Question

The scale on the map is $1:50000$. The area of a field on the map is $1.2$ square centimeters. Calculate the actual area of the field in square kilometers.

Answer 1

Hint: In this question , we need to calculate the actual area of the field in square kilometers but we are given the area of the field on the map is 1.2 square centimeters. Also the scale on the map is $1:50000$. For calculating the overall area of the field we have to multiply the area of the field given on the map by the scale on the map. Along with this we are required to place the suitable unit as we want the answer to be in kilometers. By following these steps we can get the required solution.

Complete step-by-step solution:
We are given the different information , in order to solve this question are as follows :
The scale on map = $1:50000$.
The area of a field on the map = $1.2$square centimeters.
Actual area of the field can be calculated by multiplying the area of field given on the map by the the scale on map , we get :
 \Rightarrow $1.2 \times 50000 \times 50000c{m^2}$

We have to get rid of the decimal to make our calculations easier. We will multiply a decimal with 10 , then the decimal point will be moved to the right side by 1 place , which we want to eliminate. If the decimal is being moved to the right, the exponent will be negative which automatically means that the number will be divided and placed in the denominator.
So , here the decimal removed by multiplying 10 then the decimal point will be moved to the right side by 1 place and the exponent becomes -1 on the base number 10 that is = $1.2 \times {10^{ - 1}} = \dfrac{{12}}{{10}}$
Rewriting the number 1.2 as $1.2 \times {10^{ - 1}} = \dfrac{{12}}{{10}}$.
$\Rightarrow \dfrac{{12}}{{10}} \times 50000 \times 50000c{m^2}$
$\Rightarrow 12 \times 5000 \times 50000c{m^2}$
$\Rightarrow 12 \times 25 \times {10^7}c{m^2}$
$\Rightarrow 300 \times {10^7}c{m^2}$
Now , we have the units as centimeter squares but we want the units to be in kilometers square.
We will do the conversion by dividing 100.
\[
\Rightarrow 300 \times {10^7} \times {10^{ - 4}}c{m^2} \\
\Rightarrow 300 \times {10^3}{m^2} \\
\Rightarrow 3 \times {10^5}{m^2} \\
 \]
Now , we will do conversion from the square meter to square kilometer.
\[
\Rightarrow 3 \times {10^5} \times {10^{ - 6}}k{m^2} \\
\Rightarrow 3 \times {10^{ - 1}}k{m^2} \\
\Rightarrow 0.3k{m^2} \\
 \]

Therefore , the required solution is 0.3\[k{m^2}\].

Note: Do not Forget to verify the end of the result with the zeroes.
-If you multiply a decimal with 10 , then the decimal point will be moved to the right side by 1 place.
-If you multiply a decimal with 100 , then the decimal point will be moved to the right side by 2 place.
- If the decimal is being moved to the right, the exponent will be negative which automatically means that the number will be divided and placed in the denominator. Try to cancel out factors from numerator and denominator , you will get your required result.Be Careful while converting the units.