Sure! Here are the matches for the numbers with their correct descriptions:
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\(16^{-1/2}\): This expression represents the square root of 16, which is 4. However, the provided option should be 0.25 (as it indicates the inverse of the square root). Therefore, there seems to be a mismatch.
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\(0.424242424...\): This number is a repeating decimal which can be expressed as the fraction \(\frac{42}{99}\), or simplified to \(\frac{14}{33}\).
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\(101^{-1/2}\): This represents the square root of 101, which is an irrational number. However, it's closest to 0.099505... when calculated as \( \frac{1}{\sqrt{101}} \).
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\(0.133134135...\): This is also a repeating decimal, representing a fraction that would require further simplification but is generally understood to be a specific fraction itself.
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\(0.789\): This is simply a decimal number and doesn't require any transformation.
To summarize, the matches based on general mathematical understanding are:
- \(16^{-1/2}\): possibly a mismatch (consider it as the expression for \(\frac{1}{\sqrt{16}} = 0.25\) for relevance)
- \(0.424242424...\): Matched to \(\frac{14}{33}\) (the repeating decimal)
- \(101^{-1/2}\): an approximation of \(0.099505...\)
- \(0.133134135...\): a repeating decimal fraction
- \(0.789\): remains as a decimal.
If you provide the exact descriptions, I can match them more accurately.
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