Units. Physical quantities Metric system of units
Physical bodies use quantities that characterize space, time and the body in question: length l, time t and mass m. Length l is defined as the geometric distance between two points in space.
The International System of Units (SI) uses the meter (m) as a unit of length.
\[\left=m\]
The meter was originally defined as ten millionths of a quarter of the earth's meridian. By this, the creators of the metric system sought to achieve invariance and accurate reproducibility of the system. The meter standard was a ruler made of a platinum alloy with 10% iridium, the cross-section of which was given a special X-shape to increase bending rigidity with a minimum volume of metal. In the groove of such a ruler there was a longitudinal flat surface, and the meter was defined as the distance between the centers of two strokes applied across the ruler at its ends, at a standard temperature of 0$()^\circ$ C. Currently, due to increased requirements for accuracy measurements, the meter is defined as the length of the path traveled in a vacuum by light in 1/299,792,458 of a second. This definition was adopted in October 1983.
The time t between two events at a given point in space is defined as the difference in the readings of a clock (a device whose operation is based on a strictly periodic and uniform physical process).
The International System of Units (SI) uses the second (s) as the unit of time.
\[\left=c\]
According to modern concepts, 1 second is a time interval equal to 9,192,631,770 periods of radiation corresponding to the transition between two hyperfine levels of the ground (quantum) state of the cesium-133 atom at rest at 0° K in the absence of disturbance by external fields. This definition was adopted in 1967 (clarification regarding temperature and resting state appeared in 1997).
The mass m of a body characterizes the force that must be applied to bring it out of its equilibrium position, as well as the force with which it is capable of attracting other bodies. This indicates the dualism of the concept of mass - as a measure of the inertia of a body and a measure of its gravitational properties. As experiments show, the gravitational and inertial mass of a body are equal, at least within the limits of measurement accuracy. Therefore, except for special cases, they simply talk about mass - without specifying whether it is inertial or gravitational.
The International System of Units (SI) uses the kilogram as a unit of measurement for mass.
$\left=kg\ $
The international prototype of the kilogram is taken to be the mass of a cylinder made of a platinum-iridium alloy, with a height and diameter of about 3.9 cm, stored in the Breteuil Palace near Paris. The weight of this reference mass, equal to 1 kg at sea level at latitude 45$()^\circ$, is sometimes called kilogram-force. Thus, it can be used either as a standard of mass for an absolute system of units, or as a standard of force for a technical system of units in which one of the basic units is the unit of force. In practical measurements, 1 kg can be considered equal to the weight of 1 liter of pure water at a temperature of +4°C.
In continuum mechanics, the main units of measurement are thermodynamic temperature and amount of matter.
The SI unit of temperature is Kelvin:
$\left[T\right]=K$.
1 Kelvin is equal to 1/273.16 of the thermodynamic temperature of the triple point of water. Temperature is a characteristic of the energy that molecules possess.
The amount of substance is measured in moles: $\left=Mole$
1 mole is equal to the amount of substance in a system containing the same number of structural elements as there are atoms in carbon-12 weighing 0.012 kg. When using a mole, the structural elements must be specified and can be atoms, molecules, ions, electrons and other particles or specified groups of particles.
Other units of measurement of mechanical quantities are derived from the basic ones, representing their linear combination.
Derivatives of length are area S and volume V. They characterize areas of space, respectively, of two and three dimensions, occupied by extended bodies.
Units of measurement: area - square meter, volume - cubic meter:
\[\left=m^2 \left=m^3\]
The SI unit of speed is meters per second: $\left=m/s$
The SI unit of force is newton: $\left=Н$ $1Н=1\frac(kg\cdot m)(s^2)$
The same derived units of measurement exist for all other mechanical quantities: density, pressure, momentum, energy, work, etc.
Derived units are obtained from basic units using algebraic operations such as multiplication and division. Some of the derived units in the SI are given their own names, for example, the unit radian.
Prefixes can be used before unit names. They mean that a unit must be multiplied or divided by a certain integer, a power of 10. For example, the prefix “kilo” means multiplied by 1000 (kilometer = 1000 meters). SI prefixes are also called decimal prefixes.
In technical measurement systems, instead of the unit of mass, the unit of force is considered the main one. There are a number of other systems that are close to the SI, but use different base units. For example, in the GHS system, generally accepted before the advent of the SI system, the basic unit of measurement is the gram, and the basic unit of length is the centimeter.
This lesson will not be new for beginners. We have all heard from school such things as centimeter, meter, kilometer. And when it came to mass, they usually said gram, kilogram, ton.
Centimeters, meters and kilometers; grams, kilograms and tons have one common name - units of measurement of physical quantities.
In this lesson we will look at the most popular units of measurement, but we will not delve too deeply into this topic, since units of measurement go into the field of physics. Today we are forced to study part of physics because we need it for further study of mathematics.
Lesson contentUnits of length
The following units of measurement are used to measure length:
- millimeters;
- centimeters;
- decimeters;
- meters;
- kilometers.
millimeter(mm). Millimeters can even be seen with your own eyes if you take the ruler that we used at school every day
Small lines running one after another are millimeters. More precisely, the distance between these lines is one millimeter (1 mm):
centimeter(cm). On the ruler, each centimeter is indicated by a number. For example, our ruler, which was in the first picture, had a length of 15 centimeters. The last centimeter on this ruler is marked with the number 15.
There are 10 millimeters in one centimeter. You can put an equal sign between one centimeter and ten millimeters, since they indicate the same length:
1 cm = 10 mm
You can see this for yourself if you count the number of millimeters in the previous figure. You will find that the number of millimeters (distances between lines) is 10.
The next unit of length is decimeter(dm). There are ten centimeters in one decimeter. An equal sign can be placed between one decimeter and ten centimeters, since they indicate the same length:
1 dm = 10 cm
You can verify this if you count the number of centimeters in the following figure:
You will find that the number of centimeters is 10.
The next unit of measurement is meter(m). There are ten decimeters in one meter. One can put an equal sign between one meter and ten decimeters, since they indicate the same length:
1 m = 10 dm
Unfortunately, the meter cannot be illustrated in the figure because it is quite large. If you want to see the meter live, take a tape measure. Everyone has it in their home. On a tape measure, one meter will be designated as 100 cm. This is because there are ten decimeters in one meter, and one hundred centimeters in ten decimeters:
1 m = 10 dm = 100 cm
100 is obtained by converting one meter to centimeters. This is a separate topic that we will look at a little later. For now, let's move on to the next unit of length, which is called the kilometer.
The kilometer is considered the largest unit of length. There are, of course, other higher units, such as megameter, gigameter, terameter, but we will not consider them, since a kilometer is enough for us to further study mathematics.
There are a thousand meters in one kilometer. You can put an equal sign between one kilometer and a thousand meters, since they indicate the same length:
1 km = 1000 m
Distances between cities and countries are measured in kilometers. For example, the distance from Moscow to St. Petersburg is about 714 kilometers.
International System of Units SI
The International System of Units SI is a certain set of generally accepted physical quantities.
The main purpose of the international system of SI units is to achieve agreements between countries.
We know that the languages and traditions of the countries of the world are different. There's nothing to be done about it. But the laws of mathematics and physics work the same everywhere. If in one country “twice two is four,” then in another country “twice two is four.”
The main problem was that for each physical quantity there are several units of measurement. For example, we have now learned that to measure length there are millimeters, centimeters, decimeters, meters and kilometers. If several scientists speaking different languages gather in one place to solve some problem, then such a large variety of units of length measurement can give rise to contradictions between these scientists.
One scientist will state that in their country length is measured in meters. The second may say that in their country the length is measured in kilometers. The third may offer his own unit of measurement.
Therefore, the international system of SI units was created. SI is an abbreviation for the French phrase Le Système International d’Unités, SI (which translated into Russian means the international system of units SI).
The SI lists the most popular physical quantities and each of them has its own generally accepted unit of measurement. For example, in all countries, when solving problems, it was agreed that length would be measured in meters. Therefore, when solving problems, if the length is given in another unit of measurement (for example, in kilometers), then it must be converted into meters. We'll talk about how to convert one unit of measurement to another a little later. For now, let's draw our international system of SI units.
Our drawing will be a table of physical quantities. We will include each studied physical quantity in our table and indicate the unit of measurement that is accepted in all countries. Now we have studied the units of length and learned that the SI system defines meters to measure length. So our table will look like this:
Mass units
Mass is a quantity indicating the amount of matter in a body. People call body weight weight. Usually when something is weighed they say “It weighs so many kilograms” , although we are not talking about weight, but about the mass of this body.
However, mass and weight are different concepts. Weight is the force with which the body acts on a horizontal support. Weight is measured in newtons. And mass is a quantity that shows the amount of matter in this body.
But there is nothing wrong with calling body weight weight. Even in medicine they say "person's weight" , although we are talking about the mass of a person. The main thing is to be aware that these are different concepts.
The following units of measurement are used to measure mass:
- milligrams;
- grams;
- kilograms;
- centners;
- tons.
The smallest unit of measurement is milligram(mg). You will most likely never use a milligram in practice. They are used by chemists and other scientists who work with small substances. It is enough for you to know that such a unit of measurement of mass exists.
The next unit of measurement is gram(G). It is customary to measure the amount of a particular product in grams when preparing a recipe.
There are a thousand milligrams in one gram. One can put an equal sign between one gram and a thousand milligrams, since they denote the same mass:
1 g = 1000 mg
The next unit of measurement is kilogram(kg). The kilogram is a generally accepted unit of measurement. It measures everything. The kilogram is included in the SI system. Let us also include one more physical quantity in our SI table. We will call it “mass”:
There are a thousand grams in one kilogram. You can put an equal sign between one kilogram and a thousand grams, since they denote the same mass:
1 kg = 1000 g
The next unit of measurement is hundredweight(ts). In centners it is convenient to measure the mass of a crop collected from a small area or the mass of some cargo.
There are one hundred kilograms in one centner. One can put an equal sign between one centner and one hundred kilograms, since they denote the same mass:
1 c = 100 kg
The next unit of measurement is ton(T). Large loads and masses of large bodies are usually measured in tons. For example, the mass of a spaceship or car.
There are one thousand kilograms in one ton. One can put an equal sign between one ton and a thousand kilograms, since they denote the same mass:
1 t = 1000 kg
Time units
There is no need to explain what time we think is. Everyone knows what time is and why it is needed. If we open the discussion to what time is and try to define it, we will begin to delve into philosophy, and we do not need this now. Let's start with the units of time.
The following units of measurement are used to measure time:
- seconds;
- minutes;
- watch;
- day.
The smallest unit of measurement is second(With). There are, of course, smaller units such as milliseconds, microseconds, nanoseconds, but we will not consider them, since at the moment this makes no sense.
Various parameters are measured in seconds. For example, how many seconds does it take for an athlete to run 100 meters? The second is included in the SI international system of units for measuring time and is designated as "s". Let us also include one more physical quantity in our SI table. We will call it “time”:
minute(m). There are 60 seconds in one minute. One minute and sixty seconds can be equated because they represent the same time:
1 m = 60 s
The next unit of measurement is hour(h). There are 60 minutes in one hour. An equal sign can be placed between one hour and sixty minutes, since they represent the same time:
1 hour = 60 m
For example, if we studied this lesson for one hour and we are asked how much time we spent studying it, we can answer in two ways: “we studied the lesson for one hour” or so “we studied the lesson for sixty minutes” . In both cases, we will answer correctly.
The next unit of time is day. There are 24 hours in a day. You can put an equal sign between one day and twenty-four hours, since they mean the same time:
1 day = 24 hours
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According to their purpose and requirements, the following types of standards are distinguished.
Primary standard – ensures the reproduction and storage of a unit of physical quantity with the highest accuracy in the country (compared to other standards of the same quantity). Primary standards are unique measuring systems created taking into account the latest achievements of science and technology and ensuring the uniformity of measurements in the country.
Special standard - ensures the reproduction of a unit of physical quantity under special conditions in which direct transfer of the unit size from the primary standard with the required accuracy is not feasible, and serves as the primary standard for these conditions.
The primary or special standard, officially approved as the source for the country, is called the state standard. State standards are approved by Gosstandart, and for each of them a state standard is approved. State standards are created, stored and applied by the country's central scientific metrological institutes.
Secondary standard – stores the dimensions of a unit of a physical quantity obtained by comparison with the primary standard of the corresponding physical quantity. Secondary standards refer to the subordinate means of storing units and transferring their sizes during verification work and ensure the safety and least wear of state primary standards.
According to their metrological purpose, secondary standards are divided into copy standards, comparison standards, witness standards and working standards.
Reference copy – designed to convey the size of a unit of physical quantity as a working standard for a large volume of verification work. It is a copy of the state primary standard for metrological purposes only, but is not always a physical copy.
Standard of comparison – used for comparing standards that, for one reason or another, cannot be directly compared with each other.
Standard witness – designed to check the safety and immutability of the state standard and replace it in case of damage or loss. Since most state standards are created based on the use of the most stable physical phenomena and are therefore indestructible, currently only the kilogram standard has a witness standard.
Working standard – used to convey the size of a unit of physical quantity using a working measuring instrument. This is the most common type of standards that are used for verification work by territorial and departmental metrological services. Working standards are divided into categories that determine the order of their subordination in accordance with the verification scheme.
Standards of basic SI units.
Standard unit of time. The unit of time - the second - has long been defined as 1/86400 of the average solar day. Later it was discovered that the rotation of the Earth around its axis occurs unevenly. Then the definition of the unit of time was based on the period of rotation of the Earth around the Sun - the tropical year, i.e. the time interval between two spring equinoxes, following one after the other. The size of a second was defined as 1/31556925.9747 of a tropical year. This made it possible to increase the accuracy of determining the unit of time by almost 1000 times. However, in 1967, the 13th General Conference on Weights and Measures adopted a new definition of the second as the time interval during which 9192631770 oscillations occur, corresponding to the resonant frequency of the energy transition between the levels of the hyperfine structure of the ground state of the cesium-133 atom in the absence of disturbance by external fields. This definition is implemented using cesium frequency references.
In 1972, the transition to the Universal Coordinated Time system was made. Since 1997, state primary control and the state verification scheme for time and frequency measuring instruments are determined by the rules of interstate standardization PMG18-96 “Interstate verification scheme for time and frequency measuring instruments.”
The state primary standard of a time unit, consisting of a set of measuring instruments, ensures the reproduction of time units with a standard deviation of the measurement result not exceeding 1 * 10 -14 for three months.
Standard unit of length. In 1889, the meter was adopted as equal to the distance between two lines marked on a metal rod of an X-shaped cross-section. Although the international and national meter standards were made of an alloy of platinum and iridium, which is distinguished by significant hardness and great resistance to oxidation, it was not completely certain that the length of the standard would not change over time. In addition, the error in comparing platinum-iridium line meters with each other is + 1.1 * 10 -7 m (+0.11 microns), and since the lines have a significant width, the accuracy of this comparison cannot be significantly increased.
After studying the spectral lines of a number of elements, it was found that the orange line of the krypton-86 isotope provides the greatest accuracy in reproducing a unit of length. In 1960, the 11th General Conference on Weights and Measures adopted the expression of the size of the meter in these wavelengths as its most accurate value.
The krypton meter made it possible to increase the accuracy of reproducing a unit of length by an order of magnitude. However, further research made it possible to obtain a more accurate meter standard based on the wavelength in vacuum of monochromatic radiation generated by a stabilized laser. The development of new reference complexes for reproducing the meter led to the definition of the meter as the distance that light travels in a vacuum in 1/299792458 of a second. This definition of the meter was enshrined in law in 1985.
The new standard complex for reproducing the meter, in addition to increasing the accuracy of measurement in necessary cases, also makes it possible to monitor the constancy of the platinum-iridium standard, which has now become a secondary standard used to convey the size of the unit as a working standard.
Standard unit of mass. When establishing the metric system of measures, the mass of one cubic decimeter of pure water at the temperature of its highest density (4 0 C) was taken as a unit of time.
During this period, precise determinations of the mass of a known volume of water were made by successively weighing in air and water an empty bronze cylinder, the dimensions of which were carefully determined.
Based on these weighings, the first prototype of the kilogram was a platinum cylindrical weight with a height of 39 mm equal to its diameter. Like the prototype of the meter, it was transferred to the National Archives of France for storage. In the 19th century, several careful measurements of the mass of one cubic decimeter of pure water at a temperature of 4 0 C were repeated. It was found that this mass was slightly (approximately 0.028 g) less than the prototype kilogram of the Archive. In order not to change the value of the original unit of mass during further, more accurate weighings, the International Commission on the Prototypes of the Metric System in 1872. it was decided to take the mass of the prototype kilogram of the Archive as a unit of mass.
In the production of platinum-iridium kilogram standards, the international prototype was taken to be the one whose mass differed least from the mass of the Archive kilogram prototype.
Due to the adoption of the conventional prototype of the unit of mass, the liter turned out to be not equal to the cubic decimeter. The value of this deviation (1l=1.000028 dm 3) corresponds to the difference between the mass of the international prototype of a kilogram and the mass of a cubic decimeter of water. In 1964, the 12th General Conference on Weights and Measures decided to equate the volume of 1 liter to 1 dm 3.
It should be noted that at the time the metric system of measures was established there was no clear distinction between the concepts of mass and weight, therefore the international prototype of the kilogram was considered the standard of the unit of weight. However, already with the approval of the international prototype of the kilogram at the 1st General Conference on Weights and Measures in 1889, the kilogram was approved as the prototype of mass.
A clear distinction between the kilogram as a unit of mass and the kilogram as a unit of force was given in the decisions of the 3rd General Conference on Weights and Measures (1901).
The state primary standard and verification scheme for means of changing mass are determined by GOST 8.021 - 84. The state standard consists of a set of measures and measuring instruments:
· national prototype of the kilogram - copy No. 12 of the international prototype of the kilogram, which is a weight made of a platinum-iridium alloy and is intended to convey the size of a unit of mass to the weight R1;
· national prototype of the kilogram - copy No. 26 of the international prototype of the kilogram, which is a weight made of a platinum-iridium alloy and intended to verify the invariance of the size of a unit of mass, reproduced by the national prototype of the kilogram - copy No. 12, and replacing the latter during its comparisons at the International Bureau of Measures and scales;
· weights R1 and a set of weights made of platinum-iridium alloy and designed to transfer the size of a unit of mass to standards - copies;
· standard scales.
The nominal mass value reproduced by the standard is 1 kg. The state primary standard ensures the reproduction of a unit of mass with a standard deviation of the measurement result when compared with the international prototype of the kilogram, not exceeding 2 * 10 -3 mg.
Standard scales, which are used to compare the mass standard, with a weighing range of 2*10 -3 ... 1 kg have a standard deviation of the observation result on the scales of 5 * 10 -4 ... 3 * 10 -2 mg.
Let's consider the basic electrical quantities that we study first at school, then in secondary and higher educational institutions. For convenience, we will summarize all the data in a small table. Definitions of individual quantities will be given after the table in case of any misunderstandings.
| Magnitude | SI unit | Name of electrical quantity |
|---|---|---|
| q | Kl - pendant | charge |
| R | Om - om | resistance |
| U | V – volt | voltage |
| I | A – ampere | Current strength (electric current) |
| C | F – farad | Capacity |
| L | Gn - Henry | Inductance |
| sigma | CM - Siemens | Electrical conductivity |
| e0 | 8.85418781762039*10 -12 F/m | Electrical constant |
| φ | V – volt | Electric field point potential |
| P | W – watt | Active power |
| Q | VAR – volt-ampere-reactive | Reactive power |
| S | Va – volt-ampere | Full power |
| f | Hz - hertz | Frequency |
There are decimal prefixes that are used in the name of the quantity and serve to simplify the description. The most common of them are: mega, miles, kilo, nano, pico. The table shows other prefixes, except those mentioned.
| Decimal multiplier | Pronunciation | Designation (Russian/international) |
|---|---|---|
| 10 -30 | cuecto | q |
| 10 -27 | ronto | r |
| 10 -24 | iocto | and/y |
| 10 -21 | zepto | s/z |
| 10 -18 | atto | a |
| 10 -15 | femto | f/f |
| 10 -12 | pico | p/p |
| 10 -9 | nano | n/n |
| 10 -6 | micro | μ/μ |
| 10 -3 | Milli | m/m |
| 10 -2 | centi | c |
| 10 -1 | deci | d/d |
| 10 1 | soundboard | yes/da |
| 10 2 | hecto | g/h |
| 10 3 | kilo | k/k |
| 10 6 | mega | M |
| 10 9 | giga | G/G |
| 10 12 | tera | T |
| 10 15 | peta | P/P |
| 10 18 | exa | E/E |
| 10 21 | zeta | Z/Z |
| 10 24 | yotta | Y/Y |
| 10 27 | Ronna | R |
| 10 30 | quecca | Q |
Current strength is 1A- this is a value equal to the ratio of a charge of 1 C passing through a surface (conductor) in 1 s of time to the time of passage of the charge through the surface. For current to flow, the circuit must be closed.
Current strength is measured in amperes. 1A=1Kl/1c
In practice there are
1uA = 0.000001A
Electrical voltage– potential difference between two points of the electric field. The magnitude of electrical potential is measured in volts, therefore voltage is measured in volts (V).
1 Volt is the voltage that is necessary to release 1 Watt of energy in a conductor when a current of 1 Ampere flows through it.
In practice there are
Electrical resistance– the characteristic of a conductor to prevent electric current from flowing through it. It is defined as the ratio of the voltage at the ends of the conductor to the current in it. Measured in ohms (ohms). Within certain limits the value is constant.
1 Ohm is the resistance of a conductor when a direct current of 1A flows through it and a voltage of 1V arises at the ends.
From the school physics course we all remember the formula for a homogeneous conductor of constant cross-section:
R=ρlS – the resistance of such a conductor depends on the cross-section S and length l
where ρ is the resistivity of the conductor material, tabular value.
Between the three quantities described above, Ohm's law exists for a DC circuit.
The current in the circuit is directly proportional to the voltage in the circuit and inversely proportional to the resistance of the circuit - .
Electrical capacity is the ability of a conductor to accumulate electrical charge.
Capacitance is measured in farads (1F).
1F is the capacitance of a capacitor between the plates of which a voltage of 1V occurs when charged at 1C.
In practice there are
1pF = 0.000000000001F
1nF = 0.000000001F
Inductance is a quantity that characterizes the ability of a circuit through which an electric current flows to create and accumulate a magnetic field.
Inductance is measured in henries.
1Gn = (V*s)/A
1H is a value equal to the self-inductive emf that occurs when the current in the circuit changes by 1A within 1 second.
In practice there are
1mH = 0.001H
Electrical conductivity– a value indicating the ability of a body to conduct electric current. Reciprocal of resistance.
Electrical conductivity is measured in siemens.
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Magnitude 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 indicate 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 quantity has countless values, for example the length can be equal to: 1 cm, 2 cm, 3 cm, etc.
The same quantity can be expressed in different units, for example kilogram, gram and ton are units of weight. The same quantity 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 find out the exact length of a room. This means 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 it fits exactly 7 times along the length of the room, then its length is 7 meters.
As a result of measuring the quantity, we obtain or named number, for example 12 meters, or several named numbers, for example 5 meters 7 centimeters, the totality of which is called compound named number.
Measures
In each state, the government has established certain units of measurement for various quantities. An accurately calculated unit of measurement, adopted as a standard, is called standard or exemplary unit. Model units of the meter, kilogram, centimeter, etc. were made, according to which units for everyday use were made. Units that have come into use and are approved by the state are called measures.
The measures are called homogeneous, if they serve to measure quantities of the same kind. So, gram and kilogram are homogeneous measures, since they are used to measure weight.
Units
Below are units of measurement of various quantities that are often found in mathematics problems:
Weight/mass measures
- 1 ton = 10 quintals
- 1 quintal = 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 = 10,000 sq. meters
- 1 sq. meter = 10000 sq. centimeters
- 1 sq. centimeter = 100 square meters millimeters
- 1 cu. meter = 1000 cubic meters decimeters
- 1 cu. decimeter = 1000 cubic meters centimeters
- 1 cu. centimeter = 1000 cubic meters millimeters
Let's consider another quantity 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
A month is taken to be 30 days unless it is necessary to specify the date and name of the month. January, March, May, July, August, October and December - 31 days. February in a simple year is 28 days, February in a leap year is 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 as 365 days, and the fourth year following them as 366 days. A year containing 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 Earth's revolution 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, i.e., by one day. Therefore, one day is added to every fourth year (February 29).
You will learn about other types of quantities as you further study various sciences.
Abbreviated names of measures
Abbreviated names of measures are usually written without a dot:
|
Weight/mass measures
|
Area measures (square measures)
|
|
Measures of time
|
Measure of vessel capacity
|
Measuring instruments
Special measuring instruments are used to measure various quantities. Some of them are very simple and designed for simple measurements. Such instruments include a measuring ruler, tape measure, measuring cylinder, etc. Other measuring instruments are more complex. Such devices include stopwatches, thermometers, electronic scales, etc.
Measuring instruments usually have a measuring scale (or scale for short). This means that there are line divisions on the device, and next to each line division the corresponding value of the quantity is written. The distance between the two strokes, next to which the value of the value is written, can be additionally divided into several smaller divisions; these divisions are most often not indicated by numbers.
It is not difficult to determine what value each smallest division corresponds to. 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 identical divisions. Therefore, each division (the distance between the nearest strokes) corresponds to 1 mm. This quantity is called at the cost of a scale division measuring device.
Before you begin measuring a value, you should determine the scale division value of the instrument you are using.
In order to determine the division price, you must:
- Find the two closest lines on the scale, next to which the values of the quantity are written.
- Subtract the smaller number from the larger value and divide the resulting number by the number of divisions between them.
As an example, let’s determine the price of the scale division of the thermometer shown in the figure on the left.
Let's take two lines, near which the numerical values of the measured value (temperature) are plotted.
For example, bars indicating 20 °C and 30 °C. 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, in order to arrive at school or work on time, you have to measure the time that will be spent on the road. Meteorologists measure temperature, barometric pressure, wind speed, etc. to predict the weather.
