Question

Convert \[2435m\] to km and express the result as a mixed fraction.

Answer 1

Hint: For solving these problems, we need to have a clear understanding of the various units in which distance is expressed and also the relation between the various units. By employing the correct formula to conversion of metres to kilometres, we can easily arrive at the desired distance in kilometres.

Complete step-by-step solution:
In physics, distance is defined as the physical measurement of how far an object has moved. Distance is a scalar quantity. SI unit of distance is a meter according to the International System of Units. Interestingly, using this as the base unit and some equations, many other derived units or quantities are formed like volume, area, acceleration, and speed. Other units of length are derived from the meter. Thus, $1$ kilometre (km) equals \[1000\] meters, $1$ centimetre (cm) equals $\dfrac{1}{100}$ meter, and so on. Even the old British and American units, such as the inch and the mile, are now defined in terms of the metric system.
Thus, employing these conversion formulas, we can write that,
$\begin{align}
  & 1km=1000m \\
 & \Rightarrow 1m=\dfrac{1}{1000}km \\
 & \Rightarrow 2435m=\dfrac{2435}{1000}km=\dfrac{487}{200}km=2\dfrac{87}{200}km \\
\end{align}$
Therefore, after converting metres into kilometres and further converting the obtained fraction into a mixed fraction, we can say that $2435m=2\dfrac{87}{200}km$ .

Note: These types of problems are pretty easy to solve, but one needs to be careful otherwise small miscalculations can lead to a totally different answer. We need to carefully employ the formula for conversion of metres to kilometres, and further convert the obtained fraction into a mixed form to arrive at the correct answer and get the desired conversion.