To answer this question, we need to take into account that negative numbers are always lesser than a positive number, and, between two negative numbers, the one that has the greatest distance from 0 is lesser than the other negative number.
We have the numbers:
[tex]-6.44,\frac{12}{50},\bar{0.2},-\sqrt[]{40}[/tex]
With the help of a calculator, we can find the value of all these numbers in decimal expression:
[tex]\frac{12}{50}=\frac{6}{25}=0.24[/tex]
The number above is a terminating decimal. Only have two decimals.
[tex]\bar{0.2}=0.222222222222\ldots[/tex]
The latter is a periodic decimal number.
[tex]-\sqrt[]{40}=-6.32455532034[/tex]
Now, we can observe the negative numbers:
[tex]-6.44,-\sqrt[]{40}=-6.32455532034[/tex]
The number with the greatest absolute value, that is, with the greatest distance from 0 is -6.44, since:
[tex]|-6.44|=6.44,|-6.32455532034|=6.32455532034[/tex]
Therefore, we have the least number is -6.44, then -√40.
Now, which one is the greatest?:
[tex]\frac{12}{50}=0.24,\bar{0.2}=0.222222222\ldots[/tex]
We can apply the same here. The one with the greatest absolute value is 0.24.
Therefore, to order these numbers from least to greatest is:
[tex]-6.44<-\sqrt[]{40}<\bar{0.2}<0.24[/tex]
