[Maths Class Notes] on Unit of Measurement Pdf for Exam

From early times to the present day, the acceptance, description and practical use of the units of measurement have played an important role in human endeavour. There is a wide range of unit systems that have been prominent over the years. For various activities, the primitive communities needed rudimentary measures such as fashioning clothes, building dwellings of suitable size and form, or exchanging raw materials or food. 

The Definition of Unit

In maths, a unit can be defined as the place of one or the rightmost number. The basic units that are utilised for measurement are also defined as units. The non-mathematical definition says that the unit is the individual person or item which is considered complete; however, it is also a part of the community or the whole.  

The unit of measurement, for instance, is the definite magnitude of quantity which is used as the norm for measurement of the same form of quantity, adopted and specified by the law or convention. You can express some other quantity of that type as the multiple of the measuring unit. The measurement unit is the standard quantity of the physical property which is used as the factor for expressing the quantity of that specific property that exists.

The Different Systems of Measurement

The unit system tends to vary for different countries. Some of the different types of units that are prevalent today include the FPS system of units, the CGS system of units, the SI system of units, and the MKS system of units. The major systems for measurement that are commonly used today are the Imperial system, the Metric system, and Natural systems. We will have a brief look at these different systems.

• Imperial System: The imperial unit, also called the British imperial system is the standard or default system for weights and measures. This was officially used in Britain from 1824 until the metric system was launched in 1965. 

• Metric System: The metric system is the international system of units which is the latest and the international standard system. This system is denoted by  SI. Standardising is one of the important aspects of modern systems. Every unit has a widely known size.

• Natural System: The natural units are the physical units for measurement that are based only on the physical constants which are common. The elementary charge e is the natural unit for the electric charge, and the light speed c is the natural unit for velocity.

Numerical Problems

The numerical problems associated with the units of measurement are commonly featured in the exams to test the preparation of the students. This is why it is important for the students to prepare comprehensively for the exams by referring to the sample numerical problems with solutions related to units of measurement. You can to check out the sample numerical problem with a solution on the unit of measurement provided by .

From the early ages to the present, the description, acceptance, and practical usage of units of measurement have played a crucial role in human endeavour. A multitude of unit systems used to be very prominent. For many activities, primitive communities required rudimentary measures like building dwellings of a suitable size and form, fashioning clothes, or exchanging food or raw materials.

How to Define Unit?

The basic question the student gets on this topic is “What is Unit?”.

In Mathematics, the word unit can be defined as a rightmost number or the place of one. The basic units that are used for measurement can also mean a unit.

The non-mathematical definition states that a unit is an individual item or person that is considered individual and complete but is also part of a whole or community.

What is the Unit of Measurement?

A unit of measurement is a definite magnitude of a quantity that is used as a norm for measurement of the same form of quantity, specified and adopted by convention or law. It is possible to express some other quantity of that kind as a multiple of the measuring unit.

A unit of measurement is a standardized quantity of physical property, used as a factor to express the quantity of that property that exists. Among the first devices invented by humans were measuring units.

A length, for instance, is a physical quantity. A meter is a unit of length that represents a predetermined definite length. We simply mean 10 times the definite predetermined length called “meter” when we say 10 meters (or 10 m). Measuring is a method of measuring how large or small a physical quantity is relative to the same form of simple reference quantity.

Different Systems of Measurement

There are apparent limitations to the use of a single unit of measurement for a certain number. For example, the use of the same unit for the distance between two cities and the length of a pencil is impractical. Historically, they will therefore evolve independently. Using unit prefixes is one way to make it easier to read big numbers or small fractions.

As science advanced, a need emerged to link various quantities, such as length and weight, and volume, to the measurement systems. The attempt to link various conventional systems to each other revealed several contradictions and contributed to the creation of new units and systems.

The unit system varies from country to country and the CGS system of units, the FPS system of units, the MKS system of units, and the SI system of units are some of the different unit systems.

Different Systems of Measurement in Common Usage Include:

Imperial System

Imperial units, sometimes referred to as the British Imperial System is the standard system of weights and measures officially used in Great Britain from 1824 until the metric system was introduced in 1965. The Customary System of weights and measures of the United States is derived from the British Imperial System. Imperial units, in metric terms, are now legally defined.

Metric System

The International System of Units is the latest international standard metric scheme (abbreviated to SI). Standardizing is an important aspect of modern systems. Every unit has a size that is widely known.

Natural Systems

Natural units are physical units of measurement based only on physical constants that are common. The elementary charge e is a natural unit of electric charge, and the speed of light c is a natural unit of velocity.

International System of Units (SI)

Among the various systems of units used in the world, the International System of Units, or SI system of units, is the most commonly used and universally recognized system.

Seven standard base units are given by the SI method of measurement. But some physical quantities are best represented by derived units, such as power, area, and volume. These units are derived from the variations of two or more of the seven base units.

In the SI system, there are seven fundamental units:

• For distance estimation, Meter (m).

• For mass, Kilogram (kg).

• For a time, Second(s).

• For temperature range, Kelvin (K).

• For electric current, Ampere (A).

• For the volume of a substance, mole (mol).

• For luminous power, Candela (cd).

Application of Unit of Measurement to Real-World Consequences

In everyday life, people use measuring units so often that they rarely think about what they are doing. A motorist goes to the gas station and pumps 5 litres (a volume measure) of petrol into the motor. The motorist uses Rupees, which is another unit of measure, in the form of paper currency, a debit card, or a credit card, economic rather than scientific, to pay for petrol.

The failure of the NASA Mars Climate Orbiter, which was mistakenly destroyed on a trip to Mars in September 1999 instead of entering orbit because of miscommunications about the value of forces, is an example of the significance of the accepted units. Various computer programs used different units of measurement. Significant amounts of effort, time, and cash were lost.

A chemist or any scientist requires standardized measurements because, in order for an experiment to be useful, it must be possible to replicate the experiment. The results of the experiment are useless if the chemist doesn’t know exactly how much of a certain element he or she mixed with another to form a given compound.

Columbus wrongly believed that the mile referred to in the Arabic calculation of 56⅔ miles for the scale of a degree was the same as the actually much shorter Italian mile of 1,480 meters while preparing his journey across the Atlantic Ocean in the 1480s. Therefore, his calculation was about 25 percent too small for the size of the degree and circumference of the Planet.

Basic Numerical Problems:

Q. Derive the units for Force by using standard fundamental SI units.

Ans: First let us describe what is force?

Force is given by the product of mass times acceleration. 

So we can write F = m [times] a……………….(1)

Mass is a standard base unit having the units as Kilogram (Kg).

Acceleration is a derived unit that is defined as the rate of change velocity of an object with respect to time, which is given as 

[a = frac{v}{t}]…………………..(2)

Here time(t) is a base unit having the units as Seconds(s).

A velocity is also a derived unit which is defined as a rate of change position with respect to time, which can be written as

[v = frac{d}{t}]…………………(3)

Distance and time are base units having units as Metre(m) and Seconds(s) respectively. So we get the units of Velocity as m/s. Now substituting this in equation (2) we get the unit of acceleration, [a = frac{m}{s^{2}}]…………………..(4)

Now to find the units of Force substitute equation (4) in (1)

[F = frac{Kg times m}{s^{2}}]

Which can be further written as

[F = Kg times m times s^{-2} ]

So, this is the derived unit for Force.