The composition of weather, mood and special units
The weather is sunny today. The sunlight pours down without reservation, and every inch of the air seems to be filled with joy. Such wonderful weather really makes people extremely happy.
In the world of measurement units, there are some unique ways of composition. There is a form of unit that is composed by using a unit as the denominator and fixing the numerator as 1. Just like the unit of linear expansion coefficient, "per degree Celsius (1/°C)", which describes the proportional relative change in the length of an object when the temperature rises by 1 degree Celsius. This kind of unit can accurately reflect the characteristics of an object's change with temperature and has important applications in materials science, engineering fields, etc. For example, in construction engineering, understanding the linear expansion coefficient of building materials can avoid structural problems caused by material deformation due to temperature changes.
Another type is composed of units of the International System of Units and non - SI units selected by the country. For example, the unit of electrical energy, "kilowatt - hour (kW·h)", which ingeniously combines the SI unit of power, the kilowatt, with the commonly used unit of time, the hour. In daily life, the electricity meters in our homes measure the amount of electricity consumed, and the unit is "kilowatt - hour", which is what we commonly call "degree". Through this unit, we can clearly know how much electrical energy we have consumed and then reasonably plan our electricity usage.
Usage methods of legal measurement units
Reading and writing rules
1. Reading and writing of unit names: The names of legal measurement units refer to the Chinese names before the units, which are divided into full names and abbreviations. When there is no risk of confusion, the abbreviations have the same function as the full names, and the abbreviations are also stipulated as the Chinese symbols of the units. For the names of single units, we directly read and write them according to the given Chinese characters. For example, "meter", "second", "kilogram", etc., which are simple and direct without causing ambiguity.
2. Reading and writing order of combined units: The reading and writing order of combined units should be consistent with the order of their international symbol representation. However, for the names of units in power form, the name of the exponent should be read before the name of the unit represented by the exponent. Taking the density unit kg/m³ as an example, its Chinese name is kilogram per cubic meter. This rule helps us read combined units accurately and avoid misunderstandings.
3. Reading and writing of mathematical symbols in the international symbols of compound units
Multiplication sign ·: The multiplication sign has no corresponding name in a compound unit and does not need to be read out. For example, for kW·h, we directly call it kilowatt-hour instead of reading it as kilowatt point hour.
Division sign /: The division sign corresponds to the reading and writing of the Chinese character (per). No matter how many units there are in the denominator, the character only appears once at the place where there is a division sign. For example, the luminous exitance is lm/m², which is read as lumen per square meter; the specific heat unit is J/(kg·℃), and its Chinese name is (joule per kilogram per degree Celsius), and it cannot be read as (joule per kilogram per degree Celsius).
Power Xⁿ: For the exponent in a power, the corresponding name is generally the number followed by the words power. However, when the second or third power of a length unit is used to represent area or volume, the name of the exponent should be read and written as square or cubic. When the exponent is -1, the name of the unit starts with the word per. For example, the area unit m² is read as square meter, and the volume unit m³ is read as cubic meter; the speed unit m/s can be understood as m·s⁻¹ and is read as meter per second.
4. Writing of the symbols of combined units in multiplicative form: For the symbols of combined units formed in multiplicative form, there are two forms of international symbols. Taking the moment as an example, one is N·m and the other is Nm. However, there is only one form of Chinese symbols, that is, ·. If a unit symbol is also a prefix symbol, to avoid confusion, this unit cannot be placed at the very front. For example, the unit of moment should be Nm, not mN, because mN is easily mistaken for millinewton.
5. Writing forms of combined units in the form of division: For combined units formed in the form of division, there are three forms of international symbols. For example, the density unit has forms such as kg/m³ and kg·m⁻³. There are two forms of Chinese symbols, namely /³ and ·⁻³.
6. Precautions for writing international symbols: When writing international symbols, pay attention to the capitalization of letters. All the letters used should be in upright style and no plural forms should be used. The numerator and the denominator should be on the same horizontal line. When the denominator consists of the multiplication of two or more units, the entire denominator should generally be enclosed in parentheses. This can ensure the standardization and accuracy of writing international symbols.
Rules for the use of legal measurement units
1. Usage scenarios of unit names and symbols: Unit names are generally used in narrative texts, while unit symbols are used in places where concise and clear expressions are required, such as formulas, data tables, curves, product nameplates, technical standards, verification regulations, and instructions for use. They can also be used in narrative texts. The international symbols of units are preferred, but international symbols cannot be used as ordinary words. For example, 17 yuan per kilogram of meat cannot be written as 17 yuan per kg of meat.
2. Rules for adding prefixes to combined units: When adding a prefix to a combined unit in the form of multiplication, the prefix is generally added before the first unit in the combined unit; when adding a prefix to a combined unit in the form of division, the prefix is generally added before the first unit in the numerator, and generally no prefix is added to the denominator, except for kg and length units. Such rules help to standardize the way of adding prefixes and avoid confusion.
3. Holistic use of units: The name or symbol of a unit should be used as a whole. When writing and pronouncing, the name of a unit cannot be arbitrarily split, and no numerical values can be inserted into it. For example, 20℃ should be read as 20 degrees Celsius rather than Celsius 20 degrees. The exponents of decimal multiple and sub - multiple units apply to the entire unit including the prefix. For example, 1cm² = 1(cm)² = 1(10⁻²m)² = 10⁻⁴m², not 10⁻²m².
4. Usage restrictions of prefixes: Prefixes cannot be used alone or in overlapping form. For example, 10 μF cannot be written as 10 μ, and 10 pF cannot be written as 10 μμF. At the same time, prefixes cannot be added to non - decimal units, such as [angular] minute, [angular] second, "hour", "day", etc. Among the 16 non - SI units selected by the state, only five units, namely "ton", "liter", "electron - volt", "decibel", and "tex", can sometimes have prefixes added. Prefixes cannot be added to the other 11 units and "degree Celsius".
5. Avoid mixing different units
Mixing of Chinese names and Chinese symbols: The Chinese names and Chinese symbols of units should not be mixed. Mathematical symbols such as ·, /, Xⁿ should not appear in the unit names. For example, the name of the moment unit is Newton - meter, and it should not be written as Newton·meter. The units used in the Chinese symbols of units should all be the abbreviations of the units. Only when there is no abbreviation can the full - name be used, and multiplication, division and exponents should all use mathematical symbols. For example, the Chinese symbol of the moment unit is N·m, and it should not be written as Newton - meter.
Mixed use of international symbols and Chinese symbols: The international symbols and Chinese symbols of units cannot be mixed, but "℃" is an exception. It is both the international symbol of degrees Celsius and can be used as a Chinese symbol.
6. Correct expression of quantities
Unit position: The name or symbol of a unit should be placed after the entire numerical value. For example, 1.75m should not be written as 1m75; 20.5″ should not be written as 20″.5. If the quantity being represented is the sum or difference of quantities, then the numerical values should be grouped with parentheses, and the common unit symbol should be placed after all the numerical values, or written as the sum or difference of each quantity. For example, l = 12m - 7m = (12 - 7)m = 5m, and it should not be written as 12 - 7m; t = 28.4℃ ± 0.5℃ = (28.4 ± 0.5)℃, and it should not be written as 28.4 ± 0.5℃.
Quantity of units used: Generally, only one unit should be used in a measured value for decimal units. For example, 1.81 m should not be written as 1 m 81 cm. For non - decimal units, it is allowed to use several units in a measured value, such as 25°37′11″ and 3 h 45 min 15 s.
Selection of multiple or fractional units: When selecting multiple or fractional units, the numerical value should generally be within the range of 0.1 - 1000. For example, 0.00394m should be written as 3.94mm.
Writing when a numerical value has many digits: When a numerical value has many digits, starting from the decimal point and moving either left or right, leave a space of 1/4 of a character width every three digits to facilitate reading. For example, 2764532m/s should be written as 2 764 532m/s.
Common errors in the use of measurement units
In actual use, there are some common errors. For example, using "kilolitre" to represent the volume unit "litre", using "metric ton" to represent the mass unit "ton", using "hectogram" to represent the mass unit of 100 grams, using "centimetre" to represent the length unit "centimeter", using "metre" to represent "meter", using "degree" to represent the electrical energy unit "kilowatt - hour", using "C.C" to represent the volume unit "ml", using "T" to represent "t", using "kgS" to represent the mass unit "kg", using "″" to represent the time unit "s", etc. We should avoid these errors and correctly use the legal measurement units.
Error theory and data processing
Error theory
Errors and Their Classification
1. Basic knowledge (basic concepts)
True value of a quantity: The true value of a quantity refers to the objective and real magnitude that the measured quantity possesses at a certain moment, a certain position or state. This is an ideal concept. In practice, it is generally impossible to know exactly and cannot be directly obtained through measurement. However, we can obtain a quantity value close to the true value through measurement. The higher the measurement accuracy, the closer the obtained quantity value is to the true value.
Actual value: A quantity value that meets the specified accuracy and is used to replace the true value is called the actual value. Under normal circumstances, through verification, the quantity value measured by a metrological standard of a higher level is regarded as the actual value. For example, in metrological work, the value measured by a more accurate standard instrument can be used as the actual value for subsequent analysis and calculation.
Measurement error: The difference between the measurement result and the true value of the measured quantity is the measurement error, also known as the absolute measurement error. Its calculation formula is: Measurement error = Measurement result - True value. Measurement error can be expressed either by absolute error or by relative error. The absolute error can intuitively reflect the degree of deviation of the measurement result from the true value, while the relative error can better reflect the accuracy of the measurement.
2. Definition and classification of errors
Absolute error: The difference between the measured value and the true value of a quantity is the absolute error, which is usually simply referred to as the error. Its calculation formula is: Absolute error = Measured value - True value. The absolute error may be a positive value or a negative value. A positive value indicates that the measured value is greater than the true value, and a negative value indicates that the measured value is less than the true value.
Relative error: The ratio of the absolute error to the true value of the measured quantity is called the relative error. Since the measured value is close to the true value, the ratio of the absolute error to the measured value can also be approximately used as the relative error. The relative error can more accurately reflect the relative accuracy of the measurement and is very useful when comparing the accuracy of different measurement results.