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Zorluk: ZorFractions, Decimals, and Percentages

Four different brands of a sports drink contain different proportions of electrolytes by weight. The proportions for each brand are listed below:

* Brand P: 512\frac{5}{12} of its weight is electrolytes
* Brand Q: 41.8%41.8\% of its weight is electrolytes
* Brand R: 0.4160.416 of its weight is electrolytes
* Brand S: 1330\frac{13}{30} of its weight is electrolytes

Arrange the brands in order from the least proportion of electrolytes to the greatest proportion of electrolytes.

  1. 1Brand R
  2. 2Brand P
  3. 3Brand Q
  4. 4Brand S

Cevap

The correct order from least to greatest proportion of electrolytes is Brand R, Brand P, Brand Q, and Brand S.
To compare the values, converting each to a decimal is the most reliable strategy. Brand R is already a decimal (0.4160.416). Converting Brand P yields 512≈0.4167\frac{5}{12} \approx 0.4167. Converting Brand Q yields 41.8%=0.41841.8\% = 0.418. Converting Brand S yields 1330≈0.4333\frac{13}{30} \approx 0.4333. Comparing these decimals reveals that 0.416<0.4167<0.418<0.43330.416 < 0.4167 < 0.418 < 0.4333, corresponding to the sequence: Brand R, Brand P, Brand Q, Brand S.

Adım Adım Çözüm

1
Identify and list all values given for each brand.
Brand P: 512\frac{5}{12}, Brand Q: 41.8%41.8\%, Brand R: 0.4160.416, Brand S: 1330\frac{13}{30}.
This establishes the raw numbers that need comparison.
2
Convert each value into a decimal format to allow direct comparison, rounding to four decimal places where necessary.
Brand R: 0.41600.4160; Brand P: 5÷12≈0.41675 \div 12 \approx 0.4167; Brand Q: 41.8%=0.418041.8\% = 0.4180; Brand S: 13÷30≈0.433313 \div 30 \approx 0.4333.
Converting to decimals standardizes the formats and makes close comparisons straightforward.
3
Compare the standardized decimal values from smallest to largest.
0.4160<0.4167<0.4180<0.43330.4160 < 0.4167 < 0.4180 < 0.4333, which corresponds to the order: Brand R, Brand P, Brand Q, Brand S.
Ordering the values correctly identifies the brands from the least proportion of electrolytes to the greatest.

Anahtar Kavram

Comparing and ordering rational numbers by converting fractions, decimals, and percents into a single consistent format.

Alternatif Yöntem

Instead of converting to decimals, all values can be converted to percentages: Brand R is 41.6%41.6\%, Brand P is 512×100%≈41.67%\frac{5}{12} \times 100\% \approx 41.67\%, Brand Q is 41.8%41.8\%, and Brand S is 1330×100%≈43.33%\frac{13}{30} \times 100\% \approx 43.33\%. Comparing these values gives 41.6%<41.67%<41.8%<43.33%41.6\% < 41.67\% < 41.8\% < 43.33\%.
Tahmini Süre:1m 30s
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Fractions, Decimals, and Percentages

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