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The International System of Units

Introduction

We use measurement to assign a numerical value to an object’s physical characteristics, such as length, speed, temperature, weight, or capacity. To determine the measure for each attribute, measurement tools, formulas, and units of measurement are used.

We may learn and understand the size or quantity of the objects around us through measurement. With this knowledge, we may make educated decisions and solve problems by comparing objects, estimating how many of the objects we need to use, and learning more about a situation and our surroundings.

In this article, we will explore the International System of Units ( SI ) and the basic units examples of these units.

What is The International System of Units? 

Definition

The International System of Units sometimes referred to as the metric system, is the standard unit of measurement throughout the world. The abbreviation SI, which stands for the System of Units, is derived from the French term Système international d’unités. The meter-kilogram-second (MKS) system, an earlier unit of measurement, serves as the foundation for the SI standard.

The SI includes units for every measurement type, but its core consists of seven “base units.”

( 1 ) Meter: Unit of length
( 2 ) Kilogram: Unit of mass
( 3 ) Seconds: Unit of time
( 4 ) Ampere: Unit of electric current
( 5 ) Kelvin: Unit of thermodynamic temperature
( 6 ) Mole: Unit of the amount of substance
( 7 ) Candela: Unit of luminous intensity

International System of Units ( SI ) Base Units

The SI standard was built on the basis of seven base units. The standard also provided definitions for various derived units. In addition to being explicitly expressed, all SI units can also be expressed in terms of standard multiples or fractions. Prefix multipliers and powers of 10 define multiple and fractional SI units. 

The following defines the seven base units:

( 1 ) Meter ( m ): Unit of length

In 1 / 299,792,458 or 3.33564095 x 10-9 of a second, light can travel one meter through a vacuum. The initial definition of the meter said that it was one ten-millionth (0.0000001 or 10-7) of the circumference of the earth measured in a great circle traveling through Paris, France. -from the geographic north pole to the equator.

( 2 ) Kilogram ( kg ): Unit of mass

The Planck constant ( 6.62607015 10-34 J s ) is now used to determine the value of the kilogram. Prior to 2018, the kilogram was the mass of a specific international prototype made of platinum-iridium that was stored at the BIPM headquarters. Before that, one liter (10-3 cubic meters) of clean water was used to determine the mass of a kilogram.

( 3 ) Seconds ( s ): Unit of time

The change between 2 hyperfine measures of the Cesium-133 atom in an unaltered ground state produces radiation that lasts for 9.192631770 periods or one second. It takes light 299,792,458 (2.99792458 x 108) meters to travel through a vacuum in one second.

( 4 ) Ampere ( A ): Unit of electric current

The elementary charge serves as the basis for determining the ampere’s value today. Prior to 2018, the ampere was determined by the force between two current-carrying conductors, and the vacuum magnetic permeability was set at 4π × 10-7 H m-1.

( 5 ) Kelvin ( K ): Unit of thermodynamic temperature

The Boltzmann constant, which has a value of 1.380649 10-23 J/K-1, is now used to determine the value of the Kelvin. Before 2018, a Kelvin was believed to be equivalent to 1/273.16 (3.6609 x 10-3) of the triple point of pure water’s thermodynamic temperature (H2O).

( 6 ) Mole ( mol ): Unit of the amount of substance

The Avogadro constant, equal to 6.02214076 x 1023 mol-1, is used to calculate the mole value. Exactly 6.022169 x 1023 elementary entities make up one mole.

( 7 ) Candela ( cd ): Unit of luminous intensity

The candela value is now based on the 683 lm/W luminous effectiveness of monochromatic radiation with a frequency of 540 1014 Hz. Before 2018, the candela was a unit of measurement for electromagnetic radiation with a specific direction, a frequency of 540 terahertz, and an intensity of 1/683 (1.46 x 10-3) watt per steradian (5.40 x 1014 hertz).

Prefixes of SI Units

With the International System of Units (SI), precise written technical expression is made possible regardless of linguistic variations like spelling and pronunciation. Arabic symbols for numbers and a unit symbol, frequently with a prefix sign that modifies unit magnitude, are used to express the values of quantities.

Because they are based on the number 10, SI units are simple to use. Powers of ten are used to multiply or divide basic units to create larger or smaller units.

Prefixes for larger quantities or whole units

NameSymbolMultiplying FactorScientific NotationEnglish Word
yottaY10000000000000000000000001024Septillion
zettaZ1000000000000000000000 1021Sextillion
exaE10000000000000000001018Quintillion
petaP10000000000000001015Quadrillion
teraT10000000000001012Trillion
gigaG1000000000 109Billion
megaM1000000106Million
kilok1000103Thousand
hectoh100102Hundred
dekada10101Ten

Prefixes for smaller quantities or subunits

NameSymbolMultiplying FactorScientific NotationEnglish Word
decid0.110-1Tenth
centic0.0110-2Hundredth
millim0.00110-3Thousandth
microμ0.000 00110-6Millionth
nanon0.000 000 00110-9Billionth
picop0.000 000 000 00110-12Trillionth
femtof0.000 000 000 000 00110-15Quadrillionth
attoa0.000 000 000 000 000 00110-18Quintillionth
zeptoz0.000 000 000 000 000 000 00110-21Sextillionth
yoctoy0. 000 000 000 000 000 000 000 00110-24Septilliontth

SI Derived Units

A system of quantity equations is used to define additional quantities, known as derived quantities, in terms of the seven base quantities. These equations and the seven SI base units yield the SI-derived units for these derived quantities. In the table below, examples of such SI-derived units are provided:

UnitSymbolQuantity
square meterm2area
cubic meterm3volume
meter per secondm / sspeed, velocity
meter per second squaredm / s2acceleration
reciprocal matterm-1wave matter
kilogram per cubic meterkg / m3mass density
cubic meter per kilogram m3 / kgspecific volume
ampere per square meterA / m2current density
ampere per meterA / mmagnetic field strength
mole per cubic metermol / m3amount of substance concentration
candela per square metercd / m2luminance
kilogram per kilogram
( may be represented by the number 1 )
kg / kg = 1mass fraction

Common SI Units

Base Units

The table below shows the SI base units.

UnitSymbolQuantity
metermlength
Kilogramkgmass
secondstime
ampereAelectric current
kelvinKThermodynamic temperature
candelacdluminous intensity
molemolamount of substance

Area

The table below shows the common SI units for the area.

UnitSymbolHow many meters?
kilometerkm1000
centimetercm0.01
millimetermm0.001
micrometerμm0.000001
nanometernm0.000000001
UnitSymbolHow many square meters?
square kilometerkm2 or sq km1 000 000
hectareha10 000
area100
Square centimetercm2 or sq cm0.0001

Mass and Weight

The table below shows the common SI units for mass and weight.

UnitSymbolHow many grams?
metric tont1 000 000
gramg1
centigramcg0.01
milligrammg0.001
microgramμg0.000001

Volume

The table below shows the common SI units for volume.

UnitSymbolHow many cubic meters?
cubic meterm31
cubic centimetercm3, cu cm, cc0.000001

Capacity

The table below shows the common SI units for capacity.

UnitSymbolHow many liters?
kiloliterkl1 000
literl1
centilitercl0.01
milliliterml0.001
microliterμl0.000001

More Examples

Example 1

Provide the shorthand for each unit and explain it using the base unit.

( a ) decimeter ( b ) microsecond ( c ) nanogram ( d ) micrometer

Solution

( a ) decimeter 

The symbol for the decimeter is dm. Since deci is 1/10th , 1 dm = 0.1 m.

( b ) microsecond

The symbol for microsecond is μs. Since micro means 1/ 1 000 000th, 1 μs = 0.000 001 s.

( c ) nanogram

The symbol for nanogram is ng and is equal to 0.000 000 001 g.

( d ) micrometer

The symbol for micrometer is μm. 1 micrometer ( μm ) = 0.000001 m

Example 2

Answer each.

( a ) How many centimeters are in 1 meter? 

( b ) How many meters in 1 km?

Solution

( a ) How many centimeters are in 1 meter? 

There are 100 centimeters in one meter.

( b ) How many meters in 1 km?

There are 1000 meters in 1 kilometer.

Example 3

Complete the table of the SI base units below. 

UnitSymbolQuantity
meterm( 1 )
kilogram( 2 )mass
( 3 )stime
ampere( 4 )electric current
( 5 )KThermodynamic temperature
candelacd( 6 )
mole( 7 )amount of substance

Solution

Here is the complete answer.

UnitSymbolQuantity
metermlength
kilogramkgmass
secondstime
ampereAelectric current
kelvinKThermodynamic temperature
candelacdluminous intensity
molemolamount of substance

Answers: 

( 1 ) length
( 2 ) kg
( 3 ) second
( 4 ) A
( 5 ) kelvin
( 6 ) luminous intensity
( 7 ) mol

Summary

The International System of Units sometimes referred to as the metric system, is the standard unit of measurement throughout the world. The abbreviation SI, which stands for the System of Units, is derived from the French term Système international d’unités.

The SI includes units for every measurement type, but its core consists of seven “base units.”

( 1 ) Meter: Unit of length
( 2 ) Kilogram: Unit of mass
( 3 ) Seconds: Unit of time
( 4 ) Ampere: Unit of electric current
( 5 ) Kelvin: Unit of thermodynamic temperature
( 6 ) Mole: Unit of the amount of substance
( 7 ) Candela: Unit of luminous intensity

SI Base Units

The SI standard was built on the basis of seven base units. The standard also provided definitions for various derived units. In addition to being explicitly expressed, all SI units can also be expressed in terms of standard multiples or fractions. Prefix multipliers and powers of 10 define multiple and fractional SI units. 

SI Derived Units

A system of quantity equations is used to define additional quantities, known as derived quantities, in terms of the seven base quantities. These equations and the seven SI base units yield the SI-derived units for these derived quantities.

UnitSymbolQuantity
square meterm2area
cubic meterm3volume
meter per secondm / sspeed, velocity
meter per second squaredm / s2acceleration
reciprocal matterm-1wave matter
kilogram per cubic meterkg / m3mass density
cubic meter per kilogramm3 / kgspecific volume
ampere per square meterA / m2current density
ampere per meterA / mmagnetic field strength
mole per cubic metermol / m3amount of substance concentration
candela per square metercd / m2luminance
kilogram per kilogram ( may be represented by the number 1 )kg / kg = 1mass fraction

Prefixes of SI Units

NameSymbolMultiplying FactorScientific NotationEnglish Word
yottaY10000000000000000000000001024Septillion
zettaZ1000000000000000000000 1021Sextillion
exaE1 000 000 000 000 000 0001018Quintillion
petaP1 000 000 000 000 0001015Quadrillion
teraT1 000 000 000 0001012Trillion
gigaG1 000 000 000 109Billion
megaM1 000 000106Million
kilok1 000103Thousand
hectoh100102Hundred
dekada10101Ten
NameSymbolMultiplying FactorScientific NotationEnglish Word
decid0.110-1Tenth
centic0.0110-2Hundredth
millim0.00110-3Thousandth
microμ0.00000110-6Millionth
nanon0.00000000110-9Billionth
picop0.00000000000110-12Trillionth
femtof0.00000000000000110-15Quadrillionth
attoa0.00000000000000000110-18Quintillionth
zeptoz0.00000000000000000000110-21Sextillionth
yoctoy0.00000000000000000000000110-24Septilliontth

Frequently Asked Questions on SI Units ( FAQs )

What is SI Unit?

To avoid unit misunderstanding in technical and scientific study, the SI unit is an international standard of measures that are utilized globally. The benefit of having a standard unit system is that it makes it simpler for people to understand measurements expressed in that system on a global scale.

The table below shows the seven basic SI Units.

UnitSymbolQuantity
metermlength
kilogramkgmass
secondstime
ampereAelectric current
kelvinKThermodynamic temperature
candelacdluminous intensity
molemolamount of substance

What are the common prefixes for the basic unit of length?

Prefixes are added to the names of the units to denote powers of 10. The table below shows the common prefixes for the basic unit length.

PrefixMultiply Basic UnitMeter ( m ): basic unit of length
nano ( n )0.000000001nanometer ( nm ) = 0.000000001 m
micro ( μ )0.000001micrometer ( μm ) = 0.000001 m
milli ( m )0.001millimeter ( mm ) = 0.001 m
centi ( c )0.01centimeter ( cm ) = 0.01 m
deci ( d )0.1decimeter ( dm ) = 0.01 m
kilo ( k )1000kilometer ( km ) = 1000 m

What are the seven base units of the International System?

The seven SI base units are as follows:

( 1 ) Meter: Unit of length
( 2 ) Kilogram: Unit of mass
( 3 ) Seconds: Unit of time
( 4 ) Ampere: Unit of electric current
( 5 ) Kelvin: Unit of thermodynamic temperature
( 6 ) Mole: Unit of the amount of substance
( 7 ) Candela: Unit of luminous intensity

What is meant by SI-derived units?

A system of quantity equations is used to define additional quantities, known as derived quantities, in terms of the seven base quantities. These equations and the seven SI base units yield the SI-derived units for these derived quantities.

What is the difference between base units and derived units?

SI Base Units

The SI standard was built on the basis of seven base units. The standard also provided definitions for various derived units. In addition to being explicitly expressed, all SI units can also be expressed in terms of standard multiples or fractions. Prefix multipliers and powers of 10 define multiple and fractional SI units. 

SI Derived Units

A system of quantity equations is used to define additional quantities, known as derived quantities, in terms of the seven base quantities. These equations and the seven SI base units yield the SI-derived units for these derived quantities.

What are the common SI units for the area?

The table below shows the common SI unit for the area.

UnitSymbolHow many square meters?
square kilometerkm2 or sq km1 000 000
hectareha10 000
area100
Square centimetercm2 or sq cm0.0001

What are the prefixes used in SI units?

Using the International System of Units (SI) allows technical writing to be accurate regardless of linguistic variances like spelling and pronunciation. The values of quantities are expressed using Arabic symbols for integers and a unit symbol, frequently with a prefix sign that alters unit magnitude.

Prefixes for larger quantities or whole units

NameSymbolMultiplying FactorScientific NotationEnglish Word
yottaY10000000000000000000000001024Septillion
zettaZ1000000000000000000000 1021Sextillion
exaE1 000 000 000 000 000 0001018Quintillion
petaP1 000 000 000 000 0001015Quadrillion
teraT1 000 000 000 0001012Trillion
gigaG1 000 000 000 109Billion
megaM1 000 000106Million
kilok1 000103Thousand
hectoh100102Hundred
dekada10101Ten

Prefixes for smaller quantities or subunits

NameSymbolMultiplying FactorScientific NotationEnglish Word
decid0.110-1Tenth
centic0.0110-2Hundredth
millim0.00110-3Thousandth
microμ0.000 00110-6Millionth
nanon0.000 000 00110-9Billionth
picop0.000 000 000 00110-12Trillionth
femtof0.000 000 000 000 00110-15Quadrillionth
attoa0.000 000 000 000 000 00110-18Quintillionth
zeptoz0.000 000 000 000 000 000 00110-21Sextillionth
yoctoy0.00000000000000000000000110-24Septilliontth

Why are SI units important?

We use measurement to assign a numerical value to an object’s physical characteristics, such as length, speed, temperature, weight, or capacity. To determine the measurement for each attribute, measurement tools, formulas, and units of measurement are used.

The International System of Units sometimes referred to as the metric system, is the standard unit of measurement throughout the world. The abbreviation SI, which stands for the System of Units, is derived from the French term Système international d’unités. The meter-kilogram-second (MKS) system, an earlier unit of measurement, serves as the foundation for the SI standard.

Since the International Standard of Units offers a consistent and coherent set of units for all physical quantities, deriving from a small number of basic units, the SI system is significant in science and technology. The benefit of having a standard unit system is that it makes it simpler for people to understand measurements expressed in that system on a global scale.

The fact that SI only uses one unit for each quantity is its most significant benefit (type of measurement). This implies that there is never a need to convert between units (within the system) and that there are no conversion factors that students need to remember. For instance, the meter is the distinct SI unit of length (m). This is particularly crucial in disciplines like thermodynamics, where you frequently require very complex compound units like watts per Kelvin per square meter.

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