home Credit cards Multiples and submultiples. Introduction Distance in physics and biology

Multiples and submultiples. Introduction Distance in physics and biology

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1 gigameter [Hm] = 10000000 hectometer [Hm]

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 league naval league (British) maritime league (international) league (statutory) mile nautical mile (British) nautical mile (international) mile (statutory) mile (USA, geodetic) mile (Roman) 1000 yards furlong furlong (USA, geodetic) chain chain (USA, geodetic) rope (English rope) genus genus (USA, geodetic) pepper floor (English) . pole) fathom, fathom fathom (US, geodetic) cubit yard foot foot (US, geodetic) link link (US, geodetic) cubit (UK) hand span finger nail inch (US, geodetic) barley grain (eng. barleycorn) thousandth of a microinch angstrom atomic unit of length x-unit Fermi arpan soldering typographical point twip cubit (Swedish) fathom (Swedish) caliber centiinch ken arshin actus (Ancient Roman) vara de tarea vara conuquera vara castellana cubit (Greek) long reed reed long elbow 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 day light week Billion light years Distance from the Earth to the Moon cables (international) cable length (British) cable length (USA) nautical mile (USA) light minute rack unit horizontal pitch cicero pixel line inch (Russian) inch span foot fathom oblique fathom verst boundary verst

Convert feet and inches to meters and vice versa

foot inch

More about length and distance

General information

Length is the largest measurement of the body. In three-dimensional space, length is usually measured horizontally.

Distance is a quantity that determines how far two bodies are from each other.

Measuring distance and length

Units of distance and length

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

Distance in physics and biology

In biology and physics, lengths are often measured at much less than one millimeter. For this purpose, a special value has been adopted, the micrometer. One micrometer is equal to 1×10⁻⁶ meters. In biology, the size of microorganisms and cells is measured in micrometers, and in physics, the length of infrared electromagnetic radiation is measured. A micrometer is also called a micron and is sometimes, especially in English literature, 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).

Navigation distance

Shipping uses nautical miles. One nautical mile is equal to 1852 meters. It was originally measured as an arc of one minute along the meridian, that is, 1/(60x180) 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 knots. One sea knot equals a speed of one nautical mile per hour.

Distance in astronomy

In astronomy, large 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 equal to 10,000,000,000,000 or 10¹³ kilometers. This is the distance that light travels in a vacuum in one Julian year. This quantity 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 arcsecond is 1/3600 of a degree, or approximately 4.8481368 microrads in radians. Parsec can be calculated using parallax - the effect of visible changes in body position, depending on the observation point. When making measurements, lay a segment E1A2 (in the illustration) 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 laid 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 plot a segment through point S, perpendicular to E1E2, it will pass through the intersection point of segments E1A2 and E2A1, I. The distance from the Sun to point I is segment SI, it is equal to one parsec, when the angle between segments A1I and A2I is two arcseconds.

On the image:

A1, A2: apparent star position
E1, E2: Earth position
S: Sun position
I: point of intersection
IS = 1 parsec
∠P or ∠XIA2: parallax angle
∠P = 1 arcsecond

Other units

League- an obsolete unit of length previously used 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 travels in an hour. Sea League - three nautical miles, approximately 5.6 kilometers. Lieu is a unit approximately equal to a league. In English, both leagues and leagues are called the same, league. In literature, 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 ancient value equal to the distance from the tip of the middle finger to the elbow. This value was widespread in the 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, which adopts the metric system, yards are used to measure fabric and the length of swimming pools and sports fields such as golf courses and soccer fields.

Definition of meter

The definition of 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. The meter was later equated to the wavelength of the orange line of the electromagnetic spectrum of the krypton ⁸⁶Kr atom in a 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.

Computations

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 unitconversion.org functions.

International system units(Systeme International d'Unitees), system of units of physical quantities adopted by the 11th General Conference on Weights and Measures(1960). The abbreviated designation of the system is SI (in Russian transcription - SI). The International System of Units was developed to replace the complex set of systems of units and individual non-systemic units that developed on the basis metric system of measures, and simplifying the use of units. The advantages of the International System of Units are its universality (covers all branches of science and technology) and coherence, i.e. the consistency of derived units that are formed according to equations that do not contain proportionality coefficients. Thanks to this, when calculating, if you express the values of all quantities in units of the International System of Units, you do not need to enter coefficients into the formulas that depend on the choice of units.

The table below shows the names and designations (international and Russian) of the main, additional and some derivative units of the International System of Units. Russian designations are given in accordance with current GOSTs; The designations provided for by the draft new GOST "Units of Physical Quantities" are also given. The definition of basic and additional units and quantities, the relationship between them is given in articles about these units.

Basic and derived units of the International System of Units

Magnitude	Unit name	Designation
Magnitude	Unit name	international	Russian
Basic units
Length	meter	m	m
Weight	kilogram	kg	kg
Time	second	s	With
Electric current strength	ampere	A	A
Thermodynamic temperature	kelvin	TO	TO
The power of light	candela	CD	cd
Quantity of substance	kilomole	kmol	kmol
Additional units
Flat angle	radian	rad	glad
Solid angle	steradian	sr	Wed
Derived units
Square	square meter	m 2	m 2
Volume, capacity	cubic meter	m 3	m 3
Frequency	hertz	Hz	Hz
Speed	meter per second	m/s	m/s
Acceleration	meters per second squared	m/s 2	m/s 2
Angular velocity	radians per second	rad/s	rad/s
Angular acceleration	radian per second squared	rad/s 2	rad/s 2
Density	kilogram per cubic meter	kg/m 3	kg/m 3
Force	newton	N	N
Pressure, mechanical stress	Pascal	Pa	Pa (N/m2)
Kinematic viscosity	square meter per second	m2/s	m 2 /s
Dynamic viscosity	pascal second	Pa·s	Pass
Work, energy, amount of heat	joule	J	J
Power	watt	W	W
Amount of electricity	pendant	WITH	Cl
Electrical voltage, electromotive force	volt	V	IN
Electric field strength	volt per meter	V/m	V/m
Electrical resistance	ohm	w	Ohm
Electrical conductivity	Siemens	S	Cm
Electrical capacity	farad	F	F
Magnetic flux	weber	Wb	Wb
Inductance	Henry	H	Gn
Magnetic induction	tesla	T	Tl
Magnetic field strength	ampere per meter	A/m	Vehicle
Magnetomotive force	ampere	A	A
Entropy	joule per kelvin	J/K	J/C
Specific heat capacity	joule per kilogram kelvin	J/(kg K)	J/(kg K)
Thermal conductivity	watt per meter kelvin	W/(mK)	W/(m K)
Radiation intensity	watt per steradian	W/sr	Tue/Wed
Wave number	unit per meter	m -1	m -1
Light flow	lumen	lm	lm
Brightness	candela per square meter	cd/m2	cd/m2
Illumination	luxury	lx	OK

The first three basic units (meter, kilogram, second) allow the formation of coherent derivative units for all quantities that have a mechanical nature, the rest were added to form derived units of quantities that are not reducible to mechanical ones: ampere - for electrical and magnetic quantities, kelvin - for thermal, candela - for light and mole - for quantities in the field of physical. chemistry and molecular physics. Additionally, the units of radians and steradians are used to form derived units of quantities that depend on plane or solid angles. To form the names of decimal multiples and submultiples, special units are used. SI prefixes: deci(to form units equal to 10 -1 relative to the original), centi (10 -2), Milli (10 -3), micro (10 -6), nano (10 -9), pico(10 -12), femto (10 -15), atto (10 -18), soundboard (10 1), hecto (10 2), kilo (10 3), mega (10 6), giga (10 9), tera(10 12); cm. Multiple units, Submultiples.

1.1. Connect the names of natural phenomena and the corresponding types of physical phenomena with lines.

1.2. Check the box next to the properties that both the stone and the rubber band have.
✓ Brittle at low temperatures.

1.3. Fill in the blanks in the text so that you get the names of sciences that study various phenomena at the intersection of physics and astronomy, biology, and geology.
Studies the movement of blood through the vessels of the body bio physics.
The propagation of a blast wave in the thickness of the Earth is studied geo physics.
The reason for the glow of stars and changes in the Universe is studied astro physics.

1.4. Write to standard form the following numbers according to the above sample.

2.1. Circle the properties that the physical body may not have.

2.2. The figure shows bodies consisting of the same substance. Write down the name of this substance.

2.3. Choose two words from the suggested words that denote the substances from which the corresponding parts of a simple pencil are made, and write them in the empty boxes.

2.4. Using the arrows, “sort” the words into baskets according to their names, which reflect different physical concepts.

2.5. Write down the numbers according to the example given.

3.1. During a physics lesson, the teacher placed identical-looking magnetic arrows placed on the tips of needles on the students' desks. All the arrows turned around their axis and froze, but at the same time some of them turned out to be turned to the north with the blue end, and others with the red end. The students were surprised, but during the conversation some of them expressed their hypotheses as to why this could happen. Mark which hypothesis put forward by students can be refuted and which cannot by crossing out the unnecessary word in the right column of the table.

3.2. Choose the correct continuation of the phrase “In physics, a phenomenon is considered to actually occur if...”
✓ it was observed by several scientists

3.3. Complete the proposal.
Observations of natural phenomena differ from experiments in that experiments are experiments in which a person creates and maintains certain conditions. Observations of natural phenomena do not imply human intervention.

3.4. Choose the correct continuation of the phrase.
On July 21, 1969, an American spacecraft with astronauts on board landed on the Moon for the first time. This event is…
✓ experiment

3.5. Even in ancient times, people observed that:

4.1. Finish the sentence.
A physical quantity is a characteristic of a body or phenomenon that can be measured and compared.

4.2. Fill in the missing words and letters into the text.
In the International System of Units (SI):

4.3. a) Express multiple units of length in meters and vice versa.

b) Express the meter in submultiples and vice versa.

c) Express the second in submultiples and vice versa.

d) Express the length values in SI base units.

e) Express the values of time intervals in SI base units.

f) Express the following quantities in SI base units.

4.4. Measure the width l of the textbook page with a ruler. Express the result in centimeters, millimeters and meters.
l = 16,7 cm = 167 mm = 0,167 m

4.5. A wire was wound around the rod as shown in the figure. The winding width turned out to be l=9 mm. What is the diameter d of the wire? Express your answer in the indicated units.

4.6. Write down the values of length and area in the indicated units according to the example given.

4.7. Determine the area of triangle S1 and trapezoid S2 in the indicated units.

4.8. Write the volume values in SI base units using the example given.

4.9. First, hot water with a volume of 0.2 m3 was poured into the bath, then cold water with a volume of 2 liters was added. What is the volume of water in the bath?
0.2 m3 + 2 l = 0.2 m3 + 0.002 m3 = 0.202 m3

4.10. Complete the sentence. “The price of a thermometer scale division is _____.”

5.1. Use the picture and fill in the gaps in the text.

5.2. Write down the volume of water in the vessels, taking into account the measurement error.

5.3. Write down the length of the table measured with different rulers, taking into account the measurement error.

5.4. Record the readings of the clock shown in the figure.

5.5. The students measured the length of their tables using different instruments and recorded the results in a table.

6.1. Underline the names of devices that use an electric motor.
Iron, elevator, TV, coffee grinder, mobile phone , calculator.

6.2. Home experiment.
1. Measure the diameter d and circumference l of five cylindrical objects using a thread and a ruler (see figure). Write down the names of objects and measurement results in the table. Use items of different sizes. For example, the first column of the table already contains the values obtained for a vessel with a diameter d = 11 cm and a circumference l = 35 cm.

2. Using the table, plot the dependence of the circumference l of an object on its diameter d. To do this, you need to construct six points on the coordinate plane according to the table data and connect them with a straight line. For example, a point with coordinates (d, l) for the vessel has already been constructed on the plane. Similarly, on the same plane, construct points for other bodies.

3. Using the resulting graph, determine what the diameter d of the cylindrical part of a plastic bottle is if its circumference is l = 19 cm.
d = 60 cm

6.3. Home experiment.
1. Measure the dimensions of the matchbox using a ruler with millimeter divisions and write down these values, taking into account the measurement error.
Box length a = ( 50 ± 0,5 ) mm.
Box width b = ( 32 ± 0,5 ) mm.
Box height c = ( 12 ± 0,5 ) mm.

The previous entry means that the true values of the length, width and height of the box lie within:
a: from 49,5 before 50,5 mm;
b: from 31,5 before 32,5 mm;
from: from 11,5 before 12,5 mm.
2. Calculate within what limits the true value of the volume of the box lies.
from (49.5*31.5*11.5) mm3 to (50.5*32.5*12.5) mm3
The volume of the box ranges from 17931.4 mm3 before 20515.6 mm3.

1.1. Connect the names of natural phenomena and the corresponding types of physical phenomena with lines.

1.2. Check the box next to the properties that both the stone and the rubber band have.

1.3. Fill in the blanks in the text so that you get the names of sciences that study various phenomena at the intersection of physics and astronomy, biology, and geology.

1.4. Write the following numbers in standard form using the example above.

2.1. Circle the properties that the physical body may not have.

2.2. The figure shows bodies consisting of the same substance. Write down the name of this substance.

2.3. Choose two words from the suggested words that denote the substances from which the corresponding parts of a simple pencil are made, and write them in the empty boxes.

2.4. Using the arrows, “sort” the words into baskets according to their names, which reflect different physical concepts.

2.5. Write down the numbers according to the example given.

3.2. Choose the correct continuation of the phrase “In physics, a phenomenon is considered to actually occur if...”

3.3. Complete the proposal.

3.4. Choose the correct continuation of the phrase.

3.5. Even in ancient times, people observed that:

4.1. Finish the sentence.

4.2. Fill in the missing words and letters into the text.
In the International System of Units (SI):

4.3. a) Express multiple units of length in meters and vice versa.

b) Express the meter in submultiples and vice versa.

c) Express the second in submultiples and vice versa.

d) Express the length values in SI base units.

e) Express the values of time intervals in SI base units.

f) Express the following quantities in SI base units.

4.4. Measure the width l of the textbook page with a ruler. Express the result in centimeters, millimeters and meters.

4.5. A wire was wound around the rod as shown in the figure. The winding width turned out to be l=9 mm. What is the diameter d of the wire? Express your answer in the indicated units.

4.6. Write down the values of length and area in the indicated units according to the example given.

4.7. Determine the area of triangle S1 and trapezoid S2 in the indicated units.

4.8. Write the volume values in SI base units using the example given.

4.9. First, hot water with a volume of 0.2 m3 was poured into the bath, then cold water with a volume of 2 liters was added. What is the volume of water in the bath?

4.10. Complete the sentence. “The price of a thermometer scale division is _____.”

5.1. Use the picture and fill in the gaps in the text.

5.2. Write down the volume of water in the vessels, taking into account the measurement error.

5.3. Write down the length of the table measured with different rulers, taking into account the measurement error.

5.4. Record the readings of the clock shown in the figure.

5.5. The students measured the length of their tables using different instruments and recorded the results in a table.

6.1. Underline the names of devices that use an electric motor.

3. Using the resulting graph, determine what the diameter d of the cylindrical part of a plastic bottle is if its circumference is l = 19 cm.
d = 6 cm

6.3. Home experiment.
1. Measure the dimensions of the matchbox using a ruler with millimeter divisions and write down these values, taking into account the measurement error.

The previous entry means that the true values of the length, width and height of the box lie within:

2. Calculate within what limits the true value of the volume of the box lies.

Non-system units of measurement

The international system of units and the units themselves have evolved over centuries, and certain traditions and habits have emerged. Thus, on all sea vessels, the speed of movement is measured in knots (1 knot is equal to 1 nautical mile per hour), to measure the capacity of oil in the United States, a barrel is used (1 barrel = 158.988 × 10 -3 m3), a unit of pressure has long been arose - the atmosphere.

There are many units that are not included in the International System and other systems of units, but, nevertheless, they are widely used in science, technology, and everyday life. Such units are called non-systemic. Respectively systemic are the units included in one of the accepted systems.

In accordance with GOST 8.417, non-system units are divided into four types in relation to system ones:

1) allowed for use along with SI units, for example: unit of mass - ton; flat angle – degree, minute, second; volume – liter; time – minute, hour, day, etc.;

2) allowed for use in special areas, for example: astronomical unit, parsec, light year - units of length in astronomy; diopter – a unit of optical power in optics; electron-volt is a unit of energy in physics; kilowatt-hour – unit of energy for meters; hectare – a unit of area in agriculture and forestry, etc.;

3) temporarily accepted for use along with SI units, for example: nautical mile, knot - in maritime navigation; carat – a unit of mass in jewelry; bar – a unit of pressure in physics, etc. These units should gradually be phased out in accordance with international agreements;

4) withdrawn from use (i.e., for new developments, the use of these units is not recommended), for example: millimeter of mercury, kilogram-force per square centimeter - pressure units; angstrom, micron – units of length; ar – unit of area; quintal – unit of mass; horsepower is a unit of power; calorie – a unit of heat, etc.

There are multiple and submultiple units of quantities.

Multiple unit is a unit of physical quantity that is an integer number of times greater than a systemic or non-systemic unit. For example, the unit of length kilometer is equal to 10 3 m, i.e. is a multiple of a meter.

submultiple unit– a unit of physical quantity, the value of which is an integer number of times less than a systemic or non-systemic unit. For example, the unit of length millimeter is equal to 10 -3 m, i.e. is a lobe.

For the convenience of using SI units of physical quantities, prefixes have been adopted to form the names of decimal multiples and submultiples, Table. 1.3.

Table 1.3.

Factors and prefixes for the formation of decimal multiples and submultiples and their names