Question

Arrange the following lengths in the order of increasing magnitudes: \[1\]metre, $1$ centimetre, 1 kilometre, $1$ millimetre.
A) $1$ metre $ < 1$ centimetre$ < 1$ kilometre $ < 1$ millimetre
B) $1$ millimetre$ < 1$ metre$ < 1$ centimetre$ < 1$ kilometre
C) $1$ millimetre$ < 1$ centimetre$ < 1$ metre$ < 1$ kilometre
D) $\text{None of these}$

Answer 1

Hint: In order to get an idea of the magnitude of any physical parameters, certain prefixes are used before their units to denote its order. The SI unit of length is metre.

Complete answer:
SI unit: The International System of Units (Système International d'unités) is a modern form of metric system which defines the units assigned to all the seven base quantities. All the other physical parameters can be defined with the help of two or more of these base quantities. The seven base quantities are – Length, Time, Mass, Thermodynamic Temperature, Amount of substance, Electric Current and Luminous Intensity.
The base quantity that we are dealing with in this question is Length. Its SI unit is ‘metre $\left( m \right)$’. It is defined as the distance travelled by light in vacuum in $\dfrac{1}{{299792458}}$ second.
Now, this SI unit can be used to measure length in a lot of scenarios, but can also be useless in a lot of scenarios. Like while calculating the diameter of an atom or while measuring the distance between two planets. These are the scenarios where ‘metre’ is not the ideal unit for denoting the magnitude of length. And that’s why prefixes are used. These prefixes denote a certain power of ten multiplied to the SI unit of any base quantity so that different prefixes can be used to denote quantities of different magnitudes. Some of the magnitudes with their exponential equivalents are given below:
Milli $ \to {10^{ - 3}}$
Centi$ \to {10^{ - 2}}$
Deci$ \to {10^{ - 1}}$
Deca$ \to {10^1}$
Hecto$ \to {10^2}$
Kilo$ \to {10^3}$
Based on the information given above, the correct order is,
$1$ millimetre$ < 1$ centimetre$ < 1$metre$ < 1$kilometre

Thus, the correct answer is option C.

Note: Before the SI unit, several other systems existed and were used like the CGS system, MKS system and the FPS system which recognised only three quantities as the base quantities: length, mass and time. It was not until the formation of the SI unit, that the other four physical quantities were also included in the group.