Question

Find the difference between these measurements.
\[32\,m\,75\,mm\,\,\,\,and\,\,\,\,\,14\,m\,25\,cm\]

Answer 1

Hint: First write both the measurements. Now identify all the different units present in both the measurements. Then try to convert this measurement into the sum of above identified units. After that try to use inter-relation and convert both the units into a single one. After getting both the measurements in the same unit you can find the difference of them by subtracting them directly. This difference is our required result.

Complete step-by-step answer:
The two measurements in the question are written as:
\[32\,m\,75\,mm\,\,\,\,;\,\,\,\,\,14\,m\,25\,cm\]
Let us assume value of first measurement as a, then \[a = 32\,m\,75\,mm\]
Let us assume value of second measurement as b, then \[b = 14\,m\,25\,cm\]
We will solve both measurements in two different cases as below:
Case I: The method of solving for value of a is described below:
By writing the value of a as it is given in question, we get:
\[a = 32\,m\,75\,mm\]
By writing the value of a as a sum of 2 units, we get:
\[a = 32\,m\, + 75\,mm\]
By basic relations of units, we can say the relation:
\[1\,mm = 0.001\,m\]
By multiplying with 75 on both the sides, we get it as:
\[75\,mm = 0.075\,m\]
By substituting this value in equation of a, we get it as:
\[a = 32\,m + 0.075\,m\]
By simplifying the above equation, we get value of a as:
\[a = 32\,.075\,m\] ……………….(1)

Case II: The method of solving for value of b is depicted below:
By writing the value of b as it is given in question, we get:
\[b = 14\,m\,25\,cm\]
By writing the value of a as a sum of 2 units, we get:
\[b = 14\,m\, + 25\,cm\]
By basic relations of units, we can say the relation:
\[1\,cm = 0.01\,m\]
By multiplying with 25 on both the sides, we get it as:
\[25\,mm = 0.25\,m\]
By substituting this value in equation of b, we get it as:
\[a = 14\,m + 0.25\,m\]
By simplifying the above equation, we get value of b as:
\[a = 14\,.25\,m\] ……………….(2)
Now, we need a difference between both, let it be x.
\[x = a - b\]
By substituting equation (1), equation (2) here, we get x values as:
\[x = 32.075 - 14.25\]
By simplifying, we get the difference value as below:
\[x = 17.825m\]
By using relations difference can be written as follows:
Difference between measurements is \[17\,m\,\,82cm\,\,5\,mm\].

Note: You can also solve by converting everything into mm then you will get a result in mm but the value will be the same. Be careful in case of m, generally students write 32.75 instead of 32.075 but be careful that 0 is important else your result will change.