Answer :
To determine which number has a repeating decimal form, let's analyze each given option step-by-step.
### Option A: [tex]\(\sqrt{15}\)[/tex]
[tex]\(\sqrt{15}\)[/tex] is an irrational number, meaning its decimal representation is non-repeating and non-terminating. Thus, it does not have a repeating decimal form.
### Option B: [tex]\(\frac{11}{25}\)[/tex]
A fraction [tex]\(\frac{11}{25}\)[/tex] can be checked for a repeating decimal by examining its simplified denominator. If the denominator after simplification contains only the prime factors 2 and/or 5, the decimal will be terminating.
[tex]\[ \frac{11}{25} = 0.44 \][/tex]
Since it terminates, it does not have a repeating decimal form.
### Option C: [tex]\(\frac{3}{20}\)[/tex]
Similarly, for [tex]\(\frac{3}{20}\)[/tex]:
[tex]\[ \frac{3}{20} = 0.15 \][/tex]
Since it also terminates, it does not have a repeating decimal form.
### Option D: [tex]\(\frac{2}{6}\)[/tex]
For [tex]\(\frac{2}{6}\)[/tex], we first simplify the fraction:
[tex]\[ \frac{2}{6} = \frac{1}{3} \][/tex]
Now, let's convert [tex]\(\frac{1}{3}\)[/tex] to a decimal:
[tex]\[ \frac{1}{3} = 0.33333333\ldots \][/tex]
We see that it repeats with "3" repeating indefinitely. Therefore, [tex]\(\frac{1}{3}\)[/tex] (and hence [tex]\(\frac{2}{6}\)[/tex]) has a repeating decimal form.
### Conclusion
Among the given options, [tex]\(\frac{2}{6}\)[/tex] has a repeating decimal form. Therefore, the correct answer is:
[tex]\[ \boxed{D} \][/tex]
### Option A: [tex]\(\sqrt{15}\)[/tex]
[tex]\(\sqrt{15}\)[/tex] is an irrational number, meaning its decimal representation is non-repeating and non-terminating. Thus, it does not have a repeating decimal form.
### Option B: [tex]\(\frac{11}{25}\)[/tex]
A fraction [tex]\(\frac{11}{25}\)[/tex] can be checked for a repeating decimal by examining its simplified denominator. If the denominator after simplification contains only the prime factors 2 and/or 5, the decimal will be terminating.
[tex]\[ \frac{11}{25} = 0.44 \][/tex]
Since it terminates, it does not have a repeating decimal form.
### Option C: [tex]\(\frac{3}{20}\)[/tex]
Similarly, for [tex]\(\frac{3}{20}\)[/tex]:
[tex]\[ \frac{3}{20} = 0.15 \][/tex]
Since it also terminates, it does not have a repeating decimal form.
### Option D: [tex]\(\frac{2}{6}\)[/tex]
For [tex]\(\frac{2}{6}\)[/tex], we first simplify the fraction:
[tex]\[ \frac{2}{6} = \frac{1}{3} \][/tex]
Now, let's convert [tex]\(\frac{1}{3}\)[/tex] to a decimal:
[tex]\[ \frac{1}{3} = 0.33333333\ldots \][/tex]
We see that it repeats with "3" repeating indefinitely. Therefore, [tex]\(\frac{1}{3}\)[/tex] (and hence [tex]\(\frac{2}{6}\)[/tex]) has a repeating decimal form.
### Conclusion
Among the given options, [tex]\(\frac{2}{6}\)[/tex] has a repeating decimal form. Therefore, the correct answer is:
[tex]\[ \boxed{D} \][/tex]
