Convert the given angle to DMS (degree-minute-second) form. Round to the nearest second if necessary.

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Assume the angle is given in decimal degrees as $$ \theta $$. The conversion to degrees, minutes, and seconds (DMS) is performed as follows:

1. Write
   $$
   \theta = D + \delta,
   $$
   where $$ D $$ is the integer (whole number) part of $$ \theta $$ and 
   $$
   \delta = \theta - D
   $$
   is the fractional part.

2. Multiply the fractional part by 60 to obtain the minutes:
   $$
   \text{minutes value} = \delta \times 60.
   $$
   Let 
   $$
   M = \lfloor \delta \times 60 \rfloor,
   $$
   where $$ \lfloor \cdot \rfloor $$ denotes the floor (the greatest integer less than or equal to the value).

3. Determine the remaining fraction after extracting minutes:
   $$
   \varepsilon = (\delta \times 60) - M.
   $$

4. Multiply that remaining fraction by 60 to obtain the seconds:
   $$
   S = \varepsilon \times 60.
   $$
   Round $$ S $$ to the nearest whole number if necessary.

Thus, the angle $$ \theta $$ in DMS form is given by:
$$
D^\circ\, M'\, S''.
$$

For an example, suppose
$$
\theta = 123.4567^\circ.
$$

1. The degree part is:
   $$
   D = 123.
   $$

2. The fractional part is:
   $$
   \delta = 0.4567.
   $$

3. Convert the fractional part to minutes:
   $$
   0.4567 \times 60 = 27.402.
   $$
   Therefore,
   $$
   M = 27 \quad \text{and} \quad \varepsilon = 0.402.
   $$

4. Convert the remaining fraction to seconds:
   $$
   S = 0.402 \times 60 \approx 24.12.
   $$
   Rounding to the nearest second gives $$ S \approx 24 $$.

The DMS form of $$ 123.4567^\circ $$ is:
$$
123^\circ\, 27'\, 24''.
$$
To convert an angle from decimal degrees to degrees, minutes, and seconds (DMS), follow these steps: 1. **Degrees (D):** Take the integer part of the decimal degrees. 2. **Minutes (M):** Multiply the fractional part by 60 to get minutes. Take the integer part of this result. 3. **Seconds (S):** Multiply the remaining fractional part by 60 to get seconds. Round to the nearest whole number if necessary. **Example:** For $$ 123.4567^\circ $$: - Degrees: 123 - Minutes: $$ 0.4567 \times 60 = 27.402 $$ → 27 minutes - Seconds: $$ 0.402 \times 60 \approx 24.12 $$ → 24 seconds So, $$ 123.4567^\circ = 123^\circ\, 27'\, 24'' $$.

Convert the given angle to DMS (degree-minute-second) form. Round to the nearest second if necessary.

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