Question

The scale of a particle map is 1 : 1,00,000. on the map, the school is shown to be 2.5 cm away from Jatinder's house. How far is his house from the school? Express this answer in km.

Answer 1

Hint: Here we will first find the distance of school from Jatinder’s house to school according to the given map and then convert that distance into kilometers to get the desired answer.
In the particle map 1 unit distance is representing 1,00,000 units distance in the real time.

Complete step-by-step answer:
Here it is given that
The scale of the map is 1 : 1,00,000.

Map distance from house to school = 2.5cm.
Since, in the particle map 1 unit distance is representing 1,00,000 units distance in the real time
Hence the original distance from house to school is given by:-
\[
   = 100,000 \times 2.5cm \\
   = 250000cm \\
 \]
Now first we will convert the above quantity into meters.
Now since we know that
1 meter=100 cm
Therefore in order to convert \[250000cm\]into meters we need to divide it by 100
Hence on dividing we get:-
\[
  {\text{distance}} = \dfrac{{250000}}{{100}}meters \\
\Rightarrow {\text{distance}} = 2500meters \\
 \]
Now we will convert the above distance into kilometers
Since we know that
1 kilometer=1000 meters
Therefore in order to convert \[2500meters\]into kilometers we need to divide it by 1000
Therefore on dividing by 1000 we get:-
\[
  {\text{distance}} = \dfrac{{2500}}{{1000}}kilometers \\
 \Rightarrow {\text{distance}} = 2.5km \\
 \]

$\therefore$ The distance between the house and the school is 2.5km.

Note:
The conversion of metric units is given by:

10 millimeters (mm) =	1 centimeter (cm)
10 centimeters =	1 decimeter (dm) = 100 millimeters
100 centimeter =	1 meter (m) = 1,000 millimeters
1000 meters =	1 kilometer (km)

The student can also convert centimeters into kilometers by directly dividing the quantity in centimeters by 100000.
\[1km = 1,00,000cm\]
Hence,
\[1cm = \dfrac{1}{{100000}}km\]
Therefore,
\[
  250000cm = \dfrac{{250000}}{{100000}}km \\
  250000cm = 2.5km \\
 \]