Question

How do you convert \[4500\] mm to m?

Answer 1

Hint: We will first convert one metre into millimetre to find the conversion factor of a millimetre into the metre. Then, we will find the equivalent of \[4500\] millimetre in terms of the metre by multiplying the conversion factor to 4500.

Complete step by step solution:
We are required to convert \[4500\] millimetre into the metre.
Let us first find the conversion factor. In order to do this, we will find the equivalent of one metre in terms of a millimetre. Then, we will divide by the conversion factor to find the equivalent of one millimetre in terms of metre.
We know that
\[1{\rm{m}} = 100{\rm{cm}}\]……….\[\left( 1 \right)\]
Here cm stands for centimetre.
Now, we must convert centimetre to the millimetre, so that we may get the equivalent of one metre in terms of millimetres.
We know that
\[1{\rm{ cm}} = 10{\rm{ mm}}\] ……….\[\left( 2 \right)\]
Substituting equation \[\left( 2 \right)\] in equation \[\left( 1 \right)\], we get
\[1{\rm{m}} = 100 \times 10{\rm{mm}} = 1000{\rm{mm}}\] ……….\[\left( 3 \right)\]
In equation \[\left( 3 \right)\], we have converted one metre into millimetres. But, in the given question, we are required to convert millimetres into metre. So, we will divide both sides of equation \[(3)\] by 1000 to get the conversion factor for converting one millimetre into metres. Thus, we have
\[1{\rm{mm}} = \dfrac{1}{{1000}}{\rm{m}}\] ……….\[\left( 4 \right)\]
Now, to find the value of \[4500\] millimetres in terms of metres, we will multiply both sides of equation \[\left( 4 \right)\] by \[4500\]. Therefore, we have
\[{\rm{4500mm}} = \dfrac{1}{{1000}} \times {\rm{4500m}}\]
\[ \Rightarrow 4500{\rm{mm}} = 4.5{\rm{m}}\]

Therefore, we have obtained the equivalent of \[4500\] millimetres as \[4.5\] metres.

Note:
We can also find the conversion by a reverse process. We will begin by converting millimetres into centimetres. Then, we will convert this value into metres. Since \[1{\rm{ cm}} = 10{\rm{ mm}}\], we get
\[1{\rm{ mm}} = \dfrac{1}{{10}}{\rm{ cm}}\]
Also, we know that \[1{\rm{ m}} = 100{\rm{ cm}}\]. So, from this we get
\[1{\rm{ cm}} = \dfrac{1}{{100}}{\rm{ m}}\]
Thus, we get
\[1{\rm{mm}} = \dfrac{1}{{10}} \times \dfrac{1}{{100}}{\rm{m}} = \dfrac{1}{{1000}}{\rm{m}}\]
Now multiplying both sides by 4500, we get
\[ \Rightarrow {\rm{4500mm}} = \dfrac{1}{{1000}} \times {\rm{4500m}}\]
\[ \Rightarrow 4500{\rm{mm}} = 4.5{\rm{m}}\]
Therefore, we have obtained the equivalent of \[4500\] millimetres as \[4.5\] metres.