantities express different properties of an object, then they are called sizes of various kinds
, or heterogeneous quantities
. So, for example, length and mass are heterogeneous quantities. Length, area, mass, time, volume - quantities. The initial acquaintance with them takes place in elementary school, where the value, along with the number, is the leading concept. A quantity is a special property of real objects or phenomena, and the peculiarity lies in the fact that this property can be measured, that is, the quantity of a quantity can be called. Quantities that express the same property of objects are called quantities. of the same kind or homogeneous quantities. For example, the length of the table and the length of the rooms are homogeneous values. Quantities - length, area, mass and others have a number of properties. 1) Any two quantities of the same kind are comparable: they are either equal, or one is less (greater) than the other. That is, for quantities of the same kind, the relations “equal”, “less than”, “greater than” take place, and for any quantities and one and only one of the relations is true: For example, we say that the length of the hypotenuse of a right triangle is greater than any leg of a given triangle; the mass of a lemon is less than the mass of a watermelon; opposite sides of a rectangle are equal. 2) Values of the same kind can be added, as a result of addition, a value of the same kind will be obtained. Those. for any two quantities a and b, the value a + b is uniquely determined, it is called sum values a and b. For example, if a is the length of segment AB, b is the length of segment BC (Fig. 1), then the length of segment AC is the sum of the lengths of segments AB and BC; 3) Value multiply by real number, resulting in a value of the same kind. Then for any value a and any non-negative number x there is a unique value b = x a, the value b is called work the quantity a by the number x. For example, if a is the length of the segment AB multiplied by x= 2, then we get the length of the new segment AC. (Fig. 2) 4) Values of the same kind are subtracted by determining the difference of values through the sum: the difference between the values of a and b is such a value c that a=b+c. For example, if a is the length of segment AC, b is the length of segment AB, then the length of segment BC is the difference between the lengths of segments AC and AB. 5) Values of the same kind are divided, defining the quotient through the product of the value by the number; private quantities a and b is a non-negative real number x such that a = x b. More often this number is called the ratio of the values \u200b\u200bof a and b and is written in this form: a / b = x. For example, the ratio of the length of segment AC to the length of segment AB is 2. (Fig. No. 2). 6) The relation "less than" for homogeneous quantities is transitive: if A<В и В<С, то А<С. Так, если площадь треугольника F1 меньше площади треугольника F2 площадь треугольника F2 меньше площади треугольника F3, то площадь треугольника F1 меньше площади треугольника F3.Величины, как свойства объектов, обладают ещё одной особенностью – их можно оценивать количественно. Для этого величину нужно измерить. Измерение – заключается в сравнении данной величины с некоторой величиной того же рода, принятой за единицу. В результате измерения получают число, которое называют численным значением при выбранной единице. The comparison process depends on the kind of quantities under consideration: it is one for lengths, another for areas, a third for masses, and so on. But whatever this process may be, as a result of measurement, the quantity receives a certain numerical value with the chosen unit. In general, if the value a is given and the unit of the value e is chosen, then as a result of measuring the value a, such a real number x is found that a = x e. This number x is called the numerical value of the quantity a at the unit e. This can be written as follows: x \u003d m (a) .
According to the definition, any quantity can be represented as a product of a certain number and a unit of this quantity. For example, 7 kg = 7∙1 kg, 12 cm =12∙1 cm, 15h =15∙1 h. Using this, as well as the definition of multiplying a quantity by a number, one can justify the process of transition from one unit of quantity to another. Let, for example, you want to express 5/12h in minutes. Since, 5/12h = 5/12 60min = (5/12 ∙ 60)min = 25min. Quantities that are completely determined by one numerical value are called scalar quantities. Such, for example, are length, area, volume, mass and others. In addition to scalar quantities, mathematics also considers vector quantities. To determine a vector quantity, it is necessary to specify not only its numerical value, but also its direction. Vector quantities are force, acceleration, electric field strength and others. In elementary school, only scalar quantities are considered, and those whose numerical values are positive, that is, positive scalar quantities. Measuring quantities allows us to reduce their comparison to a comparison of numbers, operations on quantities to the corresponding operations on numbers. 1/. If the quantities a and b are measured using the unit e, then the relationship between the quantities a and b will be the same as the relationship between their numerical values, and vice versa. A=bm(a)=m(b), A>bm(a)>m(b), A
For example, if the masses of two bodies are such that a=5 kg, b=3 kg, then it can be argued that the mass a is greater than the mass b because 5>3. 2/ If the quantities a and b are measured using the unit e, then to find the numerical value of the sum a + b, it is enough to add numerical values of a and b. a + b \u003d c m (a + b) \u003d m (a) + m (b). For example, if a \u003d 15 kg, b \u003d 12 kg, then a + b \u003d 15 kg + 12 kg \u003d (15 + 12) kg \u003d 27 kg 3/ If the values a and b are such that b= x a, where x is a positive real number, and the value a is measured using the unit e, then to find the numerical value of the value b at unit e, it is enough to multiply the number x by the number m (a): b \u003d x a m (b) \u003d x m (a). For example, if the mass a is 3 times the mass b, i.e. b = Za and a = 2 kg, then b = Za = 3 ∙ (2 kg) = (3 ∙ 2) kg = 6 kg. The considered concepts - an object, an object, a phenomenon, a process, its magnitude, the numerical value of a magnitude, a unit of magnitude - must be able to isolate in texts and tasks. For example, the mathematical content of the sentence “We bought 3 kilograms of apples” can be described as follows: the sentence considers such an object as apples, and its property is mass; to measure mass, the unit of mass was used - kilogram; as a result of the measurement, the number 3 was obtained - the numerical value of the mass of apples with a unit of mass - kilogram. Consider the definitions of some quantities and their measurements. statistic- quantitative characteristics of socio-economic phenomena and processes in terms of qualitative certainty. A distinction is made between an indicator-category and a specific statistical indicator: specific statistic is a digital characteristic of the phenomenon or process being studied. For example: the population of Russia at the moment is 145 million people. According to the coverage of units, individual and summary indicators are distinguished. Individual indicators - characterize a separate object or a separate unit of the population (profit of the company, the size of the contribution of an individual). Consolidated indicators - characterize part of the population or the entire statistical population as a whole. They can be obtained as volumetric and calculated. Volumetric indicators are obtained by adding the values of the attribute of individual units of the population. The resulting value is called the feature volume. Estimated indicators are calculated according to various formulas and are used in the analysis of socio-economic phenomena. Statistical indicators by time factor are divided into: Statistical indicators are interconnected. Therefore, in order to form a holistic view of the phenomenon or process under study, it is necessary to consider a system of indicators. Measures and expresses the phenomena of social life with the help of quantitative categories - statistical quantities. The results are obtained primarily in the form of absolute values, which serve as the basis for the calculation and analysis of statistical indicators in the next stages of the statistical study. Absolute value- the volume or size of the studied event or phenomenon, process, expressed in appropriate units of measurement in specific conditions of place and time. The result of statistical observation are indicators that characterize the absolute dimensions or properties of the phenomenon under study for each unit of observation. They are called individual absolute indicators. If the indicators characterize the entire population as a whole, they are called generalizing absolute indicators. Statistical indicators in the form of absolute values always have units of measurement: natural or cost. Natural units of measurement are simple, compound and conditional. Simple natural units measurements are tons, kilometers, pieces, liters, miles, inches, etc. In simple natural units, the volume of the statistical population is also measured, that is, the number of its constituent units, or the volume of its individual part. Composite natural units measurements have calculated indicators obtained as a product of two or more indicators that have simple units of measurement. For example, accounting for labor costs in enterprises is expressed in man-days worked (the number of employees of the enterprise is multiplied by the number of days worked for the period) or man-hours (the number of employees of the enterprise is multiplied by the average duration of one working day and the number of working days in the period); the turnover of transport is expressed in ton-kilometers (the mass of the transported cargo is multiplied by the distance of transportation), etc. Conditionally natural units measurements are widely used in the analysis of production activities, when it is required to find the final value of the same type of indicators that are not directly comparable, but characterize the same properties of the object. Natural units are recalculated into conditionally natural ones by expressing the varieties of the phenomenon in units of some standard. For example: Translation into conventional units is carried out using special coefficients. For example, if there are 200 tons of soap with a fatty acid content of 40% and 100 tons with a fatty acid content of 60%, then in terms of 40%, we get a total volume of 350 tons of conditional soap (the conversion factor is defined as the ratio 60: 40 = 1 .5 and, consequently, 100 t 1.5 = 150 t conventional soap). Example 1 Find conditional natural value: Let's say we produce notebooks: Solution: Answer: Conditionally full size \u003d 1000 * 1 + 200 * 2 + 50 * 4 + 100 * 8 \u003d 2400 notebooks of 12 sheets In conditions of greatest importance and application are cost units: rubles, dollars, euros, conventional monetary units, etc. To assess socio-economic phenomena and processes, indicators are used in current or actual prices or in comparable prices. By itself, the absolute value does not give a complete picture of the phenomenon under study, does not show its structure, the relationship between individual parts, development over time. It does not reveal correlations with other absolute values. Therefore, statistics, not limited to absolute values, widely uses general scientific methods of comparison and generalization. Absolute values are of great scientific and practical importance. They characterize the availability of certain resources and are the basis of various relative indicators. Along with the absolute values in and various relative values are also used. Relative values are different ratios or percentages. Relative statistics- these are indicators that give a numerical measure of the ratio of two compared values. The main condition for the correct calculation of relative values is the comparability of the compared values and the existence of real connections between the phenomena under study. Relative value = compared value / basis According to the method of obtaining relative values, these are always always derivative (secondary) values. They can be expressed: Relative amount of coordination(coordination indicator) - represents the ratio of the parts of the population to each other. In this case, the part that has the largest share or is a priority from an economic, social or any other point of view is selected as the basis for comparison. OVK = indicator characterizing the part of the population / indicator characterizing the part of the population chosen as the basis of comparison The relative value of coordination shows how many times one part of the population is greater or less than the other, taken as the base of comparison, or how many percent of it is, or how many units of one part of the whole fall into 1, 10, 100, 1000, ..., units of the other (basic) part. For example, in 1999 there were 68.6 million men and 77.7 million women in Russia, so there were (77.7/68.6)*1000=1133 women per 1000 men. Similarly, you can calculate how many technicians per 10 (100) engineers; the number of boys per 100 girls among newborns, etc. Example: The company employs 100 managers, 20 couriers and 10 managers. Relative size of the structure(structure indicator) - characterizes the specific gravity of a part in its total volume. The relative size of the structure is often referred to as "specific gravity" or "proportion". OVS = indicator characterizing a part of the population / indicator for the entire population as a whole Example: The company employs 100 managers, 20 couriers and 10 managers. Total 130 people. The sum of all RBCs must be equal to 100% or one. Relative comparison value(comparison indicator) - characterizes the ratio between different populations according to the same indicators. Example 8: The volume of loans issued to individuals as of February 1, 2008 by Sberbank of Russia amounted to 520189 million rubles, by Vneshtorgbank - 10915 million rubles. Absolute value
Types of absolute values:
Forms of accounting for absolute values:
To recalculation \u003d actual consumer quality / standard (predetermined quality)
We set the standard - 12 sheets.
We calculate the conversion factor:Relative values
There are the following types of relative statistical values:
For example, the birth rate in the form of a relative value, calculated in ppm, shows the number of births per year per 1000 people.Relative amount of coordination
Solution: RHV = (100 / 20)*100% = 500%. There are 5 times more managers than couriers.
same with OBC (Example 5): (77%/15%) * 100% = 500%Relative size of the structure
Relative comparison value
Solution:
RBC = 520189 / 10915 = 47.7
Thus, the volume of loans issued to individuals by Sberbank of Russia as of February 1, 2006 was 47.7 times higher than that of Vneshtorgbank.
