SI Units In Measurement in Science And Technology

SI UNITS

An international system of units, called SI units, was adopted at the 11th General Conference on Weights and Measures (CGPM) in 1960. SI is an abbreviation of the French name “Le Systeme Internationale de Unite’s”.

You know that measurements are concerned with quantities like length, mass, time, density, etc. 

Any quantity which can be measured is called a physical quantity. The SI system of units is based on seven base units corresponding to seven base physical quantities. These are the physical quantities, in terms of which other physical quantities can be measured. The names and symbols of the base physical quantities and their corresponding SI units are given in Table. The precise definitions and the standards for the base SI units are given under Appendix-I.

Note:- The base SI units are independent of each other


Note: The other measurements for temperature are in degree Celsius (°C) and
Fahrenheit (F).

Perhaps you may be confused by mass and amount of substance and also with luminous intensity as given in Table 1.1. The mass of a body is the amount of matter contained in the body, while a mole is the amount of any substance equal to its molecular mass expressed in grams. 

For example,
          1 mole of HCl = 36.46 g
          2 moles of HCl = 36.46 × 2 = 72.92 g

Luminous intensity is the amount of light emitted by a point source per second in a particular direction.

Derived Units

The base or fundamental SI units like length, mass, time, etc. are independent of each other. The SI units for all other physical quantities such as area, density, velocity can be derived in terms of the base SI units and are called derived units. To find the derived unit for a physical quantity, we have to find out the relationship between the physical quantity and the base physical quantities. Then substitute the units of the base physical quantities to find the desired derived unit. Let us take some examples to learn how to derive units for physical quantities in terms of base units.

Example 1. Derive the SI unit for the area of a surface.

To derive the unit, we need to find out the relationship between the area and the base physical quantities. As you know that the area of a surface is the product of its length and breadth. So, as the first step, we write the area as

Area = length × breadth

Since breadth is also a kind of length, we can write,

Area = length × length

Then to find the derived unit for the area, we substitute the units of the base physical quantities as

Unit of area = metre × metre = (metre)2 = m2

Thus, the SI unit of area is m2 and is pronounced as a squared meter. Similarly, you can check that volume would have the SI unit as m3 or cubic meter.

Example 2. Find the derived unit for force.

You know that force is defined as

Force = mass × acceleration = mass × (change in velocity/time)

Since,                     change in velocity = Length/time
So,                          Force = mass × (length/time) × (1/time) = mass × (length/time2)

The SI unit of force can be found by substituting the SI units of the base physical quantities on the right side of the expression.

Thus,      ⇒            SI unit of force = kg m/s2 = kg ms–2
Some commonly encountered physical quantities other than base physical quantities, their relationship with the base physical quantities and the SI units are given in Table


Several physical quantities like force, pressure, etc. are used very often but their SI units are quite complex. Due to their complex expression, it becomes quite inconvenient to use them again and again. The derived SI units for such physical quantities have been assigned special names.

SI Prefixes

When we make measurements of physical quantities, quite often the quantity being measured is too large as compared to the base unit of the physical quantity. Look at some of the following examples,

Mass of earth = 5,970,000,000,000,000,000,000,000 kg
Radius of Sun = 6,96,000,000 m
Approximate distance between Mumbai and Delhi = 1,400,000 m

Another possibility is that the physical quantity is too small as compared to the base unit of the physical quantity. Look at some of the examples,

Radius of a hydrogen atom = 0.000,000,000,05 m
Mass of an electron (me) = 0.000,000,000,000,000,000,000,911 kg

You can see from the examples given above that when the physical quantity being measured is either too large or too small as compared to the standard unit, then the value of the physical quantity is quite inconvenient to express.

The numbers given above can be simplified by using what is called scientific notation of numbers. In this notation system, we represent the numbers as the power of ten. In this notation system, we can rewrite the above examples as

Mass of Earth = 5.97 × 1024 kg
Radius of Sun = 6.96 × 108 m
The approximate distance between Mumbai and Delhi = 1.4 × 106 m
The radius of a hydrogen atom = 5 × 10-11 m
Mass of an electron (me) = 9.11 × 10-31 kg

In scientific notation, the numbers become relatively easier but are still not convenient because they carry exponents. To simplify the numbers further, the SI system of units has recommended the use of certain prefixes. These prefixes are used along with the SI units in such a way that the physical quantity being measured can be expressed as a convenient number. The SI prefixes have been defined to cover a wide range of 10-24 to 10+24 of a unit and are given in Table 1.4.


How do we use SI prefixes?

To use SI prefixes, we have to keep a basic rule in mind. The rule is that the prefix is chosen in such a way that the resulting value of the physical quantity has a value between 0.1 and 1000. Let us illustrate it with examples.

Radius of Sun = 6.96 × 108 m = 696 × 106 m = 696 Mm (696 mega metre)
Alternatively = 6.96 × 108 m = 0.696 × 109 m = 0.696 Gm (0.696 giga metre)

Note:

1. No space is required between the prefix and the symbol of the unit e.g., a nanogram is written as ng and not as n g.

2. The prefixes are used only with the units and not alone e.g., 10 μ does not convey anything, it has to be 10 μm, 10 μg, etc.

3. You can use only one prefix at a time e.g. 10–12 g is represented as 1 pg and not as 1 mg.

4. SI prefix is not used with the unit °C.

5. The power to which a prefixed unit is raised applies to the whole unit, including the prefix e.g. 1 km2 = (1000 m)2 = 106 m2 and not 1000 m2.

Having learned about the base SI units, the method of obtaining the derived SI unit for a given physical quantity, and also the need and usage of prefixing SI units, let us now learn about the grammatical rules for using SI units in general.

Rules for Representing SI Units

The SI units are the result of the attempt of scientists to evolve a common international system of units that can be used globally. It is therefore important that the words and the grammar are logical and defined unambiguously i.e. everyone uses the system of units in the same manner. To achieve this objective, several grammatical rules have been framed. The most commonly used rules are given below:

1. While writing the value of a physical quantity, the number and the unit are separated by a space. For example, 100 mg is correct but not 100mg.

2. No space is given between number and °C, degree, minute, and second of plane angle.

3. The symbols of the units are not changed while writing them in plural e.g. 10 mg is correct but not 10 mg.

4. The symbols of the units are not followed by a full stop except at the end of a sentence, e.g. 10 mg. of a compound is incorrect.

5. In writing the SI unit obtained as a combination of units space is given between the symbols. Thus m s represents meter second while ms stands for milli-second. That is if the units are written without leaving any space, the first letter may be taken as a prefix.

6. For numbers less than unity zero must be inserted to the left of the decimal point e.g. writing 0.928 g is correct but not .928 g.

7. Symbols of units derived from proper names are represented by using capital letters. When written in full, the unit should not be written in plural e.g. 30.5 joules or 30.5 J is correct but 30.5 Joules or 30.5 j is not correct.

8. When using powers with a unit name the modifier squared or cubed is used after the unit name e.g. second squared, gram cubed, etc. Area and volume are exceptions in such cases the qualifier for the power comes first e.g. square kilometers or cubic centimeter etc.

9. For representing unit symbols with a negative exponent, the use of the solidus (/) sign should be avoided. If used, no more than one solidus should be used e.g. the unit for gas constant (JK–1 mol–1) may be represented as J/K mol but not as J/K/mol.

The rules mentioned earlier for the use of SI prefixes are to be followed along with these rules.