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Which of the following expressions has the greatest value?

A. \(0.456\) B. \(\frac{1}{2}-(\frac{1}{2})^4\) C. \(\frac{300}{650}\) D. \(3(\frac{3}{19})\) E. \(\sqrt{0.17}\)

Find the best common base for these expressions.

B is \(\frac{1}{2} - \frac{1}{16}\), which gives us \(\frac{7}{16}\).

C is \(\frac{300}{650}\) or \(\frac{30}{65}\) or \(\frac{6}{13}\).

D is \(\frac{9}{19}\).

E is slightly greater than 0.4, not much more to surpass A, so we can eliminate it.

Now, let's see which of B, C, and D is the greatest. We can drop B as it does not add up to C or D - it is further away from \(\frac{1}{2}\) than C or D.

These two fractions are very close to \(\frac{1}{2}\). If we decrease the values of the denominators of each of the fraction by 1, we'll see that they equal \(\frac{1}{2}\). For these two fractions \(\frac{6}{13}\) and \(\frac{9}{19}\), the greater the value of denominator, the closer will the fraction be to \(\frac{1}{2}\). Therefore, \(\frac{9}{19}\) is greater. This fraction property can be vividly described by two fractions \(\frac{1}{2+1}=\frac{1}{3}\) and \(\frac{50}{100+1}=\frac{50}{101}\), clearly the second one is greater.

Now, we just need to compare it to A. \(\frac{9}{19} = 0.47...\).

I think this question is poor and helpful. The question involves good arithmetic knowledge. but option D is not written properly, it looks like 3 3/19 = 60/19, rather than 9/19

From option A-D , highest value came out to be D i.e. 9/19= 0.473.....To compare it to root 17....just square 0.473(17 is prime)..... comes out close to 0.22 so D is the highest value

Which of the following expressions has the greatest value?

A. \(0.456\) B. \(\frac{1}{2}-(\frac{1}{2})^4\) C. \(\frac{300}{650}\) D. \(3(\frac{3}{19})\) E. \(\sqrt{0.17}\)

IMO, answer choice E takes away from the problem. The purpose of the problem is to rationalize through the different fractions. The difference between A and E is slightly greater than three hundredths, and there isn't a good way to formulate that without a calculator or without prior experience with square roots of decimals, and therefore, I think this type of calculation isn't becoming of a 700-level test taker, even with estimation.

It might be improved if it plays off the divisor of 9 or 999, making answer choice E, \(\frac{2^{2}}{3^{3}}\) or \(\frac{450}{999}\). Hope it helps.

It took me 4 minutes to do this problem but at least I got it right. The way I figured sqrt.17 is that .4^2 = 16 and .5^2 = .25 so it's a whole lot closer to .4