Order the numbers from least to greatest

To order all of the numbers, we should either turn them all into fractions or into decimals. In this case, it might be easier to turn them all into decimals.

-4 1/9 = -4.1111111111 (ones going on forever)

-4.19 = -4.19

-4 = -4

-41/9 = -4.555555555 (the fives go on forever)

Now we need to order them by which one is closer away from zero. We can figure this out by finding which one has the smallest absolute value (that would mean it is closer to zero). Using this method, the answer is that -4 is first (because it doesn't have any decimal points and they all have the number 4), -4 1/9 is next because it has the next largest absolute value, and then -4.19 and then -41/9.