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Difficulty: MediumFractions, Decimals, and Percentages

A quality control laboratory tested four battery models to measure the proportion of initial charge retained after 24 hours of continuous operation. The recorded results for each model are listed below:

- Model Alpha: 1320\frac{13}{20}
- Model Beta: 64.5%64.5\%
- Model Gamma: 58\frac{5}{8}
- Model Delta: 0.6380.638

Which of the following represents the battery models arranged in order from least to greatest proportion of remaining charge?

  1. 1Model Gamma: 58\frac{5}{8}
  2. 2Model Delta: 0.6380.638
  3. 3Model Beta: 64.5%64.5\%
  4. 4Model Alpha: 1320\frac{13}{20}

Answer

The correct order from least to greatest proportion of remaining charge is Model Gamma (58\frac{5}{8}), Model Delta (0.6380.638), Model Beta (64.5%64.5\%), and Model Alpha (1320\frac{13}{20}).
Converting each model's retained charge to decimal form gives Model Gamma =58=0.625= \frac{5}{8} = 0.625, Model Delta =0.638= 0.638, Model Beta =64.5%=0.645= 64.5\% = 0.645, and Model Alpha =1320=0.650= \frac{13}{20} = 0.650. Comparing these values yields 0.625<0.638<0.645<0.6500.625 < 0.638 < 0.645 < 0.650, which matches the order Model Gamma, Model Delta, Model Beta, Model Alpha.

Step-by-Step Solution

1
Convert each given fraction, percentage, and decimal into equivalent decimal values for direct comparison.
Model Alpha =1320=0.650= \frac{13}{20} = 0.650; Model Beta =64.5%=0.645= 64.5\% = 0.645; Model Gamma =58=0.625= \frac{5}{8} = 0.625; Model Delta =0.638= 0.638.
Converting all values to decimals standardizes the quantities so they can be compared easily by place value.
2
Compare the resulting decimal numbers from least to greatest.
0.625<0.638<0.645<0.6500.625 < 0.638 < 0.645 < 0.650
Comparing digits from left to right: all have 0.60.6 in the tenths place; comparing the hundredths place shows 2<3<4<52 < 3 < 4 < 5.
3
Map the sorted decimal values back to their original model designations.
Model Gamma (58\frac{5}{8}), Model Delta (0.6380.638), Model Beta (64.5%64.5\%), Model Alpha (1320\frac{13}{20}).
This establishes the required sequence from least to greatest.

Key Concept

Converting fractions, decimals, and percentages to a common format (decimals) to order rational numbers.
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Topics

Fractions, Decimals, and Percentages

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