Question

Find in metres the height of a pile of $25$ books if each book is \[3cm{\text{ }}5mm\] thick.

Answer 1

Hint: We have to find the height in metres of a pile of $25$ books . We solve it by using the concept of conversion of units of quantities . We change the unit of the thickness into a single unit by using the relation between the two and then again changing the units of thickness of the pile of books into metres .

Complete step-by-step answer:
The system of units can be represented in terms of other systems of units . We can change the units of quantities even in different volumes . The units of measurement of a liquid quantity or we can state it as the volume of the quantity can be converted into units of measurements of lengths i.e. the units like litre and mili - litre can be changed into units of measurements metres , centi - metre etc .
Given :
Thickness of each book = \[3cm{\text{ }}5mm\]
As we know , the conversion of units
\[1{\text{ }}cm{\text{ }} = {\text{ }}10{\text{ }}mm\]
\[1{\text{ }}m{\text{ }} = {\text{ }}100{\text{ }}cm\]
So , \[1m{\text{ }} = {\text{ }}1000{\text{ }}mm\]
Thickness of one book \[ = {\text{ }}3{\text{ }} \times {\text{ }}\left( {10} \right){\text{ }} + {\text{ }}5\]
Thickness of one book \[ = {\text{ }}35{\text{ }}mm\]
Now , finding the height of pile of $25$ books
Height of pile of $25$ books \[ = {\text{ }}25{\text{ }} \times {\text{ }}305\]
Height of pile of $25$ books \[ = {\text{ }}875{\text{ }}mm\]
As , shown above \[1{\text{ }}m{\text{ }} = {\text{ }}1000{\text{ }}mm\]
So , \[1{\text{ }}mm{\text{ }} = {\text{ }}0.001{\text{ }}m\]
Height of pile of books in metre \[ = {\text{ }}875{\text{ }} \times {\text{ }}0.001\]
Height of pile of books in metre \[ = {\text{ }}0.875{\text{ }}m\]
Thus , the height of a pile of $25$ books is \[0.875{\text{ }}m\] .
So, the correct answer is “Option B”.

Note: A system of units can be changed into another system of units without affecting the actual value of the quantity . Some more conversions are stated below :
\[1{\text{ }}km{\text{ }} = {\text{ }}1000{\text{ }}m\]
\[1{\text{ }}km{\text{ }} = {\text{ }}100000{\text{ }}cm\]
\[1{\text{ }}km{\text{ }} = {\text{ }}1000000{\text{ }}mm\]