To find the length of \( PG \), we can use the relationship between the lengths in a dilation. Given that the scale factor of the dilation is \( \frac{1}{6} \) (one-sixth), we can express this relationship mathematically.
The formula for the length after dilation is:
\[ PG' = \text{scale factor} \times PG \]
Substituting the given values, we have:
\[ 0.5 = \frac{1}{6} \times PG \]
To find \( PG \), we can rearrange the equation:
\[ PG = 0.5 \div \frac{1}{6} \]
Dividing by a fraction is the same as multiplying by its reciprocal, so:
\[ PG = 0.5 \times 6 = 3 \]
Thus, the length of \( PG \) is \( \boxed{3} \) units.
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