In this lesson, we'll look at units of length, area, and a table of area units. Consider the various units of measurement for length and area, find out in which cases they are used. We systematize our knowledge using a table. Let's solve a number of examples for converting one unit of measure into another.

You are familiar with the various units of length. What units of length are convenient to use when measuring the thickness of a match or the length of a body ladybug? I think you said millimeters.

What unit of length is convenient to use when measuring the length of a pencil? Of course, in centimeters (see Fig. 1).

Rice. 1. Length measurement

What units of length are convenient to use when measuring the width or length of a window? It is convenient to measure in decimeters.

And the length of the corridor or the length of the fence? Let's use meters (see Fig. 2).

Rice. 2. Length measurement

To measure larger distances, for example, distances between cities, a larger unit of length than a meter is used - a kilometer (see Fig. 3).

Rice. 3. Length measurement

There are 1000 meters in 1 kilometer.

Express the distance in kilometers.

1 kilometer is a thousand meters, so the number of thousands will mean kilometers.

8000 m = 8 km

385007 m = 385 km 7 m

34125 m = 34 km 125 m

In the number of hundreds, tens and units indicate meters.

You can argue differently: 1 km is a thousand times more than 1 meter, which means that the number of kilometers should be 1000 times less than the number of meters. Therefore, 8000: 1000 = 8, the number 8 means the number of kilometers.

385007: 1000 = 385 (rest 7). The number 385 denotes kilometers, the remainder is the number of meters.

34125: 1000 = 34 (rest. 125), that is, 34 kilometers 125 meters.

Read the table of units of length (see Fig. 4). Try to remember it.

Rice. 4. Table of units of length

Different measurements are used to measure areas. A square centimeter is a square with a side of 1 cm (see Fig. 5), a square decimeter is a square with a side of 1 dm (see Fig. 6), square meter is a square with a side of 1 m (see Fig. 7).

Fig.5. square centimeter

Rice. 6. Square decimeter

Rice. 7. Square meter

For measuring large areas use a square kilometer - this is a square whose side is 1 km (see Fig. 8).

Rice. 8. Square kilometer

The words "square kilometer" are abbreviated with the number as follows - 1 km 2, 3 km 2, 12 km 2. In square kilometers, for example, the areas of cities are measured, the area of ​​\u200b\u200bMoscow S \u003d 1091 km 2.

Calculate how many square meters are in one square kilometer. To find the area of ​​a square, multiply the length by the width. We are given a square with a side of 1 km. We know that 1 km \u003d 1000 m, so to find the area of ​​​​such a square, we multiply 1000 m by 1000 m, we get 1,000,000 m 2 \u003d 1 km 2.

Express in square meters 2 km 2. We will argue as follows: since 1 km 2 is 1,000,000 m 2, that is, the number of square meters is a million times greater than the number of square kilometers, so we multiply 2 by 1,000,000, we get 2,000,000 m 2.

56 km 2: multiply 56 by 1,000,000, we get 56,000,000 m 2.

202 km 2 15 m 2: 202 ∙ 1,000,000 + 15 = 202,000,000 m 2 + 15 m 2 = 202,000,015 m 2.

To measure small areas, a square millimeter (mm 2) is used. This is a square whose side is 1 mm. The words "square millimeter" with a number are written as follows: 1 mm 2, 7 mm 2, 31 mm 2.

Calculate how many square millimeters are in one square centimeter. To find the area of ​​a square, multiply the length by the width. We are given a square with a side of 1 cm. We know that 1 cm = 10 mm. So, to find the area of ​​such a square, we multiply 10 mm by 10 mm, we get 100 mm 2.

Express in square millimeters 4 cm 2. We will argue as follows: since 1 cm 2 is 100 mm 2, that is, the number mm 2 is 100 times more number cm 2, so multiply 4 by 100, we get 400 mm 2.

16 cm 2: multiply 16 by 100 \u003d 1600 mm 2.

31 cm 2 7 mm 2: this is 31 ∙ 100 + 7 = 3100 + 7 = 3107 mm 2.

In life, such units of area as ar and hectare are often used. Ap is a square with a side of 10 m (see Fig. 9). With numbers ap, they write shorter: 1 a, 5 a, 12 a.

Rice. 9. 1 ar

1 a \u003d 100 m 2, therefore it is often called a hundred.

A hectare is a square with a side of 100 m (see Fig. 10). The word "hectare" with numbers is abbreviated as follows: 1 ha, 6 ha, 23 ha. 1 ha \u003d 10000 m 2.

Rice. 10. 1 hectare

Calculate how many ares are in 1 hectare.

1 ha \u003d 10000 m 2

1 a \u003d 100 m 2, then 10000: 100 \u003d 100 a

Now carefully consider the table of area units (see Fig. 11), try to remember it.

Rice. 11. Table of units of area

In the lesson, we got acquainted with a new unit of length - km and units of area - m 2, km 2, a, ha.

1. Bashmakov M.I. Nefedova M.G. Mathematics. 4th grade. M.: Astrel, 2009.
2. M. I. Moro, M. A. Bantova, G. V. Beltyukova and others. Mathematics. 4th grade. Part 1 of 2, 2011.
3. Demidova T. E. Kozlova S. A. Tonkikh A. P. Mathematics. 4th grade 2nd ed., corrected. - M.: Balass, 2013.

1. School.xvatit.com().
2. Mer.kakras.ru ().
3. dpva.info().

Homework

1. Find the area of ​​a square with a side of 15 cm.
2. Express: in square meters: 5 ha; 3 ha 18 a; 247 acres; 16 a;
3. in hectares: 420,000 m 2; 45 km 2 19 ha;
4. in ares: 43 ha; 4 ha 5 a; 30 700 m 2; 5 km2 13 ha;
5. in hectares and ares: 930 a; 45 700 m2.

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 realm of physics. Today we are forced to study part of physics, as we need it for further study of mathematics.

Lesson content

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. Between one meter and ten decimeters, you can put an equal sign, since 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 some 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. Each studied physical quantity we will include in our table and indicate the unit of measure 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 measure 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, since 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. Between one kilogram and a thousand grams, you can put an equal sign, since 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. An equal sign can be put between one centner and one hundred kilograms, since 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, the mass of a spaceship or a car.

There are a thousand kilograms in one ton. You can put an equal sign between one ton and a thousand kilograms, since 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;
• clock;
• day.

The smallest unit of measure is second(With). Of course, there are also smaller units such as milliseconds, microseconds, nanoseconds, but we will not consider them, since at the moment there is no point in this.

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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Value 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 designate 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 value has an infinite number of values, for example, the length can be equal to: 1 cm, 2 cm, 3 cm, etc.

The same value can be expressed in different units, for example, kilogram, gram, and ton are units of weight. The same quantity expressed in different units 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 know the exact length of a room. So 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 he fits exactly 7 times along the length of the room, then its length is 7 meters.

As a result of measuring the quantity, one obtains or named number, for example 12 meters, or several named numbers, for example 5 meters 7 centimeters, the totality of which is called composite named number.

Measures

In each state, the government has established certain units of measurement for various quantities. A precisely calculated unit of measurement, taken as a model, is called standard or exemplary unit. Model units of the meter, kilogram, centimeter, etc., were made, according to which units for everyday use are made. Units that have come into use and approved by the state are called measures.

The measures are called homogeneous if they serve to measure quantities of the same kind. So, grams and kilograms are homogeneous measures, since they serve to measure weight.

Units

The following are units of measurement for various quantities that are often found in math problems:

Measures of weight/mass

• 1 ton = 10 centners
• 1 centner = 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 = 10000 sq. meters
• 1 sq. meter = 10000 sq. centimeters
• 1 sq. centimeter = 100 sq. millimeters

• 1 cu. meter = 1000 cubic meters decimeters
• 1 cu. decimeter = 1000 cu. centimeters
• 1 cu. centimeter = 1000 cu. millimeters

Let's consider another value 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

The month is taken as 30 days, unless it is required to specify the day and name of the month. January, March, May, July, August, October and December - 31 days. February in a simple year - 28 days, February in leap year- 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 for 365 days, and the fourth following them - for 366 days. A year with 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 time of revolution of the Earth 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, that is, by one day. Therefore, one day (February 29) is added to every fourth year.

You will learn about other types of quantities as you further study various sciences.

Measure abbreviations

Abbreviated names of measures are usually written without a dot:

Kilometer - km Meter - m Decimeter - dm centimeter - cm Millimeter - mm	Measures of weight/mass ton - t centner - c kilogram - kg gram - g milligram - mg
Area measures (square measures) sq. kilometer - km 2 hectare - ha sq. meter - m 2 sq. centimeter - cm 2 sq. millimeter - mm 2	cube meter - m 3 cube decimeter - dm 3 cube centimeter - cm 3 cube millimeter - mm 3
Measures of time century - in year - y month - m or mo week - n or week day - from or d (day) hour - h minute - m second - s millisecond - ms	A measure of the capacity of vessels liter - l

Measuring instruments

To measure various quantities, special measuring instruments are used. Some of them are very simple and are designed for simple measurements. Such devices include a measuring ruler, tape measure, measuring cylinder, etc. Other measuring devices are more complex. Such devices include stopwatches, thermometers, electronic scales, etc.

Measuring instruments, as a rule, have a measuring scale (or short scale). This means that dash divisions are marked on the device, and the corresponding value of the quantity is written next to each dash division. The distance between two strokes, next to which the value of the value is written, can be further divided into several smaller divisions, these divisions are most often not indicated by numbers.

It is not difficult to determine which value of the value corresponds to each smallest division. 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 equal divisions. Therefore, each division (the distance between the nearest strokes) corresponds to 1 mm. This value is called scale division measuring instrument.

Before you start measuring a quantity, you should determine the value of the division of the scale of the instrument used.

In order to determine the division price, you must:

1. Find the two nearest strokes of the scale, next to which the magnitude values ​​are written.
2. Subtract the smaller value from the larger value and divide the resulting number by the number of divisions in between.

As an example, let's determine the scale division value of the thermometer shown in the figure on the left.

Let's take two strokes, near which the numerical values ​​of the measured quantity (temperature) are plotted.

For example, strokes with symbols 20 °С and 30 °С. 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.

Measure various quantities in Everyday life each and every one of us has to do. For example, to come to school or work on time, you have to measure the time that will be spent on the road. Meteorologists measure temperature to predict the weather. Atmosphere pressure, wind speed, etc.

Before you get acquainted with the units of area, you need to pay attention to how to calculate the area of ​​\u200b\u200ba figure. The first figure that is studied in school is a square. A square with a side of one unit is called a unit square. It can be 1 meter, centimeter or any other value. The area of ​​other figures is always compared to the unit square. The area of ​​a figure shows how many unit squares will fit on its surface.

Rice. 1. Unit square.

In order to calculate its area, you need to multiply the two sides.

$$S = 1cm * 1cm = 1cm^2$$

Rice. 2. Chessboard.

To calculate the area of ​​a chessboard, multiply the width by the length. That is:

$$S= 8 * 8 = 64 squares$$

And if we take 1 square of the chessboard as a unit square of 1 $cm^2$ , then the area of ​​the chessboard is $64 cm^2$.

Squares can be measured in different units, respectively, they have different designations.

Rice. 3. A square with a side that is measured in different units.

Correctly, the unit of area is called a square centimeter, or a square meter, depending on the units in which the sides are measured.

So, the units for measuring area:

• $1 cm^2$;
• $1 m^2$;
• $1 km^2$;
• $1 hectare (ha)$;
• $ 1 ar (a.) $, otherwise called weaving

We often use some units of measurement in everyday life to denote land plots. This is a hectare, weave and ares.

When solving problems, it is imperative to pay attention to units of measurement. Centimeters can only be added to centimeters, and meters can only be added to meters. Therefore, it is always necessary to ensure that in the given solution of the problem all values ​​are expressed in the same units of measurement.

In English-speaking countries (USA, Canada, Great Britain, Australia), acres, yards are used to measure land. $1 acre = 4940 yards = 4046.96 m^2$.

Task example:

No. 1. Convert $10 m^2$ to $cm^2$

Solution:

• $1 m. = 100 cm$;
• $1 m^2 = 100 x 100 = 10,000 cm^2$;
• $10 m^2 = 10 x 10,000 = 100,000 cm^2$

No. 2. How many ares in $500 m^2$?

Solution:

• $100 m^2 = 1 a$;
• $500 m^2 = 5 a$.

How are units of area related?

In order to see the relationship, you need to pay attention to the table.

Table “Area Units”

In addition, records of units of measurement with symbols ($ m ^ 2, cm ^ 2, mm ^ 2 $), you can use abbreviated records (sq. m., sq. cm, sq. mm.)

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1 decimeter [dm] = 10 centimeter [cm]

Initial value

Converted value

meter exameter petameter terameter gigameter megameter kilometer hectometer decameter decimeter centimeter millimeter micrometer micron nanometer picometer femtometer attometer megaparsec kiloparsec parsec light year astronomical unit (international) mile (statute) mile (US, geodetic) mile (Roman) 1000 yards furlong furlong (US, geodetic) chain chain (US, geodetic) rope (English rope) genus genus (US, geodetic) perch field (eng. pole) fathom fathom (US, geodetic) cubit yard foot foot (US, geodetic) link link (US, geodetic) cubit (Brit.) hand span finger nail inch inch (US, geodetic) barleycorn (eng. barleycorn) thousandth of a microinch angstrom atomic unit of length x-unit fermi arpan soldering typographic point twip cubit (Swedish) fathom (Swedish) caliber centiinch ken arshin actus (O.R.) vara de tarea vara conu quera vara castellana cubit (Greek) long reed reed long cubit palm "finger" Planck length classical electron radius Bohr radius equatorial radius of the Earth polar radius of the Earth distance from the Earth to the Sun radius of the Sun light nanosecond light microsecond light millisecond light second light hour light days light week Billion light-years Distance from the Earth to the Moon cable lengths (international) cable lengths (British) cable lengths (USA) nautical mile (USA) light minute rack unit horizontal pitch cicero pixel line inch (Russian) vershok span foot sazhen oblique sazhen verst boundary verst

Converter feet and inches to meters and vice versa

foot inch

m

Thermal resistance

More about length and distance

General information

Length is the largest measurement of the body. In three dimensions, length is usually measured horizontally.

Distance is a measure of how far two bodies are from each other.

Distance and length measurement

Distance and length units

In the SI system, length is measured in meters. Derived quantities such as kilometer (1000 meters) and centimeter (1/100 meter) are also widely used in the metric system. In countries that do not use the metric system, such as the US and the UK, units such as inches, feet, and miles are used.

Distance in physics and biology

In biology and physics, lengths are often measured much less than one millimeter. For this, a special value, a micrometer, has been adopted. One micrometer is equal to 1×10⁻⁶ meters. In biology, micrometers measure the size of microorganisms and cells, and in physics, the length of the infrared electromagnetic radiation. A micrometer is also called a micron and sometimes, especially in English literature, is denoted by the Greek letter µ. Other derivatives of the meter are also widely used: nanometers (1×10⁻⁹ meters), picometers (1×10⁻¹² meters), femtometers (1×10⁻¹⁵ meters), and attometers (1×10⁻¹⁸ meters).

Distance in navigation

Shipping uses nautical miles. One nautical mile is equal to 1852 meters. Initially, it was measured as an arc of one minute along the meridian, that is, 1/(60 × 180) of the meridian. This made latitude calculations easier, since 60 nautical miles equaled one degree of latitude. When distance is measured in nautical miles, speed is often measured in nautical knots. One knot is equal to one nautical mile per hour.

distance in astronomy

In astronomy, long distances are measured, so special quantities are adopted to facilitate calculations.

astronomical unit(au, au) is equal to 149,597,870,700 meters. The value of one astronomical unit is a constant, that is, a constant value. It is generally accepted that the Earth is located at a distance of one astronomical unit from the Sun.

Light year equals 10,000,000,000,000 or 10¹³ kilometers. This is the distance light travels in a vacuum in one Julian year. This value is used in popular science literature more often than in physics and astronomy.

Parsec approximately equal to 30,856,775,814,671,900 meters or approximately 3.09 × 10¹³ kilometers. One parsec is the distance from the Sun to another astronomical object, such as a planet, star, moon, or asteroid, with an angle of one arcsecond. One arc second is 1/3600 of a degree, or about 4.8481368 mrad in radians. Parsec can be calculated using parallax - the effect of a visible change in the position of the body, depending on the point of observation. During measurements, a segment E1A2 (in the illustration) is laid from the Earth (point E1) to a star or other astronomical object (point A2). Six months later, when the Sun is on the other side of the Earth, a new segment E2A1 is drawn from the new position of the Earth (point E2) to the new position in space of the same astronomical object (point A1). In this case, the Sun will be at the intersection of these two segments, at point S. The length of each of the segments E1S and E2S is equal to one astronomical unit. If we postpone the segment through the point S, perpendicular to E1E2, it will pass through the intersection point of the segments E1A2 and E2A1, I. The distance from the Sun to point I is the SI segment, it is equal to one parsec when the angle between the segments A1I and A2I is two arcseconds.

On the image:

• A1, A2: apparent star position
• E1, E2: Earth position
• S: position of the sun
• I: point of intersection
• IS = 1 parsec
• ∠P or ∠XIA2: parallax angle
• ∠P = 1 arc second

Other units

League- an obsolete unit of length used earlier in many countries. It is still used in some places, such as the Yucatan Peninsula and rural areas of Mexico. This is the distance a person walks in an hour. Marine League - three nautical miles, approximately 5.6 kilometers. Lie - a unit approximately equal to the league. V English language both leagues and leagues are called the same, league. In literature, the league is sometimes found in the title of books, such as "20,000 Leagues Under the Sea" - the famous novel by Jules Verne.

Elbow- an old value equal to the distance from the tip of the middle finger to the elbow. This value was widely used in ancient world, in the Middle Ages, and until modern times.

Yard used in the British imperial system and is equal to three feet or 0.9144 meters. In some countries, such as Canada, where the metric system is adopted, yards are used to measure the fabric and length of swimming pools and sports fields and grounds, such as golf and football courses.

Meter Definition

The definition of the meter has changed several times. The meter was originally defined as 1/10,000,000 of the distance from the North Pole to the equator. Later, the meter was equal to the length of the platinum-iridium standard. Later, the meter was equated to the wavelength of the orange line of the electromagnetic spectrum of the krypton atom ⁸⁶Kr in vacuum, multiplied by 1,650,763.73. Today, a meter is defined as the distance traveled by light in a vacuum in 1/299,792,458 of a second.

Computing

In geometry, the distance between two points, A and B, with coordinates A(x₁, y₁) and B(x₂, y₂) is calculated by the formula:

and within a few minutes you will receive an answer.

Calculations for converting units in the converter " Length and distance converter' are performed using the functions of unitconversion.org .