Question

The distance between city A and city B on a map given by as 6cm, if the scale represents \[\text{1cm}=\text{2}00\text{km}\] then, find the actual distance between city A and city B in meters.

Answer 1

Hint: To find the distance between cities we will multiply the scale to the total scale units between the cities. Also, we will use the conversion of distance from kilometer (km) to meters (m) as shown below,
\[\text{1km }=\text{ 1}000\text{m}\]

Complete step-by-step answer:
We have been given the distance between the city A and city B on a map as 6cm, if the scale represents \[\text{1cm}=\text{2}00\text{km}\] then we have to find the distance between city A and B in meters.

Since, it is given that \[\text{1cm }=\text{ 2}00\text{km}\]
So, we can use unitary method and get that \[6cm=6\times 200\Rightarrow 1200km\]
The distance between A and B is 1200km.
Now, we know that \[\text{1km }=\text{ 1}000\text{m}\]
Therefore, we can say that \[\Rightarrow 1200km=1200\times 1000m=1200000m\]
In scientific notation, we can write it as follows,
\[\Rightarrow 1200000m=1.2\times {{10}^{6}}m\]
Therefore, the distance between city A and B in meters is equal to \[1.2\times {{10}^{6}}m\]

Note: The general mistake that we make in the given question is that we just forget to convert the distance between the cities from kilometers to meters. Thus, we get the wrong answer. Since, we have been asked to find the distance between city A and city B in meters. Also, any mistakes while converting to scientific form must be avoided as it affects the final answer.