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Answer :
Let's solve the expression [tex]\(\sqrt{\frac{1}{25}}\)[/tex] step-by-step.
1. Expression Setup: We start with the expression [tex]\(\sqrt{\frac{1}{25}}\)[/tex].
2. Simplify the Fraction Inside the Square Root:
[tex]\[
\frac{1}{25} = 0.04
\][/tex]
3. Compute the Square Root:
[tex]\[
\sqrt{0.04} = 0.2
\][/tex]
4. Determine the Nature of the Result:
- A rational number is any number that can be written as a fraction of two integers. The number 0.2 can be written as [tex]\(\frac{1}{5}\)[/tex].
- A terminating decimal is a decimal which has a finite number of digits after the decimal point. The number 0.2 has only one digit after the decimal point, so it is a terminating decimal.
Since [tex]\(0.2\)[/tex] fits these criteria, [tex]\(\sqrt{\frac{1}{25}}\)[/tex] is a rational terminating decimal.
Therefore, the statement that best describes [tex]\(\sqrt{\frac{1}{25}}\)[/tex] is:
```
rational terminating decimal
```
1. Expression Setup: We start with the expression [tex]\(\sqrt{\frac{1}{25}}\)[/tex].
2. Simplify the Fraction Inside the Square Root:
[tex]\[
\frac{1}{25} = 0.04
\][/tex]
3. Compute the Square Root:
[tex]\[
\sqrt{0.04} = 0.2
\][/tex]
4. Determine the Nature of the Result:
- A rational number is any number that can be written as a fraction of two integers. The number 0.2 can be written as [tex]\(\frac{1}{5}\)[/tex].
- A terminating decimal is a decimal which has a finite number of digits after the decimal point. The number 0.2 has only one digit after the decimal point, so it is a terminating decimal.
Since [tex]\(0.2\)[/tex] fits these criteria, [tex]\(\sqrt{\frac{1}{25}}\)[/tex] is a rational terminating decimal.
Therefore, the statement that best describes [tex]\(\sqrt{\frac{1}{25}}\)[/tex] is:
```
rational terminating decimal
```
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