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Question

Difficulty: HardConverting Between Fractions, Decimals, and Percents

A logistics quartermaster is auditing the remaining capacity of four different fuel storage tanks relative to their maximum volume. To plan refueling priorities, arrange the tanks from the least full to the most full based on their current capacity levels.

  1. 1Tank C: 0.6750.675 full
  2. 2Tank D: 1725\frac{17}{25} full
  3. 3Tank B: 68.5%68.5\% full
  4. 4Tank A: 1116\frac{11}{16} full

Answer

The correct order from least full to most full is Tank C (0.675), Tank D (17/25), Tank B (68.5%), and Tank A (11/16).
By converting all capacity values to percentages (68.75%68.75\%, 68.5%68.5\%, 67.5%67.5\%, and 68%68\%), their magnitudes can be directly and accurately compared. The lowest percentage is 67.5%67.5\% (Tank C), followed closely by 68%68\% (Tank D), 68.5%68.5\% (Tank B), and the highest is 68.75%68.75\% (Tank A).

Step-by-Step Solution

1
Convert all given values to a common format (such as percentages or decimals) for easy and accurate comparison.
Tank C is given as a decimal, 0.6750.675, which equals 67.5%67.5\%. Tank B is already given in percentage format at 68.5%68.5\%.
Comparing mixed forms (fractions, decimals, and percentages) is prone to estimation errors without standardizing them.
2
Convert the fraction for Tank D into a percentage.
Tank D is 1725\frac{17}{25}. Multiplying both the numerator and denominator by 44 creates a fraction out of 100100: 68100\frac{68}{100}, which equals 0.680.68 or 68%68\%.
Converting fractions to a base of 100100 makes percentage translation immediate.
3
Convert the fraction for Tank A into a percentage using long division or known fractional equivalents.
Tank A is 1116\frac{11}{16}. Since 116=0.0625\frac{1}{16} = 0.0625, multiplying by 1111 yields 0.68750.6875. Alternatively, 11÷16=0.687511 \div 16 = 0.6875. This equates to 68.75%68.75\%.
Finding the exact decimal prevents mistakes when comparing closely clustered values.
4
Order the standardized percentages sequentially from least to greatest.
67.5%<68%<68.5%<68.75%67.5\% < 68\% < 68.5\% < 68.75\%. Matching these values back to their original forms yields: Tank C, Tank D, Tank B, Tank A.
The prompt asks to arrange the tanks specifically from least full to most full.

Key Concept

Converting fractions and decimals to percentages to compare close magnitudes accurately.
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Topics

Converting Between Fractions, Decimals, and Percents

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