23°20’48” is the same as _°. Round to the nearest hundredth of a degree.
The correct answer and explanation is:
To convert 23°20’48” to decimal degrees, we follow these steps:
- Start with the degrees: The number of degrees is 23°. This remains the same in the decimal form.
- Convert minutes to a fraction of a degree:
There are 60 minutes in a degree. So, to convert 20 minutes to a fraction of a degree, divide 20 by 60: 2060=0.3333 degrees\frac{20}{60} = 0.3333 \text{ degrees} - Convert seconds to a fraction of a degree:
Similarly, there are 3600 seconds in a degree (since 60 seconds = 1 minute, and 60 minutes = 1 degree). To convert 48 seconds to a fraction of a degree, divide 48 by 3600: 483600=0.0133 degrees\frac{48}{3600} = 0.0133 \text{ degrees} - Add everything together:
Now, we add the degrees, the fraction from the minutes, and the fraction from the seconds: 23+0.3333+0.0133=23.3466 degrees23 + 0.3333 + 0.0133 = 23.3466 \text{ degrees} - Round to the nearest hundredth:
Rounding 23.3466 to the nearest hundredth gives us 23.35°.
Thus, 23°20’48” is equal to 23.35° when rounded to the nearest hundredth of a degree.
This method is useful when you need to convert a time-based angular measurement (such as degrees, minutes, and seconds) into a more straightforward decimal form, which is often required in scientific and technical contexts.