Base Quantities and Derived Quantities Definition, Units Examples

Base Quantities and Derived Quantities Definition, Units Examples

  1. Physical quantities are quantities that can be measured.
  2. Usually, a specific scientific instrument is used to measure a particular physical quantity.
    Base Quantities and Derived Quantities Definition, Units Examples 1
  3. To describe a physical quantity we first define the unit in which the measurement is made. There are many systems of units but the most common system of units used by scientists is based on the metric system.
  4. The modernised version of the metric system is called International System of Units, officially abbreviated as SI.
  5. We can represent a physical quantity by the symbol of the quantity, the numerical value of the magnitude of the quantity and the unit of measurement of the quantity. For example, Figure shows a footballer scoring a goal. The ball was kicked a distance of 8 m.
    Base Quantities and Derived Quantities Definition, Units Examples 2
  6. There are two types of physical quantities, that is, base quantities and derived quantities.
  7. Base quantities are physical quantities that cannot be defined in terms of other quantities. Table shows five base quantities and their respective SI units.
    Base quantitySymbolSI unitSymbol of SI unit
    Lengthlmeterm
    Massmkilogramkg
    TimetsecondS
    TemperatureTkelvinK
    Electric currentIampereA

    Derived quantities are physical quantities derived from combinations of base quantities through multiplication.

  8. Table shows some derived quantities and their respective derived units.
  9. Base Quantities and Derived Quantities Definition, Units Examples 3

Example 1
It was already noon when Lela woke up. The temperature was 38°C and she was sweating all over. As it was already late, she was given only 10 minutes to pack her things. She wondered how she would pack a 1.5 kg tin of milk powder, 850 cm3 of lake water, 980 g of a rare rock, a 1.2 m long stem of a special plant and finally not to forget 6.5 m2 of tent material into her bag.

Base Quantities and Derived Quantities Definition, Units Examples 4From the above description, identify the physical quantities and then classify them into base quantities and derived quantities.
Solution:
The physical quantities are temperature (38°C), time (10 minutes), mass (1.5 kg and 980 g), length (1.2 m), volume (850 cm3) and area (6.5 m2).
Classification:
Base quantity: Mass, length, temperature, time
Derived quantity: Area, volume v

Prefixes

  1. Prefixes are used to simplify the description of physical quantities that are either very big or very small in SI units.
  2. Table lists some commonly used SI prefixes and their multiplication factors.
    PrefixSymbolValue
    picoP10-12
    nanon10-9
    microp10-6
    millim10-3
    centic10-2
    decid10-1
    kilok103
    megaM106
    gigaG109
    teraT1012

Base Quantities and Derived Quantities Definition, Units Examples 5

Example 2
It is difficult for Hawa to figure out the mass of a piece of paper which is 0.0042 kg and the mass of a cat which is 5800 g. To simplify the description of these physical quantities, prefixes are used.
Base Quantities and Derived Quantities Definition, Units Examples 6Please help Hawa to express
(a) 0.0042 kg in g,
(b) 5800 g in kg.
Solution:
Base Quantities and Derived Quantities Definition, Units Examples 7

Example 3
Convert
(a) 0.000 006 Mm to cm,
(b) 570 000 cm to km.
Base Quantities and Derived Quantities Definition, Units Examples 8
Solution:
Base Quantities and Derived Quantities Definition, Units Examples 9

Scientific Notation

  1. The distance of Pluto from the Earth is about 6 000 000 000 000 m and the radius of a hydrogen atom is about 0.000 000 000 05 m. These quantities are either too large or too small and a simpler way of expressing them is by using standard form of representation or scientific notation.
  2. In a standard form or scientific notation, a numerical magnitude can be written as:
    A × 10n, where 1 ≤ A < 10 and n is an integer
    Hence, the distance of Pluto from the Earth can be written as 6 × 1012 m and the radius of a hydrogen atom as 5 × 10-11 m.
    Base Quantities and Derived Quantities Definition, Units Examples 12

Example 4
For each of the following, express the magnitude using scientific notation.
(a) The length of a virus = 0.000 000 08 m
(b) The mass of a ship = 75 000 000 kg
Solution:
Base Quantities and Derived Quantities Definition, Units Examples 10

Conversion of Units Involving Derived Quantities

When converting the units of a derived quantity, each of its base units involved must be converted. The following Example illustrates the conversion of derived units.
Base Quantities and Derived Quantities Definition, Units Examples 13Example 5
Convert each of the following from one particular unit to another and represent the quantity in standard form.
(a) Convert the area of a button from 1.2 cm2 into m2.
(b) Convert the volume of a water tank from 2.5 m3 into cm3.
(c) Convert the density of mercury from 13.6 g cm-3 into kg m-3.
Solution:
Base Quantities and Derived Quantities Definition, Units Examples 11