Question

Match the number with the correct description.(5 points)
Put responses in the correct input to answer the question.
16−−√
0.424242424...
101−−−√
0.133134135...
0.789

Answer 1

Sure! Here are the matches for the numbers with their correct descriptions:

1. **\(16^{-1/2}\)**: 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.

2. **\(0.424242424...\)**: This number is a repeating decimal which can be expressed as the fraction **\(\frac{42}{99}\)**, or simplified to **\(\frac{14}{33}\)**.

3. **\(101^{-1/2}\)**: This represents the square root of 101, which is an irrational number. However, it's closest to **0.099505...** when calculated as \( \frac{1}{\sqrt{101}} \).

4. **\(0.133134135...\)**: This is also a repeating decimal, representing a fraction that would require further simplification but is generally understood to be a specific fraction itself.

5. **\(0.789\)**: 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.