Question

{\text{1 km = __decimeter}}
(A) ${10^4}$
(B) ${10^5}$
(C) ${10^3}$
(D) ${10^6}$

Answer 1

The units of length are expressed in terms of quantities of different magnitudes. The quantities are expressed with different prefixes indicating different orders of magnitude.

Complete Step by Step Solution: An order of magnitude is an approximation of the logarithm of a value relative to some contextually understood reference value, usually ten, interpreted as the base of the logarithm and the representative of values of magnitude one.
Mathematically, $N = a \times {10^b}$ where $\dfrac{1}{{\sqrt {10} }} < a < \sqrt {10}$. Then, $b$ represents the order of magnitude of the number. The order of magnitude can be any integer.
The SI unit of length is meters and is represented by the symbol $m$. Now we know, ${\text{1 m = 100 cm}}$.
In between centimetre and metre, there is another unit called decimetre.
From the metric system, we can write that, $1dm = 10cm$.
Thus, ${\text{1m = 100 cm = 1000 dm}}$. The unit decimeter is represented by the symbol ${\text{dm}}$.
To measure larger lengths, we have the unit, kilometre, which again is represented by the symbol $km$.
To express metres in terms of kilometres, ${\text{1km = 1000m}}$.
As already stated earlier, ${\text{1m = 100 cm = 1000 dm}}$,
${\text{1km = 1000m}}$
Hence we get,
$\Rightarrow {\text{1km = 1}}{{\text{0}}^{\text{6}}}{\text{dm}}$
The value of 1kilometre is thus equivalent to the 1 million decimetre.

Hence, the correct answer is Option D.

Note: The metric system is a system of measurement that uses the meter, litre, and gram as base units of length (distance), capacity (volume), and weight (mass) respectively.
To measure smaller or larger quantities, we use units derived from the metric units.
The units to the right of the base unit are smaller than the base unit. As we move to the right, each unit is 10 times smaller or one-tenth of the unit to its left. So, a ‘deci’ means one-tenth of the base unit, ‘centi’ is one-tenth of ‘deci’ or one-hundredth of the base unit and ‘milli’ is one-tenth of ‘centi’ or one-thousandth of the base unit.
The units to the left of the base unit are bigger than the base unit. As we move to the left, each unit is 10 times greater than the unit to its right. So, a ‘deca’ means ten times of the base unit, ‘hecto’ isten times of ‘deca’ or hundred times of the base unit and ‘killo’ is ten times of ‘hecto’ or thousand times of the base unit.
Length is expressed as Millimeter (mm), Decimeter (dm), Centimeter (cm), Meter (m), and Kilometer (km) are used to measure how long or wide or tall an object is.