convert 140.365 degrees to degree minute second form. if necessary, round your answer to the nearest second

To convert \( 140.365^\circ \) to degrees, minutes, and seconds:

### Step 1: Extract the degree portion
The whole number part of \( 140.365^\circ \) is \( 140^\circ \).

### Step 2: Convert the decimal part to minutes
The decimal part is \( 0.365 \). Multiply this by 60 to convert it to minutes:
\[
0.365 \times 60 = 21.9 \, \text{minutes}
\]
The whole number part is \( 21 \, \text{minutes} \).

### Step 3: Convert the decimal part of the minutes to seconds
Take the decimal part of \( 21.9 \) minutes, which is \( 0.9 \), and multiply it by 60 to convert to seconds:
\[
0.9 \times 60 = 54 \, \text{seconds}
\]

### Final Answer:
\( 140.365^\circ = 140^\circ 21' 54'' \).

No rounding is necessary, as the seconds value is already an integer.

Would you like further details or have any questions?

Here are some related questions:
1. How do you convert radians to degrees, minutes, and seconds?
2. What is the relation between arc length and angle in degrees?
3. How do you calculate angular velocity given degrees per second?
4. What is the process for converting DMS form back to decimal degrees?
5. How are angles used in spherical geometry?

**Tip**: To quickly convert between decimal degrees and DMS, you can use calculators or tools specifically designed for angle conversions.

Learn how to convert 140.365 degrees to degrees, minutes, and seconds (DMS) form with a detailed step-by-step guide. This process covers key trigonometric concepts and formulas used in angle conversions. Suitable for students in Grades 9-12.

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