## A Physical Quantity

We can measure the dimension of objects by means of a physical quantity. An object can represent a physical quantity if it is measured by some means or standards. The Earth is also a physical quantity if you can measure its for example, mass, weight or radius. Consider an object such as a book and try to find how long or how wide the book is.

The measure of how long is length and that of how wide is breadth (width). These two things length and breadth are the physical quantities of the book, for example, if you note the radius of a football, the football is an object and its radius is a physical quantity. Mass of a ball is another physical quantity. So, you can measure the properties of an object using the physical quantities.

## The Units

How do you measure the length of a book? You need to make some standards of length to say the book has this much length. And those standards you use to give the physical quantities a measurable value are the units. Now you can say the book has this much length using your length standard. For example, you made a stick of a certain length and measured other lengths with that stick and found the length of your bed to be five times that stick. So here the length of the stick you made recently is your temporary length standard (you used it to measure other lengths).

When we make a standard to define a physical quantity, that becomes a unit. Notice that you can give your own standard to any physical quantity, for example if you made the period of a particular pendulum to be your time standard and calculated other time periods like day, month or year, that time period will be based on your own time standard. Anyone is free to make any standards of units, so it's very important to define universal standards (the same standards in the entire world) of units also called the SI (*system international*) units. Now we discuss some universal standards (SI units) of some fundamental physical quantities like time, length and mass.

### The Standard of Time

The standard of time is represented by the word **second** and denoted by the letter **s**. The universal standard of time is the time period equal to 9192631770 times the period of vibration of radiation from caesium atom. In other words the standard of time, the second is a certain period of time equal to 9192631770 times the period of vibration from caesium atom. We use this standard to measure other time intervals or periods. For example, a particular time period is 1s, 21s, 3s, 15s and so on.

### The Standard of Length

The universal standard of length is the distance that the light travels in 1/2299792458 second. It is called **meter** and denoted by the letter **m**. The standard of length is used to measure other lengths. For example the length of a particular rod is 1m, 5m, 2m and so on.

### The Standard of Mass

The universal standard of mass has the name **kilogram** and denoted by **kg**. The standard of mass is the mass of particular alloy of platinum and iridium kept at the International Bureau of Weights and Measures at Severs, near Paris, France. We calculate the mass of a physical quantity using this standard such as 1kg, 2kg, 32kg, etc.

## Unit Prefixes

Some prefixes can be used to the standards of physical quantities (units) to define new units in terms of those standards. The table below shows the prefixes that can be used before the name of the standard of unit and their examples.

Prefix | Prefix Symbol | Numerical Value | Examples of Meter |
---|---|---|---|

yotta | Y | ${{10}^{24}}$ | 1Ym = 1 yottameter = ${{10}^{24}}$m |

zetta | Z | ${{10}^{21}}$ | 1Zm = 1 zettameter = ${{10}^{21}}$m |

exa | E | ${{10}^{18}}$ | 1Em = 1 exameter = ${{10}^{18}}$m |

peta | P | ${{10}^{15}}$ | 1Pm = 1 petameter = ${{10}^{15}}$m |

tera | T | ${{10}^{12}}$ | 1Tm = 1 terameter = ${{10}^{12}}$m |

giga | G | ${{10}^{9}}$ | 1Gm = 1 gigameter = ${{10}^{9}}$m |

mega | M | ${{10}^{6}}$ | 1Mm = 1 megameter = ${{10}^{6}}$m |

kilo | k | ${{10}^{3}}$ | 1km = 1 kilometer = ${{10}^{3}}$m |

deci | d | ${{10}^{-1}}$ | 1dm = 1 decimeter = ${{10}^{-1}}$m |

centi | c | ${{10}^{-2}}$ | 1cm = 1 centimeter = ${{10}^{-2}}$m |

milli | m | ${{10}^{-3}}$ | 1mm = 1 millimeter = ${{10}^{-3}}$m |

micro | $\mu $ | ${{10}^{-6}}$ | 1$\mu $m = 1 micrometer = ${{10}^{-6}}$m |

nano | n | ${{10}^{-9}}$ | 1nm = 1 nanometer = ${{10}^{-9}}$m |

pico | p | ${{10}^{-12}}$ | 1pm = 1 picometer = ${{10}^{-12}}$m |

femto | f | ${{10}^{-15}}$ | 1fm = 1 femtometer = ${{10}^{-15}}$m |

atto | $a$ | ${{10}^{-18}}$ | 1$a$m = 1 attometer = ${{10}^{-18}}$m |

zepto | z | ${{10}^{-21}}$ | 1zm = 1 zeptometer = ${{10}^{-21}}$m |

yocto | y | ${{10}^{-24}}$ | 1ym = 1 yoctometer = ${{10}^{-24}}$m |

Some examples of time are

1 nanosecond (1ns) = ${{10}^{-9}}$s

1 microsecond (1$\mu $s) = ${{10}^{-6}}$s

1 millisecond (1ms) = ${{10}^{-3}}$s

Some examples of mass are

1 kilogram (kg) = 1000 gram (g)

1 gram (g) = 1000 milligram (mg)

Here the unit kilogram is the SI unit not the gram. There are also other units other than the SI units used in specific regions of the world. And we are not going to discuss them here. We will only assume the SI units. There are two types of SI units - one type is SI base units and another is SI derived units. The following table shows 7 SI base units and their corresponding physical quantities.

SI Unit | Symbol | Physical Quantity |
---|---|---|

meter | m | length |

second | s | time |

kilogram | kg | mass |

kelvin | K | temperature |

ampere | A | current |

candela | cd | luminous intensity |

mole | mol | amount of substance |

The 7 SI base units in the above table can be used to derive all other SI units called SI derived units. The two units radian for plane angle and steradian for solid angle are neither SI base units nor SI derived units. These two are expressed as SI supplementary units and don't hold the agreement to be the SI base units yet.