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Difficulty: MediumFractions, Decimals, and Percentages

A sports analyst tracks four basketball players' shooting efficiencies over a season, expressed in different numerical formats:

- Player P: 916\frac{9}{16}
- Player Q: 0.580.58
- Player R: 54.5%54.5\%
- Player S: 1120\frac{11}{20}

Place the players in order of their shooting efficiency from least to greatest.

  1. 1Player R: 54.5%54.5\%
  2. 2Player S: 1120\frac{11}{20}
  3. 3Player P: 916\frac{9}{16}
  4. 4Player Q: 0.580.58

Answer

Player R (54.5%54.5\%), Player S (1120\frac{11}{20}), Player P (916\frac{9}{16}), Player Q (0.580.58)
To order the shooting efficiencies from least to greatest, convert each representation into a decimal: Player R is 54.5%=0.54554.5\% = 0.545, Player S is 1120=0.55\frac{11}{20} = 0.55, Player P is 916=0.5625\frac{9}{16} = 0.5625, and Player Q is 0.580.58. Comparing these decimals gives 0.545<0.55<0.5625<0.580.545 < 0.55 < 0.5625 < 0.58, corresponding to the sequence: Player R, Player S, Player P, Player Q.

Step-by-Step Solution

1
Convert all given values into a common format, such as decimals.
Player P: 916=0.5625\frac{9}{16} = 0.5625; Player Q: 0.580.58; Player R: 54.5%=0.54554.5\% = 0.545; Player S: 1120=0.55\frac{11}{20} = 0.55
Converting fractions and percentages into decimals allows for direct numerical comparison.
2
Compare the resulting decimal values.
0.545<0.55<0.5625<0.580.545 < 0.55 < 0.5625 < 0.58
Aligning decimals by place value confirms the ascending sequence.
3
Match the ordered decimals back to the original player designations.
Player R (0.5450.545) < Player S (0.550.55) < Player P (0.56250.5625) < Player Q (0.580.58)
This establishes the correct order from least to greatest efficiency.

Key Concept

Comparing and ordering numbers by converting fractions, decimals, and percentages into a unified numerical representation.
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Topics

Fractions, Decimals, and Percentages

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