To compare the numbers \(3 \frac{2}{5}\), \(2 \frac{1}{5}\), and \(4.6\), we'll convert them into equivalent decimal or improper fraction forms.
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Convert mixed numbers to improper fractions:
- \(3 \frac{2}{5} = \frac{3 \times 5 + 2}{5} = \frac{15 + 2}{5} = \frac{17}{5}\)
- \(2 \frac{1}{5} = \frac{2 \times 5 + 1}{5} = \frac{10 + 1}{5} = \frac{11}{5}\)
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Convert to decimal:
- \(3 \frac{2}{5} = 3 + 0.4 = 3.4\)
- \(2 \frac{1}{5} = 2 + 0.2 = 2.2\)
- \(4.6\) is already in decimal form.
Now, we can list them as decimals:
- \(3 \frac{2}{5} = 3.4\)
- \(2 \frac{1}{5} = 2.2\)
- \(4.6 = 4.6\)
Now we can arrange these from greatest to least:
- \(4.6\)
- \(3.4\) (or \(3 \frac{2}{5}\))
- \(2.2\) (or \(2 \frac{1}{5}\))
So, the order from greatest to least is: 4.6, 3 2/5, 2 1/5.