Formulas and units of quantities. Number of formula units Units of measurement of mechanical and thermal quantities

METHODOLOGICAL INSTRUCTIONS

For the preparation of tests, coursework, final qualification papers, master's theses

For students of the Financial and Economic Institute

Considered at a meeting of the Institute’s Educational and Methodological Commission,

protocol dated 08.11.2013 No. 4

Chairman

Educational and Methodological Commission of the Institute E.S. Korchemkina

Tyumen 2013


These guidelines have been prepared on the basis of the following regulatory and technical documents:

GOST 7.32-2001. Research report. Structure and design rules;

GOST 7.1-2003. Bibliographic record. Bibliographic description. General requirements and drafting rules;

GOST 7.0.12-2011. Bibliographic record. Abbreviation of words and phrases in Russian;

General rules

The student's educational research work (hereinafter referred to as the work) must be printed on one side of a sheet of white paper in A 4 format.

The title page of the work is drawn up in accordance with Appendices 1, 2, 3, 4, 5, 6, 7.

The text of the work should be printed, observing the following margin sizes: right - 10 mm, left - 25 mm, top and bottom - 20 mm.

The text of the work is printed at 1.5 intervals using the font - Regular, Times New Roman, font size - 14. The saturation of letters and characters should be even within the line, page and entire work. It is allowed to enter individual words, formulas, and symbols into the text only in black ink and approximately the density of the main text. The paragraph indent is equal to 5 printed characters (1.25 cm).

Each new chapter begins on a new page. The same rule applies to other main structural parts of the work: list of abbreviations, introduction, conclusion, list of sources used, appendices.

The names of the structural elements of the work: “CONTENTS”, “LIST OF ABBREVIATIONS”, “INTRODUCTION”, “CONCLUSION”, “LIST OF SOURCES”, “APPENDICES”, as well as the names of the chapters of the main part are the headings of the structural elements of the work. They should be placed in the center of the line without a period and printed in capital letters, in regular font, without underlining.

Numbering issues

2.1. The pages of the work should be numbered in Arabic numerals. All pages are numbered in order from the title page to the last page. The number 1 is not placed on the title page; the number 2 is placed on the next page. The page number is printed centered at the top of the page without any additional characters (dots, dashes).


2.2. Illustrations and tables located on separate sheets are included in the overall page numbering.

2.3. The main part of the work should be divided into chapters, paragraphs, paragraphs and subparagraphs.

2.4. Chapters must have serial numbers within the work, indicated in Arabic numerals with a dot. The chapter title is printed in capital letters without a period at the end, without underlining. It is not allowed to carry a word to the next line, or to use Roman numerals, mathematical symbols and Greek letters.

Each chapter is printed from a new sheet. The distance between the title of the chapter (paragraph) and the following text should be equal to two and a half spaces. If a chapter is divided into paragraphs, there should be no text between the title of the chapter and the paragraph.

2.5. Paragraphs are numbered within the chapter. The paragraph number consists of the chapter and paragraph numbers separated by a dot, for example, 1.1., a dot is placed at the end of the paragraph number.

Paragraph headings should begin to be printed with a paragraph indentation, with a capital letter, without underlining, without a period at the end. The distance between the title of the paragraph and the following text should be equal to two and a half spaces. If a paragraph is divided into paragraphs, then there should be no text between them.

2.6. Items must be sequentially numbered within each paragraph. The paragraph number includes the chapter number and the serial number of the paragraph and paragraph, separated by a dot; a dot is not placed at the end of the paragraph number, for example, 1.1.1., 1.1.2., and is printed with a paragraph indent. An item may have a title, which is written in capital letters and indented. There is no free line left between the paragraph title and the following text. If a clause is divided into subclauses, there should be no text between them.

2.7. The subclause number includes the number of the chapter, paragraph, clause and the serial number of the subclause, separated by a dot; at the end of the subclause number there is a dot, for example, 1.1.1.1., 1.1.1.2, etc. A subitem may have a title, which is written in capital letters and indented. No free line is left between the title of the subparagraph and the subsequent text.

2.8. If the title includes several sentences, they are separated by periods. Hyphenation of words in headings is not allowed. There is no period at the end of the title. The title of a paragraph, paragraph and subparagraph should not be the last line on the page.

2.9. If a chapter or paragraph has only one paragraph, or a paragraph has one subparagraph, then the paragraph (subparagraph) should not be numbered.

Presentation of the text

3.1. The text of the work should be short, clear and not allow for different interpretations. When setting out mandatory requirements, the words “shall”, “should”, “necessary”, “required”, “not allowed”, “prohibited”, “should not” should be used. The text is presented in an impersonal form. For example: “...measured...”, “accepted...” or “.....referred to...”.

3.2. The following is not allowed in the text:

– use colloquial speech, technicalism, professionalism;

– apply for the same concept various scientific and economic terms that are similar in meaning (synonyms), as well as foreign words if there are equivalent words and terms in Russian;

– abbreviate the designations of units of physical quantities, if they are used without numbers, for example, m, s, you should write “1 m, 1 s or meter, second”, with the exception of units of physical quantities in the heads and sides of tables, in decoding of the letter designations included in formulas and drawings;

– use the mathematical minus sign (–) before negative values ​​of quantities (the word “minus” should be written);

– use mathematical signs without numerical values, for example, > (greater than),< (меньше), = (равно), ≠ (не равно), а также знаки № (номер), % (процент);

– abbreviation of words and phrases.

3.3. Only generally accepted abbreviations are allowed in the text:

– in the middle of sentences – “see”, “t. e.";

– at the end of sentences – “etc.,” “etc.,” “etc.”;

– with the surname or name of the institution – abbreviations of academic degrees and titles, for example, Doctor of Economics. Sciences Ivanov K.M.; Ph.D. legal Sciences Petrov Yu.S.

– if there is a digital designation – “s.” (page), "g." (year), "yy." (years), for example, S. 5, 2006

Abbreviations of the following words and phrases are not allowed: “since”, “so-called”, “thus”, “so”, “for example”.

3.4. Names should be written in the following order: surname, first name, patronymic (or surname, initials, but it is not allowed to transfer initials separately from the surname to the next line).

Formulas and units of quantities

4.1. Formulas are written on a separate line and centered. One free line should be left above and below each formula.

4.2. After the formula, place a list of all symbols accepted in the formula with a decoding of their meanings and an indication of the dimension (if necessary). Letter designations are given in the same sequence in which they are given in the formula.

4.3. Formulas are numbered consecutively throughout the entire work using Arabic numerals. In this case, the formula number is indicated in parentheses in the extreme right position on the line. One formula is designated – (1).

4.4. In formulas, as symbols of physical quantities, the designations established by the relevant state standards (GOST 8.417) should be used. Explanations of symbols and numerical coefficients included in the formula, if they are not explained earlier in the text, must be given directly below the formula and must correspond to the type and size of font adopted when writing the formula itself. Explanations for each symbol should be given on a new line in the sequence in which the symbols are given in the formula.

4.6. The first line of the explanation should begin indented with the word “where” without a colon after it. The “–” (dash) signs are located on the same vertical line.

For example,

R = ∑ pi (Yi + Z i + Wi) (5)

where R is the magnitude of environmental risk;

∑ – sum sign;

pi – probability of occurrence of the i-th hazardous factor affecting the environment and population;

Yi – damage from the impact of the i-th hazardous factor;

Z i – loss or damage to a person’s property;

W i – expenses that a person incurred to restore the right.

4.7. Punctuation marks before and after the formula are placed according to their meaning. Formulas that follow one after another and are not separated by text are separated by a comma.

4.8. If the formula does not fit on a line, then part of it is transferred to another line only on the mathematical sign of the main line, be sure to repeat the sign in the second line. When transferring a formula to the multiplication sign, use the “×” sign. When writing formulas, breaking lines are not allowed. In a multi-line formula, the formula number is placed against the last line.

4.9. Conventional letters, images or signs must comply with those adopted in state standards (GOST 8.417).

4.10. If it is necessary to use symbols, images or signs that are not established by current standards, they should be explained in the text or in the list of symbols.

4.11. The text should use standardized units of physical quantities, their names and designations in accordance with GOST 8.417.

4.12. The unit of physical quantity from the number is indicated separated by a space, including percentages, for example, 5 m, 99.4%.

4.13. Intervals of values ​​in the form “from and to” are written through dashes without spaces. For example, 8-11% or s. 5-7, etc.

4.14. When citing digital material, only Arabic numerals should be used, with the exception of the generally accepted numbering of quarters and half-years, which are indicated by Roman numerals. Cardinal numbers in the text are given without case endings.

4.1. Formulas are written on a separate line and centered. One free line should be left above and below each formula.

4.2. After the formula, place a list of all symbols accepted in the formula with a decoding of their meanings and an indication of the dimension (if necessary). Letter designations are given in the same sequence in which they are given in the formula.

4.3. Formulas are numbered consecutively throughout the entire work using Arabic numerals. The formula number is indicated in parentheses at the far right position on the line. One formula is designated – (1).

4.4. In formulas, as symbols of physical quantities, the designations established by the relevant state standards (GOST 8.417) should be used. Explanations of symbols and numerical coefficients included in the formula, if they are not explained earlier in the text, must be given directly below the formula and must correspond to the type and size of font adopted when writing the formula itself. Explanations for each symbol should be given on a new line in the sequence in which the symbols are given in the formula.

4.6. The first line of the explanation should begin indented with the word “where” without a colon after it. The “–” (dash) signs are located on the same vertical line.

For example,

R = ∑ pi (Yi + Z i + Wi) (5)

where R is the magnitude of environmental risk;

∑ – sum sign;

pi – probability of occurrence of the i-th hazardous factor affecting the environment and population;

Yi – damage from the impact of the i-th hazardous factor;

Z i – loss or damage to a person’s property;

W i – expenses that a person incurred to restore the right.

4.7. Punctuation marks before and after the formula are placed according to their meaning. Formulas that follow one after another and are not separated by text are separated by a comma.

4.8. If the formula does not fit on a line, then part of it is transferred to another line only on the mathematical sign of the main line, be sure to repeat the sign in the second line. When transferring a formula to the multiplication sign, use the “×” sign. When writing formulas, breaking lines are not allowed. In a multi-line formula, the formula number is placed against the last line.

4.9. Conventional letters, images or signs must comply with those adopted in state standards (GOST 8.417).

4.10. If it is necessary to use symbols, images or signs that are not established by current standards, they should be explained in the text or in the list of symbols.

4.11. The text should use standardized units of physical quantities, their names and designations in accordance with GOST 8.417.

4.12. The unit of physical quantity from the number is indicated separated by a space, including percentages, for example, 5 m, 99.4%.

4.13. Intervals of values ​​in the form “from and to” are written through dashes without spaces. For example, 8-11% or s. 5-7, etc.

4.14. When citing digital material, only Arabic numerals should be used, with the exception of the generally accepted numbering of quarters and half-years, which are indicated by Roman numerals. Cardinal numbers in the text are given without case endings.

Any measurement associated with finding numerical values physical quantities, with their help, the patterns of the phenomena that are being studied are determined.

Concept physical quantities, For example, strength, weight, etc., is a reflection of the objectively existing characteristics of inertia, extension, and so on inherent in material objects. These characteristics exist outside and independently of our consciousness, not depending on the person, the quality of the means and methods used in measurements.

Physical quantities that characterize a material object under given conditions are not created by measurements, but are simply determined using them. Measure For any quantity, this means determining its numerical relationship with some other homogeneous quantity, which is taken as a unit of measurement.

Based on this, measurement is the process of comparing a given quantity with a certain value of it, which is taken as unit of measurement.

Formula for the relationship between the quantity for which the derived unit is established and quantities A, B, C, ... units of measurement they are installed independently, general view:

Where k- numerical coefficient (in a given case k=1).

The formula for connecting a derived unit with basic or other units is called formuladimensions, and the exponents dimensions For convenience in the practical use of units, concepts such as multiple and submultiple units were introduced.

Multiple unit- a unit that is an integer number of times larger than a system or non-system unit. A multiple unit is formed by multiplying the basic or derived unit by the number 10 to the appropriate positive power.

submultiple unit- a unit that is an integer number of times smaller than a system or non-system unit. A submultiple unit is formed by multiplying the basic or derived unit by the number 10 to the corresponding negative power.

Definition of the term “unit of measurement”.

Unification of the unit of measurement deals with a science called metrology. Exactly translated, it is the science of measurement.

Looking at the International Dictionary of Metrology, we find out that unit of measurement is a real scalar quantity that is defined and accepted by convention, with which it is easy to compare any other quantity of the same kind and express their relationship using a number.

A unit of measurement can also be considered as a physical quantity. However, there is a very important difference between a physical quantity and a unit of measurement: a unit of measurement has a fixed, agreed upon numerical value. This means that different units of measurement are possible for the same physical quantity.

For example, weight can have the following units: kilogram, gram, pound, pood, centner. The difference between them is clear to everyone.

The numerical value of a physical quantity is represented using the ratio of the measured value to the standard value, which is unit of measurement. The number whose unit of measurement is indicated is named number.

There are basic and derived units.

Basic units set for such physical quantities that are selected as basic in a particular system of physical quantities.

Thus, the International System of Units (SI) is based on the International System of Units, in which the basic quantities are seven quantities: length, mass, time, electric current, thermodynamic temperature, amount of matter and luminous intensity. This means that in SI the basic units are the units of quantities that are indicated above.

Basic Unit Size are established by agreement within a specific system of units and are fixed either using standards (prototypes) or by fixing the numerical values ​​of fundamental physical constants.

Derived units determined through the basic method of using those connections between physical quantities that are established in the system of physical quantities.

There are a huge number of different systems of units. They differ both in the systems of quantities on which they are based and in the choice of basic units.

Usually, the state, through laws, establishes a certain system of units that is preferable or mandatory for use in the country. In the Russian Federation, the main units of quantities are the SI system.

Systems of units of measurement.

Metric systems.

  • MKGSS,

Systems of natural units of measurement.

  • Atomic system of units,
  • Planck units
  • Geometric system of units,
  • Lorentz-Heaviside units.

Traditional systems of measures.

  • Russian system of measures,
  • English system of measures,
  • French system of measures,
  • Chinese system of measures,
  • Japanese system of measures,
  • Already outdated (ancient Greek, ancient Roman, ancient Egyptian, ancient Babylonian, ancient Hebrew).

Units of measurement grouped by physical quantities.

  • Mass units (mass),
  • Temperature units (temperature),
  • Distance units (distance),
  • Area units (area),
  • Units of volume (volume),
  • Units of measurement of information (information),
  • Time units (time),
  • Pressure units (pressure),
  • Units of heat flux (heat flux).

3.4. Names should be written in the following order: first name, patronymic, last name (or - initials, last name, but it is not allowed to transfer the initials separately from the last name to the next line).

4. Formulas and units of quantities

4.1. Formulas are written on a separate line and centered. One free line should be left above and below each formula.

4.2. After the formula, place a list of all symbols accepted in the formula with a decoding of their meanings and an indication of the dimension (if necessary). Letter designations are given in the same sequence in which they are given in the formula.

4.3. Formulas are numbered consecutively throughout the entire work using Arabic numerals. In this case, the formula number is indicated in parentheses in the extreme right position on the line. One formula stands for –

4.4. In formulas, as symbols of physical quantities, the designations established by the relevant state standards (GOST 8.417) should be used. Explanations of symbols and numerical coefficients included in the formula, if they are not explained earlier

V text, must be given directly below the formula and must correspond to the type and size of the font adopted when writing the formula itself. Explanations for each symbol should be given on a new line in the sequence in which the symbols are given in the formula.

4.6. The first line of the explanation should begin indented with the word “where” without a colon after it. Signs“–” (dash) are located on the same vertical line.

For example,

NPV = ∑

−I,

(1+ r)

t= 1

where NPV is net present value;

CF – total cash flow during time period t; I – investment amount;

r – discount rate; n – number of periods.

4.7. Punctuation marks before and after the formula are placed according to their meaning. Formulas that follow one after another and are not separated by text are separated by a comma.

4.8. If the formula does not fit on a line, then part of it is transferred to another line only on the mathematical sign of the main line, be sure to repeat the sign in the second line. When transferring a formula to the multiplication sign, use the “×” sign. When writing formulas it is not allowed

breaking lines. In a multi-line formula, the formula number is placed against the last line.

4.9. Conventional letters, images or signs must comply with those adopted in state standards (GOST 8.417).

4.10. If it is necessary to use symbols, images or signs that are not established by current standards, they should be explained in the text or in the list of symbols.

4.11. The text should use standardized units of physical quantities, their names and designations in accordance with GOST

4.12. The unit of physical quantity from the number is indicated separated by a space, including percentages, for example, 5 m, 99.4%.

4.13. Intervals of values ​​in the form “from and to” are written through dashes without spaces. For example, 8-11% or s. 5-7, etc.

4.14. When citing digital material, only Arabic numerals should be used, with the exception of the generally accepted numbering of quarters and half-years, which are indicated by Roman numerals. Cardinal numbers in the text are given without case endings.

5. Design of illustrations

The illustration must have a title that is placed underneath it. If necessary, explanatory data (text below the figure) is also placed under the illustration.

Illustrations are designated by the word "Fig." and are numbered sequentially in Arabic numerals within the chapter, with the exception of illustrations given in the appendix. The illustration number is placed below the explanatory caption. There is no period at the end of the title of the illustration.

The illustration number must consist of the chapter number and the serial number of the illustration, separated by a dot. For example: Fig. 1.2. Second drawing of the first chapter.

An example of the design of a drawing with a caption is given

Rice. 1.2. Shares of factors influencing the efficiency of document flow

6. Design of tables

6.1. Digital material, comparison and identification of certain patterns are presented in the form of tables. A table is a method of presenting information in which digital or textual material is grouped into columns delimited from one another by vertical and horizontal lines.

6.2. According to the content, the tables are divided into analytical and non-analytical. Analytical tables are the result of processing and analysis of digital indicators. After such tables, a generalization is made as new (inferential) knowledge, which is introduced into the text with the words: “the table allows us to conclude that...”, “from the table it is clear that...”, “the table allows us to conclude that ...", etc. Often such tables make it possible to identify and formulate certain patterns. Non-analytical tables usually contain raw statistical data that is necessary only for information or statement. It is recommended that these tables be included in appendices.

6.3. Typically, a table consists of the following elements: serial number, thematic header, sidebar, vertical column headings (table header), horizontal and vertical columns.

6.4. All tables, if there are several of them, are numbered in Arabic numerals, without indicating the number sign, within the chapter. The number is placed in the upper right corner above the table title after the word “Table...”, for example,

Table 1.2, Table 2.1.9. The table number indicates: the first digit is the chapter number, the second digit is the serial number of the table in the chapter. There is no dot at the end of the table number. Tables are provided with thematic headings, which are placed in the center of the page and written in capital letters without a period at the end. The names of tables are not shown in bold.

6.5. The table runs on one page. If the table does not fit on one page, then it is transferred to others, while the table title is placed on the first page, and on the following pages the table header should be repeated and under it should be placed the inscription: “Continuation of table 1.2.” If the table header is cumbersome, it is allowed not to repeat it. In this case, the columns are numbered and their numbering is repeated on the following pages.

6.6. The table should not contain empty columns. If digital or other data is not given in the column, then a dash is inserted.

6.7. The table is placed after the first mention of it in the text. It is permissible to place the table along the long side of the sheet so that it can be read clockwise, with the page number placed in the lower middle of the short part of the sheet.

6.8. Column No. is not included in the tables.

6.9. Non-standard abbreviations are not allowed in table headings. In graph names, inscriptions are written in the nominative case, singular.

6.10. It is allowed to use a font size and spacing smaller in the table than in the text (point size 12, single spacing). Horizontal and vertical lines delimiting the rows of the table may not be drawn if their absence does not make it difficult to use the table.

6.11. Headings of columns and table rows should be written with a capital letter, and column subheadings with a lowercase letter if they form one sentence with the heading, or with a capital letter if they have an independent meaning. There are no periods at the end of headings and subheadings of tables. Headings and subheadings of columns are indicated in the singular. The heading of each column should be located directly above it.

6.12. The numbers in the columns of the tables must be placed so that the digits of the numbers in the entire column are located one above the other if they relate to the same indicator. In one column, the same number of decimal places must be observed for all values.

6.13. All data given in the table must be reliable, homogeneous and comparable, and their grouping must be based on essential features. Below the table (not at the bottom of the page!) you must indicate the source (see Table 1.2.).

Thus, the statistical tables and figures contained in the text must be correctly formatted. The general requirement is this: if a table, chart or graph is removed from the text, then its meaning and source of data must be completely clear. Hence,