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Let $x$ be the number. Julia had to obtain $6x$ and due to her distraction, she obtained $\frac{x}{6}$. Therefore, her error was $6x - \frac{x}{6} = \frac{35x}{6}$. Thus, in percentage terms, the error was

$$
\frac{\frac{35x}{6}}{6x} = \frac{35}{36} \approx 0.9722 = 97.22\%
$$

The correct option is (b).

Solution 2: If $N$ is the value Julia was supposed to obtain, then with her error, she found $\frac{N}{36}$, so the absolute error committed was $N - \frac{N}{36} = \frac{35}{36}N$. Therefore, the relative error was

$$
\frac{35}{36} \times 100\% = 97.22\%
$$