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Difficulty: MediumFractions, Decimals, and Percentages

Four different saline solutions contain varying concentrations of dissolved salt: Solution P contains 720\frac{7}{20}, Solution Q contains 36.5%36.5\%, Solution R contains 38\frac{3}{8}, and Solution S contains 0.380.38 salt concentration. Place the four solutions in order from least concentration to greatest concentration.

  1. 1Solution P: 720\frac{7}{20}
  2. 2Solution Q: 36.5%36.5\%
  3. 3Solution R: 38\frac{3}{8}
  4. 4Solution S: 0.380.38

Answer

The correct order from least to greatest concentration is Solution P (7/20), Solution Q (36.5%), Solution R (3/8), and Solution S (0.38).
Converting each quantity to a decimal gives Solution P = 0.350, Solution Q = 0.365, Solution R = 0.375, and Solution S = 0.380. Ordering these decimal values from smallest to largest yields Solution P, Solution Q, Solution R, and Solution S.

Step-by-Step Solution

1
Convert all concentration values into equivalent decimal representations.
Solution P: 720=0.350\frac{7}{20} = 0.350; Solution Q: 36.5%=0.36536.5\% = 0.365; Solution R: 38=0.375\frac{3}{8} = 0.375; Solution S: 0.38=0.3800.38 = 0.380.
Converting all numbers to decimals allows for direct numerical comparison.
2
Compare the decimal values digit by digit from left to right.
0.350<0.365<0.375<0.3800.350 < 0.365 < 0.375 < 0.380
Comparing the hundredths and thousandths places establishes the precise order.
3
Map the ordered decimal values back to their corresponding original solutions.
Solution P (0.3500.350), Solution Q (0.3650.365), Solution R (0.3750.375), Solution S (0.3800.380).
To complete the sequence from least to greatest.

Key Concept

Converting fractions, decimals, and percentages to a common numerical form (decimals) to compare and order them.
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Topics

Fractions, Decimals, and Percentages

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