All 5 numerators are 0.03
So, we'll use the property that says "the bigger the denominator, the smaller the value of the fraction"
For example, 17/31 is less than 17/30
And 321/555 is less than 321/534
And 12/6 is less than 12/4

Now let's check the denominators among the answer choices....
The biggest denominator is 7.1, so the correct answer is E

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Each of these can be written as a multiple of (3/71)

A) \(\frac{3}{71}\) * [(\(10^{-2}\))/(\(10^{-5}\))], which is nothing but [(\(10^{-2}\))X(\(10^5\))], which is \(10^3\)
B) \(\frac{3}{71}\) * [(\(10^{-2}\))/(\(10^{-4}\))], which is nothing but [(\(10^{-2}\))X(\(10^4\))], which is \(10^2\)
C) \(\frac{3}{71}\) * [(\(10^{-2}\))/(\(10^{-3}\))], which is nothing but [(\(10^{-2}\))X(\(10^3\))], which is \(10^1\)
D) \(\frac{3}{71}\) * [(\(10^{-2}\))/(\(10^{-2}\))], which is nothing but [(\(10^{-2}\))X(\(10^2\))], which is \(10^0\) = 1
E) \(\frac{3}{71}\) * [(\(10^{-2}\))/(\(10^{-1}\))], which is nothing but [(\(10^{-2}\))X(\(10^1\))], which is \(10^-1\)= 0.1

So E is the least.

all the possible answers' nominators are 0.03

therefore, the one with the bigger denominator has to be the one with the lowest value (value of the fraction and value of the denominator are always negatively correlated)

Thus, E is the correct answer

If students didn't see the fast answer (in my above post), here's another (slightly longer approach):

Let's create equivalent fractions with the same denominator.
Let's make each denominator 7.1

A. \(\frac{0.03}{0.00071}\)
To get a denominator of 7.1, we must take 0.00071 and move the decimal 4 places to the right.
So, we'll multiply numerator and denominator by 10,000
When we do this, we get: \(\frac{300}{7.1}\)

B. \(\frac{0.03}{0.0071}\)
To get a denominator of 7.1, we must take 0.0071 and move the decimal 3 places to the right.
So, we'll multiply numerator and denominator by 1,000
When we do this, we get: \(\frac{30}{7.1}\)

C. \(\frac{0.03}{0.071}\)
To get a denominator of 7.1, we must take 0.071 and move the decimal 2 places to the right.
So, we'll multiply numerator and denominator by 100
When we do this, we get: \(\frac{3}{7.1}\)

D. \(\frac{0.03}{0.71}\)
To get a denominator of 7.1, we must take 0.71 and move the decimal 1 place to the right.
So, we'll multiply numerator and denominator by 10
When we do this, we get: \(\frac{0.3}{7.1}\)

E. \(\frac{0.03}{7.1}\)
This already has a denominator of 7.1

Now that we have the same denominator, we can that \(\frac{0.03}{7.1}\) is the smallest fraction.
Answer: E

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Given that the demonimator is same value 71 in each case, the problem can be solved by considering 3/71 in each options and expressing them as power of 10.Going by that option E is the right choice.it is the least since the denominator is greater that the numerator.

All the numerators are the same. Hence the fraction with the largest denominator will be the smallest fraction. Option E has the largest denominator among all options.

Hence Option E is the answer.

Bunuel. Do you have any shortcut solution to share other than division?

I think that the fastest approach is given HERE. All the numerators are equal, so the smallest fraction will be the one with largest denominator (true for positive fractions).
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number with greatest denominator would be lowest. In given options, in option E denominator is greatest and whole number is smallest. So Answer is E

The math here is this, as stated by the other posters:
1. If the numerators are the same, the fraction with the smallest denominator has the largest value. The fraction with the largest denominator has the smallest value.
2. If the denominators are the same, the fraction with the smallest numerator has the smallest value. The fraction with the largest numerator has the largest value.

If you "get" rule one, this is an easy question that takes you 25 seconds to solve - the GMAT is rewarding you for mastery of a logical relationship between values. So, learning this rule has clear rewards.
If you don't "get" rule one, for problems such as this plan to set the denominators equal to one another and compare numerators. This will take about 1:30 on this question, so still a very valid approach.

Jayson Beatty
Indigo Prep
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All the numerators are the same. E has the largest denominator. So the least value will be E.

The answer is E.
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