Question

If \[1{{m}^{2}}=xm{{m}^{2}}\] then the value of \[x\] is.

Answer 1

Hint: From the question given we have to find the value of \[x\].To find the value of \[x\] we have to use dimensional conversions or unit conversions by using this we will get the value of \[x\].we have to get the relation between meter square and millimeter square.

Complete step by step solution:
Here, in the given question \[{{m}^{2}}\] means meter square and \[m{{m}^{2}}\] means millimeter square.
From the units and dimensions, we know the relation between meter, centimeter and millimeter.
First of all, the relation between meter and centimeter is
\[\Rightarrow 1m=100cm\]
Here cm means centimeter.
Now, the relation between centimeter and millimeter is
\[\Rightarrow 1cm=10mm\]
Now, the relation between meter square and centimeter square is
Squaring on both sides to the relation between meter and centimeter we get the relation between meter square and centimeter square,
\[\Rightarrow 1m=100cm\]
Squaring on both sides, we get
\[\Rightarrow {{\left( 1m \right)}^{2}}={{\left( 100cm \right)}^{2}}\]
\[\Rightarrow 1{{m}^{2}}=10000c{{m}^{2}}\]
Now the relation between centimeter square and millimeter square is
Squaring on both sides to the relation between centimeter and millimeter we get the relation between centimeter square and millimeter square,
 \[\Rightarrow 1cm=10mm\]
Squaring on both sides, we get
\[\Rightarrow {{\left( 1cm \right)}^{2}}={{\left( 10mm \right)}^{2}}\]
\[\Rightarrow 1c{{m}^{2}}=100m{{m}^{2}}\]
Now, from the above relations we have to get the relation between meter and millimeter.
We know that
 \[\Rightarrow 1m=100cm\]
also, we know that
\[\Rightarrow 1cm=10mm\]
Therefore,
\[\Rightarrow 1m=100cm=100\times 10mm=1000mm\]
Finally, we got the relation between meter and millimeter,
\[\Rightarrow 1m=1000mm\]
Now, the relation between meter square and millimeter square is
 Squaring on both sides to the relation between meter and millimeter we get the relation between meter square and millimeter square,
\[\Rightarrow 1m=1000mm\]
Squaring on both sides, we get
\[\Rightarrow {{\left( 1m \right)}^{2}}={{\left( 1000mm \right)}^{2}}\]
\[\Rightarrow 1{{m}^{2}}=1000000m{{m}^{2}}\]
By, comparing the above relation with the given equation in the question i.e. \[1{{m}^{2}}=xm{{m}^{2}}\]
We can say that the value of \[x\] is \[1000000\]
Therefore, \[1000000\]

Note:
Students should be aware of the dimensional or unit conversions. Students should not be confused with the relations between meter and centimetre and millimetre like in this question if we take 1m=100mm then the whole solution will be wrong. So students should be careful in calculations.