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Understanding how to convert from decimal degrees to degrees-minutes-seconds (DMS) is very important.
It's a standard way to express angles in various fields like navigation, astronomy, and surveying.
Here’s how we do it step-by-step:

First, separate the decimal degrees into the integer part (degrees) and the decimal part.

For example, given \( 17.33^\text{°} \), we separate it into 17 degrees and 0.33 degrees.

Next, convert the decimal part (0.33 degrees) to minutes by multiplying by 60.

\[0.33 \times 60 = 19.8 \text{ minutes} \]

Now, keep the integer minutes (19 minutes) and prepare to convert the decimal part (0.8 minutes) to seconds.

Finally, multiply the remaining decimal minutes by 60 to get the seconds.

\[0.8 \times 60 = 48 \text{ seconds} \]

Combining these gives us \( 17^\text{°} 19' 48'' \).

Be sure to note if the original angle was negative, as you need to keep the negative sign.

Handling negative angles follows the same process as positive angles, but we must keep the sign consistent.

Let’s consider the example \(-17.33^\text{°} \).

First, separate into \( -17^\text{°}\text{ and } \-0.33^\text{°} \)

Next, convert the decimal part -0.33 degrees to minutes:
\[-0.33 \times 60 = -19.8 \text{ minutes}\]

Keep \(-19\text{ minutes} \) and retain the decimal part -0.8 for seconds conversion:
\[-0.8 \times 60 = -48 \text{ seconds}\]

Combine the values:
\[-17^\text{°} 19' 48'' \]
to get the final answer.

When converting decimal degrees to minutes, multiply the decimal part by 60.

For instance, 0.33 degrees would convert as follows:
\[0.33 \times 60 = 19.8 \text{ minutes} \]

Here, 19 is the integer part, and 0.8 is the decimal part for further conversion.

After converting to minutes, sometimes there is still a decimal left.

To convert this remaining decimal to seconds, multiply by 60.

From our example:
\[0.8 \times 60 = 48 \text{ seconds} \]

This step ensures the conversion is completed and accurate.