Converting units of physical quantities to si. Unit converter

• 1 General information
• 2 History
• 3 SI units
  • 3.1 Basic units
  • 3.2 Derived units
• 4 Non-SI units
• Prefixes

General information

The SI system was adopted by the XI General Conference on Weights and Measures, some subsequent conferences made a number of changes to the SI.

The SI system defines seven major and derivatives units of measure, as well as a set of . Standard abbreviations for units of measurement and rules for writing derived units have been established.

In Russia, there is GOST 8.417-2002, which prescribes the mandatory use of SI. It lists the units of measurement, gives their Russian and international names, and establishes the rules for their use. According to these rules, international documents and only international designations are allowed to be used on instrument scales. In internal documents and publications, either international or Russian designations can be used (but not both at the same time).

Basic units: kilogram, meter, second, ampere, kelvin, mole and candela. Within the SI, these units are considered to have independent dimensions, i.e., none of the base units can be derived from the others.

Derived units are obtained from the basic ones using algebraic operations such as multiplication and division. Some of the derived units in the SI System have their own names.

Prefixes can be used before unit names; they mean that the unit of measurement must be multiplied or divided by a certain integer, a power of 10. For example, the prefix "kilo" means multiplying by 1000 (kilometer = 1000 meters). SI prefixes are also called decimal prefixes.

Story

The SI system is based on the metric system of measures, which was created by French scientists and was first widely introduced after the Great French Revolution. Before the introduction of the metric system, units of measurement were chosen randomly and independently of each other. Therefore, the conversion from one unit of measure to another was difficult. Moreover, in different places different units of measurement were used, sometimes with the same names. The metric system was to become convenient and unified system measures and weights.

In 1799, two standards were approved - for the unit of length (meter) and for the unit of weight (kilogram).

In 1874, the CGS system was introduced, based on three units of measurement - centimeter, gram and second. Decimal prefixes from micro to mega were also introduced.

In 1889, the 1st General Conference on Weights and Measures adopted a system of measures similar to the GHS, but based on the meter, kilogram and second, since these units were recognized as more convenient for practical use.

Subsequently, base units were introduced to measure physical quantities in the field of electricity and optics.

In 1960, the XI General Conference on Weights and Measures adopted the standard, which for the first time was called the "International System of Units (SI)".

In 1971, the IV General Conference on Weights and Measures amended the SI, adding, in particular, the unit for measuring the amount of a substance (mol).

The SI is now accepted as the legal system of units by most countries in the world and is almost always used in science (even in countries that have not adopted the SI).

SI units

After the designations of units of the SI System and their derivatives, a period is not put, in contrast to the usual abbreviations.

Basic units

Derived units

Derived units can be expressed in terms of base units using the mathematical operations of multiplication and division. Some of the derived units, for convenience, have been given their own names, such units can also be used in mathematical expressions to form other derived units.

The mathematical expression for a derived unit of measure follows from the physical law by which this unit of measure is determined or the definition of the physical quantity for which it is introduced. For example, speed is the distance a body travels per unit time. Accordingly, the unit of speed is m/s (meter per second).

Often the same unit of measurement can be written in different ways, using a different set of basic and derived units (see, for example, the last column in the table ). However, in practice, established (or simply generally accepted) expressions are used, which the best way reflect the physical meaning of the measured quantity. For example, to write the value of the moment of force, N×m should be used, and m×N or J should not be used.

Non-SI units

Some non-SI units of measurement are "accepted for use in conjunction with the SI" by the decision of the General Conference on Weights and Measures.

In this lesson we will learn how to convert physical quantities from one unit of measure to another. This is a useful skill that helps a lot when learning other topics.

Converting length units

From past lessons, we know that the main units of length are:

• millimeters
• centimeters
• decimeters
• meters
• kilometers

Any value that characterizes length can be converted from one unit of measure to another. For example, 25 kilometers can be converted to meters and decimeters and centimeters and even millimeters.

In addition, when solving problems in physics, it is imperative to comply with the requirements of the international SI system. That is, if the length is given not in meters, but in another unit of measurement, then it must be converted to meters, since the meter is the unit of length in the SI system.

To convert length from one unit of measure to another, you need to know what this or that unit of measure consists of. That is, you need to know that, for example, one centimeter consists of ten millimeters or one kilometer consists of a thousand meters.

Let's show on simple example how to reason when converting length from one unit of measurement to another. Suppose that there are 2 meters and you need to convert them to centimeters.

Since we are converting meters to centimeters, we first need to find out how many centimeters are contained in one meter. One meter contains one hundred centimeters:

1 m = 100 cm

If there are 100 centimeters in 1 meter, how many centimeters are there in 2 such meters? The answer suggests itself - 200 cm. And these 200 centimeters are obtained by multiplying 2 by 100. So, to convert 2 meters into centimeters, you need to multiply 2 by 100

2 × 100 = 200 cm

Now let's try to convert the same 2 meters into kilometers. Since we are converting meters to kilometers, we first need to find out how many meters are contained in one kilometer. One kilometer contains a thousand meters:

1 km = 1000 m

If one kilometer contains 1000 meters, then a kilometer that contains only 2 meters will be much smaller. To get it, you need to divide 2 by 1000

2: 1000 = 0.002 km

At first, it can be difficult to remember which action to use to convert units - multiplication or division. Therefore, at first it is convenient to use the following scheme:

The essence of this scheme is that when moving from a higher unit of measurement to a lower one, multiplication is applied. Conversely, when moving from a lower unit of measure to a higher one, division is applied.

Arrows pointing up and down indicate that the transition is from a higher unit of measure to a lower one and a transition from a lower unit of measure to a higher one, respectively. At the end of the arrow it is indicated which operation to apply: multiplication or division.

For example, let's convert 3000 meters to kilometers using this scheme.

So we have to go from meters to kilometers. In other words, go from a lower unit of measure to a higher one (a kilometer is older than a meter). We look at the diagram and see that the arrow indicating the transition from lower units to higher ones is directed upwards and at the end of the arrow it is indicated that we must apply division:

Now you need to find out how many meters are contained in one kilometer. There are 1000 meters in one kilometer. And to find out how many kilometers are 3000 such meters, you need to divide 3000 by 1000

3000: 1000 = 3 km

So, when translating 3000 meters into kilometers, we get 3 kilometers.

Let's try to convert the same 3000 meters into decimeters. Here we must move from higher units to lower ones (a decimeter is less than a meter). We look at the diagram and see that the arrow indicating the transition from higher to lower units is directed downwards and at the end of the arrow it is indicated that we must apply multiplication:

Now you need to find out how many decimeters are in one meter. There are 10 decimeters in one meter.

1 m = 10 dm

And to find out how many such decimeters are in three thousand meters, you need to multiply 3000 by 10

3000 × 10 = 30000 dm

So when converting 3000 meters to decimeters, we get 30,000 decimeters.

Mass conversion

From past lessons, we know that the basic units of mass are:

• milligrams
• grams
• kilograms
• centners
• tons

Any value that characterizes mass can be converted from one unit of measurement to another. For example, 5 kilograms can be converted to tons and centners and grams and even milligrams.

In addition, when solving problems in physics, it is imperative to comply with the requirements of the international SI system. That is, if the mass is given not in kilograms, but in another unit of measurement, then it must be converted to kilograms, since the kilogram is the unit of mass in the SI system.

To convert mass from one unit of measurement to another, you need to know what this or that unit of measurement consists of. That is, you need to know that, for example, one kilogram consists of a thousand grams or one centner consists of a hundred kilograms.

Let's use a simple example to show how to reason when converting mass from one unit of measure to another. Suppose there are 3 kilograms and you need to convert them to grams.

Since we are converting kilograms to grams, we first need to find out how many grams are contained in one kilogram. One kilogram contains one thousand grams:

1 kg = 1000 g

If there are 1000 grams in 1 kilogram, how many grams are there in 3 such kilograms? The answer suggests itself - 3000 grams. And these 3000 grams are obtained by multiplying 3 by 1000. So, to convert 3 kilograms to grams, you need to multiply 3 by 1000

3 × 1000 = 3000 g

Now let's try to convert the same 3 kilograms into tons. Since we are converting kilograms to tons, we first need to find out how many kilograms are contained in one ton. One ton contains a thousand kilograms:

If one ton contains 1000 kilograms, then a ton that contains only 3 kilograms will be much smaller. To get it, you need to divide 3 by 1000

3: 1000 = 0.003 t

As in the case with the conversion of length units, at first it is convenient to use the following scheme:

This scheme will allow you to quickly figure out what action to perform to convert units - multiplication or division.

For example, let's convert 5000 kilograms to tons using this scheme.

So we have to move from kilograms to tons. In other words, move from a lower unit of measure to an older one (a ton is older than a kilogram). We look at the diagram and see that the arrow indicating the transition from lower units to higher ones is directed upwards and at the end of the arrow it is indicated that we must apply division:

Now you need to find out how many kilograms are contained in one ton. One ton contains 1000 kilograms. And to find out how many tons is 5000 kilograms, you need to divide 5000 by 1000

5000: 1000 = 5 t

So when converting 5000 kilograms into tons, we get 5 tons.

Let's try to convert 6 kilograms to grams. Here we move from the highest unit of measure to the lowest. Therefore, we will use multiplication.

To convert kilograms to grams, you first need to find out how many grams are in one kilogram. One kilogram contains one thousand grams:

1 kg = 1000 g

If there are 1000 grams in 1 kilogram, then there will be six times as many grams in six such kilograms. So 6 must be multiplied by 1000

6 × 1000 = 6000 g

So when we convert 6 kilograms to grams, we get 6000 grams.

Time units conversion

From past lessons, we know that the basic units of time are:

• seconds
• minutes
• day

Any value that characterizes time can be converted from one unit of measurement to another. For example, 15 minutes can be converted to seconds, hours, and days.

In addition, when solving problems in physics, it is imperative to comply with the requirements of the international SI system. That is, if the time is given not in seconds, but in another unit of measurement, then it must be converted to seconds, since the second is the unit of time in the SI system.

To convert time from one unit of measurement to another, you need to know what this or that unit of time measurement consists of. That is, you need to know that, for example, one hour consists of sixty minutes or one minute consists of sixty seconds, etc.

Let's use a simple example to show how to reason when converting time from one unit of measurement to another. Suppose you want to convert 2 minutes to seconds.

Since we are converting minutes to seconds, we first need to find out how many seconds are contained in one minute. There are sixty seconds in one minute:

1 min = 60 s

If there are 60 seconds in 1 minute, how many seconds are there in 2 such minutes? The answer suggests itself - 120 seconds. And these 120 seconds are obtained by multiplying 2 by 60. So, to convert 2 minutes into seconds, you need to multiply 2 by 60

2 × 60= 120 s

Now let's try to convert the same 2 minutes into hours. Since we are converting minutes to hours, we first need to find out how many minutes are contained in one hour. There are sixty minutes in one hour:

If one hour contains 60 minutes, then an hour that contains only 2 minutes will be much less. To get it you need 2 minutes divided by 60

Dividing 2 by 60 results in a periodic fraction of 0.0 (3). This fraction can be rounded to the hundredth place. Then we get the answer 0.03

When converting time units, a scheme is also applicable that makes it easier to figure out what to use - multiplication or division:

For example, let's convert 25 minutes to hours using this scheme.

So we have to move from minutes to hours. In other words, move from a lower unit of measurement to a higher one (hours are older than minutes). We look at the diagram and see that the arrow indicating the transition from lower units to higher ones is directed upwards and at the end of the arrow it is indicated that we must apply division:

Now we need to find out how many minutes are contained in one hour. One hour contains 60 minutes. And an hour that contains only 25 minutes will be much less. To find it, you need to divide 25 by 60

Dividing 25 by 60 results in a periodic fraction of 0.41 (6). This fraction can be rounded to the hundredth place. Then we get the answer 0.42

25:60 = 0.42 h

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This lesson will not be new for beginners. We all heard from school such things as a centimeter, a meter, a kilometer. And when it came to mass, they usually said grams, kilograms, tons.

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 go deep into this topic, since units of measurement go into the field of physics. We are forced to study part of the physics, as we need it for the further study of mathematics.

Length units

The following units of measurement are used to measure length:

• millimeters
• centimeters
• decimeters
• meters
• kilometers

millimeter(mm). You can even see millimeters with your own eyes if you take the ruler that we used at school every day.

Small lines that follow each other in a row 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 figure, 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 denote the same length

1cm=10mm

You can see for yourself if you count the number of millimeters in the previous figure. You will find that the number of millimeters (distance between lines) is 10.

The next unit of length is decimeter(dm). There are ten centimeters in one decimeter. Between one decimeter and ten centimeters, you can put an equal sign, since they denote 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 measure is meter(m). There are ten decimeters in one meter. You can put an equal sign between one meter and ten decimeters, because they denote the same length:

1 m = 10 dm

Unfortunately, the meter cannot be illustrated in the figure, because it is rather large. If you want to see the meter live, take a tape measure. Everyone has it in the house. 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, which we will consider a little later. In the meantime, let's move on to the next unit of length, which is called a kilometer.

The kilometer is considered the largest unit of measurement for length. Of course, there are other older units, such as a megameter, a gigameter, a 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 denote 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 reach 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 just learned that there are millimeters, centimeters, decimeters, meters and kilometers for measuring length. If several scholars speaking different languages, will gather in one place to solve a particular problem, then such a large variety of units of measurement of length can give rise to contradictions between these scientists.

One scientist will claim that in their country length is measured in meters. The second might say that in their country, length is measured in kilometers. The third one can offer his own unit of measurement.

Therefore, the international system of units SI was created. SI is an abbreviation for the French phrase Le Système International d'Unités, SI (which in 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 the 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 to meters. We will talk about how to convert one unit of measure to another a little later. In the meantime, let's draw our international system of units SI.

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 measurement of length and learned that meters are defined in the SI system for measuring length. So our table will look like this:

Mass units

Mass is a measure of the amount of matter in a body. In the people, body weight is called 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 a 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 the mass of the body weight. Even in medicine they say "human 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 measure are used to measure mass:

• milligrams
• grams
• kilograms
• centners
• tons

The smallest unit of measurement is milligram(mg). Milligram most likely you will never put into 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 mass measurement exists.

The next unit of measure is gram(G). In grams, it is customary to measure the amount of a product when compiling a recipe.

There are a thousand milligrams in one gram. You can put an equal sign between one gram and a thousand milligrams, because they denote the same mass:

1 g = 1000 mg

The next unit of measure is kilogram(kg). The kilogram is a common unit of measure. It measures everything. The kilogram is included in the SI system. Let's 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, because they denote the same mass:

1 kg = 1000 g

The next unit of measure is centner(c). In centners, it is convenient to measure the mass of the crop harvested with small area or a mass of some cargo.

There are one hundred kilograms in one centner. Between one centner and one hundred kilograms you can put an equal sign, because they denote the same mass:

1 q = 100 kg

The next unit of measure is ton(t). In tons, large loads and masses of large bodies are usually measured. For example, mass spaceship or car.

There are a thousand kilograms in one ton. You can put an equal sign between one ton and a thousand kilograms, because they denote the same mass:

1 t = 1000 kg

Time units

We don't need to explain what time 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, then we will begin to delve into philosophy, and this is not what we need now. Let's start with time units.

The following units of measurement are used to measure time:

• seconds
• minutes
• day

The smallest unit of measurement is second(with). Of course, there are also smaller units such as milliseconds, microseconds, nanoseconds, but we will not consider them, since this moment it makes no sense.

In seconds, various indicators are measured. For example, how many seconds does it take an athlete to run 100 meters. The second is included in the international SI system of units for measuring time and is denoted as "s". Let's also include one more physical quantity in our SI table. We will call it "time":

minute(m). There are 60 seconds in one minute. You can put an equal sign between one minute and sixty seconds, since they represent the same time:

1 m = 60 s

The next unit of measure is hour(h). There are 60 minutes in one hour. You can put an equal sign between one hour and sixty minutes, since they represent the same time:

1 h = 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. Between one day and twenty-four hours you can put an equal sign, since they denote the same time:

1 day = 24 hours

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1. Length: kilometer, meter, decimeter, centimeter, millimeter, micrometer, mile, nautical mile, league, cable, fathom, furlong, rod, yard, foot, inch, verst, chain, pole, fathom, arshin, foot (old Russian .), vershok, line, point.
2. Square: sq. kilometer, sq. meter, sq. decimetre, sq. centimeter, sq. millimeter, sq. micrometer sq. mile, acre, hectare, ar (weave), sq. genus, sq. yard, sq. ft. sq. inch.
3. Volume: cube kilometer, cu. meter, cubic decimeter, cubic centimeter, cube millimeter, cube micrometer, cu. mile, liter, quart (UK), quart (US liquid), cu. genus, cub. yard, cube ft, cu. inch, pint (UK), pint (US liquid), gallon (UK), gallon (US liquid), barrel of oil, barrel (US liquid), beer barrel, fluid ounce, barrel, bucket , mug, pound of water, vodka bottle, wine bottle, cup, scale, tablespoon, teaspoon.
4. Weight: metric ton, English ton (long ton), American ton (short ton), centner, kilogram, pound, ounce, gram, carat, Berkovets, pood, half pood, steelyard, ansyr, pound, large hryvnia (hryvnia), libra, small hryvnia (hryvnia), lot, spool, share, troy pound, troy ounce, troy gran.
5. Temperature: Fagenheit temperature, Celsius temperature, Réaumur temperature, absolute temperature.
6. Speed: kilometers per hour, kilometers per minute, kilometers per second, miles per hour, miles per minute, miles per second, knots ( nautical miles per hour), meters per hour, meters per minute, meters per second, feet per hour, feet per minute, feet per second, speed of light in vacuum, speed of sound in clean water, the speed of sound in air (at 20 °C).
7. Pressure: pascal, bar, technical atmosphere (at), physical atmosphere (atm), millimeter mercury column, meter of water column, pound-force per sq. inch, kilogram force per sq. meter.
8. Consumption: m3/s, m3/min, m3/h, l/s, l/min, l/h, US gal/day, US gal/h, US gal/min, US gal/s, imp. gallons/day, imp. gal/h, imp. gal/min, imp. gal/s, cu. ft/min, cu. ft/s, bbl/h, pounds of water/min, tons of water (meter)/day.
9. Strength, weight: newton, dyne, kilogram-force, kilopond, gram-force, pond, ton-force.
10. Power: watt, kilowatt, megawatt, kilogram-force-meter per second, erg per second, Horsepower(metric), horsepower (English).
11. Number of information: bit, byte (B), Kibibyte (KiB), Mebibyte (MiB), Gibibyte (GiB), Tebibyte (TiB).
12. Time: millennium, century, decade, five years, year, half year, quarter, month, decade, week, day, hour, minute, second, millisecond, microsecond, nanosecond.
13. Caloric content of products: kcal based on the weight of the product indicated in grams.