Sure, let's match each rational number with its equivalent form.
1. [tex]\(0 . \overline{142857}\)[/tex] can be written as [tex]\(\frac{1}{7}\)[/tex].
2. [tex]\(\frac{1}{18}\)[/tex] is approximately equal to [tex]\(0.0555555...\)[/tex].
3. [tex]\(0.5\)[/tex] can be written as [tex]\(\frac{1}{2}\)[/tex].
4. [tex]\(0.05\)[/tex] can be written as [tex]\(\frac{1}{20}\)[/tex].
5. [tex]\(\frac{2}{3}\)[/tex] is approximately equal to [tex]\(0 . \overline{6}\)[/tex].
6. [tex]\(0.6\)[/tex] can be written as [tex]\(\frac{3}{5}\)[/tex].
So, pairing the rational numbers with their equivalent forms:
- [tex]\(0 . \overline{142857}\)[/tex] → [tex]\(\frac{1}{7}\)[/tex]
- [tex]\(\frac{1}{18}\)[/tex] → [tex]\(0.0555555...\)[/tex]
- [tex]\(0.5\)[/tex] → [tex]\(\frac{1}{2}\)[/tex]
- [tex]\(0.05\)[/tex] → [tex]\(\frac{1}{20}\)[/tex]
- [tex]\(\frac{2}{3}\)[/tex] → [tex]\(0 . \overline{6}\)[/tex]
- [tex]\(0.6\)[/tex] → [tex]\(\frac{3}{5}\)[/tex]