To determine which number has a repeating decimal form, we can analyze each given option one by one.
Option A: [tex]\(\sqrt{15}\)[/tex]
- The square root of 15 is an irrational number, and its decimal form is non-repeating. It continues infinitely without a repeating pattern.
Option B: [tex]\(\frac{11}{25}\)[/tex]
- To convert [tex]\(\frac{11}{25}\)[/tex] to a decimal, we perform the division:
[tex]\[
\frac{11}{25} = 0.44
\][/tex]
The decimal form is 0.44, which terminates, not repeating.
Option C: [tex]\(\frac{3}{20}\)[/tex]
- To convert [tex]\(\frac{3}{20}\)[/tex] to a decimal, we perform the division:
[tex]\[
\frac{3}{20} = 0.15
\][/tex]
The decimal form is 0.15, which terminates, not repeating.
Option D: [tex]\(\frac{2}{6}\)[/tex]
- To convert [tex]\(\frac{2}{6}\)[/tex] to a decimal, we simplify the fraction first:
[tex]\[
\frac{2}{6} = \frac{1}{3}
\][/tex]
Then, we perform the division:
[tex]\[
\frac{1}{3} = 0.3333\ldots
\][/tex]
The decimal form is 0.3333..., which is repeating (the digit '3' repeats indefinitely).
Given the analysis, the correct answer is:
[tex]\[ \text{D. } \frac{2}{6} \][/tex]
This number has a repeating decimal form.
