Question
Convert the angle to degrees, minutes, and seconds notation. \( 146.42^{\circ} \) \( 146.42^{\circ}=\square^{\circ} \square^{\prime} \square^{\prime \prime} \)
Ask by Love Bird. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( 146.42^{\circ} = 146^{\circ}\, 25^{\prime}\, 12^{\prime\prime} \)
Solution
To convert \( 146.42^{\circ} \) into degrees, minutes, and seconds:
1. **Degrees**: The whole number is the degrees.
\[
146^{\circ}
\]
2. **Minutes**: Take the decimal part \( 0.42 \) and multiply by \( 60 \).
\[
0.42 \times 60 = 25.2 \text{ minutes}
\]
So, \( 25^{\prime} \).
3. **Seconds**: Take the decimal part \( 0.2 \) from the minutes calculation and multiply by \( 60 \).
\[
0.2 \times 60 = 12 \text{ seconds}
\]
So, \( 12^{\prime\prime} \).
Putting it all together:
\[
146.42^{\circ} = 146^{\circ}\, 25^{\prime}\, 12^{\prime\prime}
\]
**Final Answer:**
\[
146.42^{\circ} = 146^{\circ}\, 25^{\prime}\, 12^{\prime\prime}
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
To convert \( 146.42^{\circ} \) to degrees, minutes, and seconds, we start with the whole number of degrees, which is \( 146^{\circ} \). The decimal part, \( 0.42 \), is multiplied by 60 to convert it to minutes: \[ 0.42 \times 60 = 25.2 \text{ minutes} \] Now, we take the whole number of minutes, which is \( 25' \). Next, we convert the decimal part of the minutes, \( 0.2 \), to seconds by multiplying it by 60: \[ 0.2 \times 60 = 12 \text{ seconds} \] So, the final conversion is: \[ 146.42^{\circ} = 146^{\circ} 25^{\prime} 12^{\prime \prime} \]
