Question

1. convert 275.1005° to degrees, minutes, seconds, rounded to the nearest second.

Explanation:

Step1: Identify degrees, decimal part

The given angle is \(275.1005^\circ\). The whole number part is the degrees: \(275^\circ\). The decimal part is \(0.1005\).

Step2: Convert decimal degrees to minutes

To convert decimal degrees to minutes, multiply the decimal part by \(60\) (since \(1^\circ = 60'\)). So, \(0.1005\times60 = 6.03'\). The whole number part of this result is the minutes: \(6'\).

Step3: Convert decimal minutes to seconds

The decimal part of the minutes is \(0.03\). To convert this to seconds, multiply by \(60\) (since \(1' = 60''\)). So, \(0.03\times60 = 1.8''\). Rounding to the nearest second, we get \(2''\) (because \(1.8\) is closer to \(2\) than to \(1\)).

Step4: Combine degrees, minutes, seconds

Putting it all together, we have \(275^\circ\), \(6'\), and \(2''\).

Answer:

\(275^\circ 6' 2''\)