During a physical endurance test, four candidates completed different portions of a 10-kil… — State PSC Exam

During a physical endurance test, four candidates completed different portions of a 10-kilometer cross-country course before a mandatory rest period. The fraction or decimal representing the portion of the course completed by each candidate is given below. Arrange the candidates in ascending order based on the portion of the course they completed (from least to most).

1Candidate Q: $0.\overline{81}$ of the course
2Candidate S: $\frac{5}{6}$ of the course
3Candidate R: $0.8\overline{4}$ of the course
4Candidate P: $\frac{17}{20}$ of the course

Answer

Candidate Q, Candidate S, Candidate R, Candidate P

To correctly order the candidates, all values must be evaluated in a uniform format. Candidate P is exactly 0.85. Candidate Q is approximately 0.818. Candidate R is approximately 0.844. Candidate S is approximately 0.833. Arranging these numerical values from least to most gives: Q (0.818...), S (0.833...), R (0.844...), P (0.850).

Step-by-Step Solution

Convert the portion completed by Candidate P into a standard decimal format.

\frac{17}{20} = \frac{17 \times 5}{20 \times 5} = \frac{85}{100} = 0.85

Converting all values to standard decimals makes it easier to directly compare their magnitudes.

Convert the portion completed by Candidate Q into an expanded decimal format.

0.\overline{81} = 0.818181\dots

Expanding the recurring bar notation clarifies the digits beyond the hundredths place.

Convert the portion completed by Candidate R into an expanded decimal format.

0.8\overline{4} = 0.844444\dots

Expanding the single recurring digit makes its exact magnitude clear for comparison.

Convert the portion completed by Candidate S into a decimal format.

\frac{5}{6} = 5 \div 6 = 0.833333\dots

Performing the division provides the decimal value needed to compare against the others.

Compare the resulting decimal values and arrange them in ascending order.

0.8181\dots < 0.8333\dots < 0.8444\dots < 0.8500

Sorting the decimals from smallest to largest yields the order: Candidate Q, Candidate S, Candidate R, Candidate P.

Key Concept

Converting mixed fraction types and recurring decimals into a uniform decimal format to accurately compare their relative magnitudes.

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