Measurement
Measurement is the comparison of an unknown quantity with known standard quantity.
We measure length of a road, we measure the height of objects with having already known length.
Importance of Measurement
 In buying and selling goods
 For making medicines
 For making food
 In performing scientific experiments in laboratories etc.
Physical Quantities
Those quantities which can be measured directly or indirectly are called physical quantities. It is of two type's fundamental and derived quantity.
 Fundamental Quantity
Those quantities which do not depend upon other physical quantities are known as fundamental quantities. There are seven fundamental quantities, they are:
 Length
 Mass
 Time
 Temperature
 Current
 Luminous Intensity
 Amount of substance
 Derived Quantities
Those quantities which depend upon other physical quantities or simply on fundamental quantities are known as derived quantities. Eg: Velocity, area, pressure etc.
Units
Units are the standard reference quantity with reference to other physical quantities of the same kind and measured with. For eg: Length of a pen is 15cm means that the measured length of a pen is 15 times the standard reference quantity which is 1cm. Units are of two types fundamental and derived units.
 Fundamental Units
Those units which are independent of any other units of physical is called fundamental unit or the units of fundamental quantities are called fundamental unit. For eg:
Physical Quantity

Name of Units

Symbols

Length

Metre

m

Mass

Kilogram

Kg

Time

Second

s

Temperature

Kelvin

K

Electric Current

Ampere

A

Luminous Intensity

Candela

Cd

Amount of Substance

Mole

mol

 Derived Unit
Those units which are dependent upon fundamental units are called derived units or the unit which is expressed in terms of two or more fundamental unit is called derived unit. Derived units are division and multiplication of seven fundamental units. Eg:
Derived Quantity

Name of Unit

Symbol

Area

Square Metre

m^{2}

Volume

Cubic Metre

m^{3}

Force

Newton

N (kgm/s^{2})

Energy

Joule

J (Nm)

System of Measurement
There are different systems of measurements used in the world. FPS, CGS, MKS and SI are some system of measurement.
 F.P.S System
The system of units in which length is measured in foot, mass in pound and time in second is called F.P.S system.
 C.G.S System
The system of units in which length is measured in centimeter, mass in gram and time in second is called C.G.S system.
 M.K.S System
In this system, length is measured in metre, mass in kilogram and time in second. It is also called as metric system.
 SI System
The full form of SI system is "System International de Units". This system is infact, the improved and modified form of M.K.S system of units. This system of units is accepted all over the world for all scientific measurements.
The system of units that is accepted by the international convention of scientist held in France in 1960 is called SI units.
Advantages of SI Units
 SI units are well defined and accepted standard units all over the world.
 It is a metric system. It means multiples and submultiples of SI units can be expressed as power of 10. It makes the calculation of very big and very small numerical values easier.
Some Measurement
 Measurement of Area
The space covered by surface is called area. It's SI unit is square metre (m^{2}). The area or regular plane surface is calculated by using some formulae whereas area of irregular plane is determined by using graph paper.
Formulae for Some Regular Plane
 Area of Rectangular Surface = length \(\times\) breadth
i.e. A = l \(\times\) b
 Area of Square Surface (A) = (length)^{2}
i.e. A = l^{2}
Submultiples and Multiples of m^{2}
100mm^{2} = 1cm^{2}

100cm^{2} = 1dm^{2}

100dm^{2} = 1m^{2}

100m^{2} = 1dam^{2}

100dam^{2} = 1hm^{2}

100hm^{2} = 1km^{2}

 Measurement of Volume
Volume is defined as the space occupied by a body SI unit of volume is cubic metre (m^{3}).
Submultiples and Multiples of m^{2}
100mm^{3} = 1cm^{3}

100cm^{3} = 1dm^{3}

100dm^{3} = 1m^{3}

100m^{3} = 1dam^{3}

100dam^{3} = 1hm^{3}

1000hm^{3} = 1km^{3}

1dm^{3} = 1 litre (1000CC) = 1000ml

Measurement of the Volume of Liquid
 We use different liquid substances like water, milks, kerosene, diesel, spirit etc. in our daily and we measured volume of these liquid by using measuring cans. The unit, litre is used to measure the volume of liquids. These cans are measuring cylinder, measuring glass, conical flask, pipette and burette etc.
 Measurement of the Volume of Solid
A matchbox, a book, a brick etc. are regular solid objects. These objects are rectangular in shape. The volume of such rectangular objects is determined by the formula:
Volume = length \(\times\) breadth \(\times\) height
e. V = l \(\times\) b \(\times\) h
To measure the length, breadth and height of regular objects, a scale is used.
There are some other objects, which are irregular in shape. The volume of these irregular objects is determined by using measuring cylinder for eg: stone.
 Measurement of the Volume of Gas:
Solid and liquids have a fixed volume and they cannot be compressed but the gas or air does not have a fixed volume because it can be compressed. So, the volume of air depends upon the pressure which is exerted on it.
Reasoning
 SI units are used for the scientific works because it is the most advanced system of measurement and it is accepted in all over the world.
 It is difficult to measure the volume of gas because gas does not have a fixed volume as it can be compressed.
Questions
 Define measurement. Why measurement is important for us?
 Write any two differences between fundamental and derived quantities.
 Define C.G.S, F.P.S and M.K.S system.
 What is SI system? Write its importance.
 How do you find the volume of a rectangular brick?
 Define area and volume.
 Write formula of area and volume with its units.
 What is physical quantity?
 Define fundamental and derived unit with examples.
 Which devices are used to measure the volume of liquid?
Numerical
 The length of a matchbox is 5cm, breadth 3cm and thickness (height) 2cm. Find its volume.
 The length of a matchbox is 10cm, breadth is 20cm and volume is 6000cm^{3}. Find its height.
 The breadth of a geometry box is 5cm and height is 15cm and its volume is 375cm^{3}. Find its length.
 The length of a cube is 8cm, height is 8cm and its volume is 512cm^{3}. Find its breadth.
 The length of a box is 15cm and its breadth is 25cm and its height is 30cm. Find its volume.