To convert the decimal degree [tex]\( 12.42^\circ \)[/tex] to degrees, minutes, and seconds (DMS), follow these steps:
1. Identify the Degrees:
- The integer part of [tex]\( 12.42^\circ \)[/tex] is the degree component.
- Thus, [tex]\( 12.42^\circ \)[/tex] has [tex]\( 12 \)[/tex] degrees.
2. Extract the Decimal Part:
- Subtract the degrees from the original number to obtain the decimal part.
- The decimal part is [tex]\( 0.42 \)[/tex].
3. Convert the Decimal to Minutes:
- Multiply the decimal part by 60 (since 1 degree = 60 minutes) to get the total minutes.
- [tex]\( 0.42 \times 60 = 25.2 \)[/tex].
4. Identify the Minutes:
- The integer part of [tex]\( 25.2 \)[/tex] is the minute component.
- Thus, we have [tex]\( 25 \)[/tex] minutes.
5. Extract the Remaining Decimal Part of Minutes:
- Subtract the integer minutes from the total minutes to get the fractional part.
- [tex]\( 25.2 - 25 = 0.2 \)[/tex].
6. Convert the Remaining Decimal to Seconds:
- Multiply the fractional part by 60 (since 1 minute = 60 seconds) to get the total seconds.
- [tex]\( 0.2 \times 60 = 12 \)[/tex].
7. Round the Seconds:
- The resulting seconds value is already an integer, so no rounding is necessary.
- Thus, we have [tex]\( 12 \)[/tex] seconds.
Combining these components, we transform [tex]\( 12.42^\circ \)[/tex] into degrees, minutes, and seconds as follows:
[tex]\[ 12^\circ 25' 12'' \][/tex]
Hence, the correct equivalent of [tex]\( 12.42^\circ \)[/tex] in DMS form is [tex]\( 12^\circ 25' 12'' \)[/tex].
Therefore, the answer is:
[tex]\[ \boxed{12^\circ 25' 12''} \][/tex]
Hence, option C ([tex]\( 12^\circ 25' 12'' \)[/tex]) is the correct choice.
