Question

A satellite was orbiting the Earth at an altitude of $300km$ . What is the altitude in millimetres?

Answer 1

Hint
In the given question, we have been provided with the altitude of the satellite or the height of the satellite above the earth’s surface and we have been asked the value of altitude in millimetres. Hence we have to perform the unit conversion and find the value of the height in the required units from the given units. The height above the surface is expressed in kilometers and is a unit of length; we have been asked to express the altitude into a smaller unit of length.
 $1km=1000m$ , $1m=1000mm$

Complete step by step answer
The satellite is orbiting the earth $300km$ above the surface, that is, the altitude of the satellite $(h)=300km$
First, we will convert kilometres into metres. We know that $1km=1000m$
We also know the conversion factor from metres into millimetres. It is given as $1m=1000mm$
Hence we can say that $1km=1000\times 1000mm={10}^{6}mm$
This is the required conversion factor from kilometre to a millimetre
We can now say that the altitude of the satellite $(h)=300km=3\times {10}^{6}mm$

Note
In the given question, we had to perform the unit conversion on a base unit, which was height or length. In cases when the question asks for the unit conversion of derived physical quantities, we have to perform dimensional analysis to convert the derived unit into a product of base units and then proceed to find the conversion factor. If the question had asked us to convert the given quantity into a difference, we would have to use the conversion factor for those pairs of units. Hence you should be aware of the conversion factors of the basic units, as the question-solving procedure would be made very easy.