Question

Fill in the blanks in the following conversions:
i.\[1{\text{ }}km{\text{ }} = {\text{ }}\_\_\_\_\_\_\_mm{\text{ }} = {\text{ }}\_\_\_\_\_\_\_\_{\text{ }}pm\]
ii.\[1{\text{ }}mg{\text{ }} = {\text{ }}\_\_\_\_\_\_\_kg{\text{ }} = {\text{ }}\_\_\_\_\_\_\_\_\_ng\]
iii.\[1{\text{ }}mL{\text{ }} = {\text{ }}\_\_\_\_\_\_\_L{\text{ }} = {\text{ }}\_\_\_\_\_\_\_\_\_\_d{m^3}\]

Answer 1

Hint: \[km\] is equal to \[1000{\text{ }}m\] and \[1{\text{ }}m\] is equal to \[{10^{12}}{\text{ }}pm\] (pm) Picometer. Similarly, \[1{\text{ }}g\] is equal to \[1000{\text{ }}kg\] and \[1{\text{ }}g\] is equal to \[{10^9}\,ng\]. Also the litre and cubic decimeter are equivalent.

Complete step by step answer:
Let’s start directly with answering the question,
In (i) we are asked to convert \[1{\text{ }}km\] to \[mm\] and \[pm\], \[km\] is kilometre, \[mm\] is millimetre and \[pm\] is Picometer.
\[1{\text{ }}km\](kilo-metre) is equal to \[1000{\text{ }}m\](metre) and \[1{\text{ }}m\](metre) is equal to \[1000{\text{ }}mm\](millimetre). So, \[1{\text{ }}km\] (kilometre) will be equal to \[1000\] times \[1000{\text{ }}mm\](millimetre) which will be \[{10^6}{\text{ }}mm\](millimetre). Also \[1{\text{ }}m\](metre) is equal to \[{10^{12}}pm\](Picometer), which means \[1000{\text{ }}m\](metre) will be equal to \[{10^{15}}pm\](Picometer).
$\therefore $ Hence the answer to (i) is $1{\text{ }}km = $${10^{6\;}}$$mm = $${10^{15}}$$pm$

In (ii) we are asked to convert \[1{\text{ }}mg\](milligram) to \[kg\](kilogram) and to \[ng\](Nanogram), \[mg\] is milligram, $g$ is gram, \[kg\] is kilogram and \[ng\] is Nanogram.
\[1{\text{ }}mg\] is equal to \[{10^{ - 3}}{\text{ }}g\] and \[1{\text{ }}g\] is equal to \[{10^{ - 3}}{\text{ }}kg\], so \[1{\text{ }}mg\] will be equal to \[{10^{ - 6}}{\text{ }}kg\]. Also, \[1{\text{ }}g\] is equal to \[{10^9}{\text{ }}ng\], so \[1{\text{ }}mg\] will be equal to \[{10^{9 - 3}}{\text{ }}ng\] which will be \[{10^6}{\text{ }}ng\].
$\therefore $ Hence the answer to (ii) is \[1{\text{ }}mg = \]\[{10^{ - 6}}\]\[kg = \]\[{10^6}\]\[ng\].

In (iii) we are asked to convert \[1{\text{ }}mL\](millilitre) to \[L\](litre) and \[d{m^3}\](decimetre), \[mL\] is millilitre, \[L\] is litre and \[d{m^3}\] is cubic decimetre.
\[1{\text{ }}mL\] is equal to \[{10^{ - 3}}{\text{ }}L\]. Also \[d{m^3}\] is equal to \[L\], hence \[1{\text{ }}L = 1{\text{ }}d{m^3}\] and \[1{\text{ }}mL{\text{ }} = {\text{ }}{10^{ - 3}}{\text{ }}d{m^3}\].
$\therefore $ Hence the answer to (iii) is \[1{\text{ }}mL = \]\[{10^{ - 3}}\]\[L = \] \[{10^{ - 3}}\]\[d{m^3}\].


Note:
The importance of conversion of units lies in the usage of them. If a unit is given in the cgs system and we need to convert it into SI system for further use at that time we need to use the conversion of units. Also different units represent different quantities and help in making the value more understandable.