2003 CEMC Pascal Problems/Problem 10

Problem

Which of the following numbers is the largest?

$\text{ (A) }\ 3.2571 \qquad\text{ (B) }\ 3.\overline{2571} \qquad\text{ (C) }\ 3.2\overline{571} \qquad\text{ (D) }\ 3.25\overline{71} \qquad\text{ (E) }\ 3.257\overline{1}$

Solution

The first four decimal places of all the numbers are the same, but all we have to do is compare the hundred thousandths places of the numbers:

$3.2571$ does not repeat, so its hundred thousandths place is just $0$

$3.\overline{2571}$ repeats and the pattern starts out with a $2$ , so its hundred thousandths place is just $2$

$3.2\overline{571}$ repeats and the pattern starts out with a $5$ , so its hundred thousandths place is just $5$

$3.25\overline{71}$ repeats and the pattern starts out with a $7$ , so its hundred thousandths place is just $7$

$3.257\overline{1}$ repeats and the pattern starts out with a $1$ , so its hundred thousandths place is just $1$

Of the answer choices, the number with the largest hundred thousandths place is $\boxed {\textbf {(D) } 3.25\overline{71}}$

~anabel.disher

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2003 CEMC Pascal Problems/Problem 10

Problem

Solution