To convert $46.42^\circ$ into degrees-minutes-seconds (D° M' S'') form:

Step-by-step Calculation:

1. Separate the whole degrees: The integer part of $46.42$ is $46^\circ$.

2. Convert the decimal part into minutes: Multiply the decimal part ($0.42$) by $60$ (since there are 60 minutes in a degree): $0.42 \times 60 = 25.2 \text{ minutes}.$ The integer part is $25'$, so we have $46^\circ 25'$.

3. Convert the remaining decimal part into seconds: Multiply the decimal part of the minutes ($0.2$) by $60$ (since there are 60 seconds in a minute): $0.2 \times 60 = 12 \text{ seconds}.$

Final Answer:

$46.42^\circ = 46^\circ 25' 12''.$

Would you like further details or have any questions?

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Related Questions:

1. How is the degrees-minutes-seconds system used in navigation or surveying?
2. Can you explain how to convert DMS back to decimal degrees?
3. What are the practical applications of DMS in trigonometry?
4. How do you round DMS values for accuracy?
5. How can I use a calculator to convert between decimal degrees and DMS?

Tip:

Always keep track of rounding when converting between decimal degrees and DMS to ensure accuracy in your results.