Correct Answer: Option C

Explanation

Convert \( (42_5) \) to base three:

First, convert to decimal:
\(42_5 = 4 \times 5 + 2 = 22_{10}\)

Now convert \( (22_{10}) \) to base three:
22 \(\div 3  = 7 \quad ; \, r1 \)
7 \(\div 3  = 2 \quad ; \, r1 \)
2 \(\div 3  = 0 \quad ; \, r2\)
Read the remainders from bottom to top:
\(22_{10} = 211_3\).

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