Q.Express the following angles in degree, minute and second.

Step 1: For a decimal degree, split off the whole degrees, multiply the remaining decimal by $60$ to get minutes, then multiply that remainder's decimal part by $60$ to get seconds.

i) $183.7° = 183° + 0.7\times60' = 183°42'0''$ (exact, since $0.7\times60=42.0$).

ii) $245.33° = 245° + 0.33\times60' = 245°19.8' = 245°19' + 0.8\times60'' = 245°19'48''$. …

Convert to decimal degree first (using θ×180/π if given in radian), then repeatedly multiply the fraction …

• Rounding the minutes to a whole number before extracting seconds, which compounds error.
• For part (iii), forgetting to first convert the radian measure to degree before splitting into D-M-S. …