Question

Which measurement is the greatest between \[6{\text{ }}km,{\text{ }}60{\text{ }}m,{\text{ }}600{\text{ }}cm\] and \[6,000{\text{ }}mm\] ?

Answer 1

Hint: We have to find which is the greatest measurement. In order to solve this question, first of all we will convert all of these into one unit. For ease, we will convert all the units into meters. Then we will compare all four side by side and find the required result.

Formulas used:
\[1{\text{ }}km = 1000{\text{ }}m\]
\[\Rightarrow 1{\text{ }}cm = \dfrac{1}{{100}}{\text{ }}m\]
\[\Rightarrow 1{\text{ }}cm = 10{\text{ }}mm\]

Complete step by step answer:
We have to find the greatest between \[6{\text{ }}km,{\text{ }}60{\text{ }}m,{\text{ }}600{\text{ }}cm\] and \[6,000{\text{ }}mm\].Now before proceeding with the question, we must know all the conversion formulas that will be required to solve this question. We will convert all the units into meters.To convert a unit from \[km\] to \[m\] , we have to multiply it by \[1000\]. Mathematically, we have
\[1{\text{ }}km = 1000{\text{ }}m{\text{ }} - - - \left( i \right)\]

To convert a unit from \[cm\] to \[m\] , we have to divide it by \[100\]
Mathematically, we have
\[1{\text{ }}cm = \dfrac{1}{{100}}{\text{ }}m{\text{ }} - - - \left( {ii} \right)\]
And to convert a unit from \[mm\] to \[m\] , we have to divide it by \[1000\]
Mathematically, we have
\[1{\text{ }}mm = \dfrac{1}{{1000}}{\text{ }}m{\text{ }} - - - \left( {iii} \right)\]
Now, in the question the first given measurement is \[6{\text{ }}km\]
Using formula \[\left( i \right)\]
\[6{\text{ }}km\] will be equal to \[6 \times 1000{\text{ }}m\]
\[ \Rightarrow 6{\text{ }}km = 6000{\text{ }}m{\text{ }} - - - \left( a \right)\]
Now the second given measurement is \[60{\text{ }}m{\text{ }} - - - \left( b \right)\]
It is already in the meter, so there is no need for conversion.

Now, the third given measurement is \[600{\text{ }}cm\]
Using formula \[\left( {ii} \right)\]
\[600{\text{ }}cm\] will be equal to \[\dfrac{{600}}{{100}}{\text{ }}m\]
\[ \Rightarrow 600{\text{ }}cm = 6{\text{ }}m{\text{ }} - - - \left( c \right)\]
Finally, the fourth given measurement is \[6,000{\text{ }}mm\]
Using formula \[\left( {iii} \right)\]
\[6,000{\text{ }}mm\] will be equal to \[\dfrac{{6000}}{{1000}}{\text{ }}m\]
\[ \Rightarrow 6,000{\text{ }}mm = 6{\text{ }}m{\text{ }} - - - \left( d \right)\]
Now compare equation \[\left( a \right),\left( b \right),\left( c \right)\] and \[\left( d \right)\] side by side, we see that the largest is \[6000{\text{ }}m\] which corresponds to \[6{\text{ }}km\] which is the required result.

Hence, \[6{\text{ }}km\] is the greatest measurement between \[6{\text{ }}km,{\text{ }}60{\text{ }}m,{\text{ }}600{\text{ }}cm\] and \[6,000{\text{ }}mm\].

Note: Note that it is not mandatory that you have to convert the units to metres, you can convert them all to any unit of your choice and get the result. Just be careful not to make mistakes when converting units.Let’s check by converting all the units into \[mm\].We know that there are \[10{\text{ }}cm\] in a \[mm\].
So, \[600{\text{ }}cm = 600 \times 10{\text{ }}mm\]
\[ \Rightarrow 600{\text{ }}cm = 6000{\text{ }}mm\]

Now we know there are \[100{\text{ }}cm\] in a \[m\] . Therefore, there are \[1000{\text{ }}mm\] in a \[m\]
So, \[60{\text{ }}m = 60 \times 1000{\text{ }}mm\]
\[ \Rightarrow 60{\text{ }}m = 60,000{\text{ }}mm\]
Now we know there are \[1000{\text{ }}m\] in a \[km\] , \[100{\text{ }}cm\] in a \[m\] and \[10{\text{ }}cm\] in a \[mm\] .Therefore, there are \[1,000,000{\text{ }}mm\] in a \[km\]

So, \[6{\text{ }}km = 6 \times 1,000,000{\text{ }}mm\]
\[ \Rightarrow 6{\text{ }}m = 6,000,000{\text{ }}mm\]
Now compare the four side by side i.e.,
\[6,000,000{\text{ }}mm,{\text{ }}60,000{\text{ }}mm,{\text{ }}6,000{\text{ }}mm\] and \[6,000{\text{ }}mm\] we get
The \[6,000,000{\text{ }}mm\] corresponds to \[6{\text{ }}km\] is the greatest.
Hence, we get the same result.