Physics conversion of units of measurement of physical quantities. Unit conversion

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

Conversion of length units

From previous lessons we know that the basic units of length are:

• millimeters
• centimeters
• decimeters
• meters
• kilometers

Any quantity that characterizes length can be converted from one unit of measurement 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 into meters, since the meter is a unit of length in the SI system.

To convert length from one unit of measurement to another, you need to know what a particular unit of measurement 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 us use a simple example to show how to reason when converting length from one unit of measurement to another. Let's assume that there are 2 meters and we 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, then how many centimeters are there in two such meters? The answer suggests itself - 200 cm. And these 200 centimeters are obtained by multiplying 2 by 100. This means that 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 operation 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 unit, multiplication is applied. Conversely, when moving from a lower unit of measurement to a higher one, division is applied.

Arrows pointing down and up indicate that there is a transition from a higher unit of measurement to a lower one and a transition from a lower unit of measurement to a higher one, respectively. At the end of the arrow it is indicated which operation to use: 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, move from a lower unit of measurement 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 to higher units is directed upward and at the end of the arrow it is indicated that we must apply division:

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

3000: 1000 = 3 km

This means that when converting 3000 meters to 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 units (a decimeter is less than a meter). We look at the diagram and see that the arrow indicating the transition from high to low 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

This means that when converting 3000 meters into decimeters, we get 30,000 decimeters.

Conversion of mass units

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

• milligrams
• grams
• kilograms
• centners
• tons

Any quantity that characterizes mass can be converted from one unit of measurement to another. For example, 5 kilograms can be converted into 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 into kilograms, since the kilogram is a unit of measurement of mass in the SI system.

To convert mass from one unit of measurement to another, you need to know what a particular 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 one hundred kilograms.

Let us show with a simple example how to reason when converting mass from one unit of measurement to another. Let's assume that there are 3 kilograms and we 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, then how many grams will there be in three such kilograms? The answer suggests itself - 3000 grams. And these 3000 grams are obtained by multiplying 3 by 1000. This means that 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 one 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 of converting length units, at first it is convenient to use the following scheme:

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

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

So we have to move from kilograms to tons. In other words, move from a lower unit of measurement to a higher one (a ton is older than a kilogram). We look at the diagram and see that the arrow indicating the transition from lower to higher units is directed upward 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 are 5000 kilograms, you need to divide 5000 by 1000

5000: 1000 = 5 t

This means that 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 measurement to the lowest. Therefore, we will use multiplication.

To convert kilograms to grams, you 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, then six such kilograms will contain six times as many grams. So 6 needs to be multiplied by 1000

6 × 1000 = 6000 g

This means that when converting 6 kilograms to grams, we get 6000 grams.

Converting time units

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

• seconds
• minutes
• day

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

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

To convert time from one unit of measurement to another, you need to know what a particular unit of time 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 us show with a simple example how to reason when converting time from one unit of measurement to another. Let's say 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, then how many seconds are there in two such minutes? The answer suggests itself - 120 seconds. And these 120 seconds are obtained by multiplying 2 by 60. This means that 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. One hour contains sixty minutes:

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

When dividing 2 by 60, the resulting periodic fraction is 0.0 (3). This fraction can be rounded to the hundredths place. Then we get the answer 0.03

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

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

So we have to go 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 to higher units is directed upward and at the end of the arrow it is indicated that we must apply division:

Now you need to find out how many minutes are 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

When dividing 25 by 60, the resulting periodic fraction is 0.41 (6). This fraction can be rounded to the hundredths 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 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 are one common name — units 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. We are forced to study some physics because we need it to further study mathematics.

Units 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 marked with 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. One 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. You can put an equal sign between one meter and ten decimeters, because 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, 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 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. You can put an equal sign between one gram and a thousand milligrams, because they mean 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, because they mean 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. You can put an equal sign between one centner and one hundred kilograms, because they mean 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, mass spaceship or car.

There are one thousand kilograms in one ton. You can put an equal sign between one ton and a thousand kilograms, because they mean 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
• 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 this 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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• 1 General information
• 2 History
• 3 SI units
  • 3.1 Basic units
  • 3.2 Derived units
• 4 Non-SI units
• Consoles

General information

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

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

In Russia, GOST 8.417-2002 is in force, 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, only international designations are allowed to be used in international documents and on instrument scales. In internal documents and publications, you can use either international or Russian designations (but not both at the same time).

Basic units: kilogram, meter, second, ampere, kelvin, mole and candela. Within the SI framework, these units are considered to have independent dimensions, that is, none of the basic units can be obtained 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 are assigned proper names.

Consoles can be used before names of units of measurement; they mean that a 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, conversion from one unit of measurement to another was difficult. In addition, different units of measurement were used in different places, sometimes with the same names. The metric system was supposed to become a convenient and uniform system of 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 GHS 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 considered more convenient for practical use.

Subsequently, basic units were introduced for measuring physical quantities in the field of electricity and optics.

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

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

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

SI units

There is no dot after the designations of SI units and their derivatives, unlike usual abbreviations.

Basic units

Derived units

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

The mathematical expression for a derived unit of measurement follows from the physical law by which this unit of measurement is defined 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 measurement for speed is m/s (meter per second).

Often the same unit of measurement can be written in different ways, using a different set of base 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 a moment of force, you should use N×m, and you should not use m×N or J.

Units not included in the SI System

Some units of measurement not included in the SI System are, by decision of the General Conference on Weights and Measures, “allowed for use in conjunction with SI.”