Rewrite  so that both are in fraction form.

Convert the division sign to multiplication, and take the reciprocal of the 2nd term.

The greatest is 0.999 (999/1000), then 0.990 (990/1000), finally 0.909 (909/1000). 

0.999 > 0.990 > 0.909

When comparing decimals, move left to right, comparing the size of the tenths, then the hundredths, then the thousandths, etc….

From least to greatest:

0.007 (), 0.07 (), 0.08 (), 0.9 (), 1.33 ( and ), 1.44 ( and ), 14

Begin by converting each fraction into a decimal:

Now we can put the decimals in order:

0.269, 0.27, 0.2788, 0.28, 0.3157

or:

No answer choice matches this order, so our answer is "None of the other answers"

With decimals, the larger number has a value in the larger spot (anything with a nonzero value in the tenths, is larger than any number with a 0 in the tenths and a digit in the hundredths, and so on). Thus the correct ordering starts with the decimal with the largest digit in the tenth spot, or .340.

After that there is only one with a nonzero value in the tenths spot, so .101 comes next.

Then there are only two that have nonzero values in the hundreths spot, and since 5 is larger than 1 the next two are .052 and then .011.

Finally, the smallest number is the one with zeroes in the tenths and hundreths spot so .009 is the smallest.

Thus resulting in,

, equivalent to two-hundredths, is the least out of the collection.

, equivalent to twenty-hundredths, is the next highest. 

, equivalent to twenty-five hundredths, is the next highest.

, equivalent to thirty-four hundredths, is the next highest.

Finally, the highest number is , equivalent to one hundred and eighty hundredths. 

1/2 is the least, then 2/3, then 3/4.

This question can be most easily answered by converting the fractions into decimals first.

The most generic process of ordering fractions that can apply to all questions begins with finding the common denominator between all fractions, preferably the least common denominator. In this question, the LCD is 40. Therefore the fractions become: . From this point, we can simply arrange the fractions based upon their numerators. This becomes: . The final step is to reduce the fractions to their original denominators, which becomes: .

If you are comfortable and competent in quickly converting fractions to decimals, then there is a quicker method than what is described above. Simply convert each fraction to a decimal, organize the decimals, and then convert the decimals back to fractions. In this question we can convert  to . Then we can reorganize this to  and convert back to .

When approaching this kind of problem, choose the method in which you are more comfortable working with. There is no sense in trying to save time by choosing a method that you are not comfortable with and increasing your risk of answering the question incorrectly.