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Difficulty: MediumFractions, Decimals, and Percentages

A laboratory technician measured the concentration of active reagent in four different solutions and recorded the values in various numerical forms: Solution W contains 716\frac{7}{16} active reagent, Solution X contains 42.5%42.5\% active reagent, Solution Y contains 0.440.44 active reagent, and Solution Z contains 49\frac{4}{9} active reagent. What is the correct order of the four solutions from the least concentration of active reagent to the greatest concentration?

  1. 1Solution X (42.5%42.5\%)
  2. 2Solution W (716\frac{7}{16})
  3. 3Solution Y (0.440.44)
  4. 4Solution Z (49\frac{4}{9})

Answer

The correct order from least to greatest concentration is Solution X (42.5%42.5\%), Solution W (716\frac{7}{16}), Solution Y (0.440.44), and Solution Z (49\frac{4}{9}).
To arrange values given in different numerical formats, convert each to decimal form: Solution X equals 0.42500.4250, Solution W equals 0.43750.4375, Solution Y equals 0.44000.4400, and Solution Z equals 0.4444...0.4444.... Arranging these decimals from least to greatest yields Solution X, Solution W, Solution Y, then Solution Z.

Step-by-Step Solution

1
Convert all values to decimal format for direct comparison.
Solution W: 716=0.4375\frac{7}{16} = 0.4375; Solution X: 42.5%=0.42542.5\% = 0.425; Solution Y: 0.44=0.44000.44 = 0.4400; Solution Z: 49=0.4444...\frac{4}{9} = 0.4444...
Converting fractions, decimals, and percentages to a single decimal format makes order comparisons straightforward.
2
Compare the resulting decimal values place by place.
0.4250<0.4375<0.4400<0.4444...0.4250 < 0.4375 < 0.4400 < 0.4444...
Comparing digits from left to right establishes the numerical sequence.
3
Match the ordered decimals back to their corresponding solution names.
Solution X (0.4250.425) < Solution W (0.43750.4375) < Solution Y (0.440.44) < Solution Z (49\frac{4}{9})
The question requires ranking the original solution labels.

Key Concept

Converting fractions, decimals, and percentages into a uniform decimal format to compare and order rational numbers
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Topics

Fractions, Decimals, and Percentages

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