Question

5 (10) convert 34°5135 into decimal degrees. round to the nearest thousandth of a degree.

Explanation:

Step1: Convert minutes to degrees

We know that \(1^\circ = 60'\), so to convert \(51'\) to degrees, we divide by \(60\). So \(51'=\frac{51}{60}\) degrees.
\(\frac{51}{60}= 0.85\) degrees.

Step2: Convert seconds to degrees

We know that \(1^\circ=3600''\), so to convert \(35''\) to degrees, we divide by \(3600\). So \(35''=\frac{35}{3600}\) degrees.
\(\frac{35}{3600}\approx0.009722\) degrees.

Step3: Add all the degree parts together

The original degree measure is \(34^\circ\), so we add the degrees from minutes and seconds to it.
\(34 + 0.85+ 0.009722=34.859722\) degrees.

Step4: Round to the nearest thousandth

Rounding \(34.859722\) to the nearest thousandth (three decimal places), we look at the fourth decimal place which is \(7\). Since \(7\gt5\), we round up the third decimal place.
So \(34.859722\approx34.860\) degrees.

Answer:

\(34.860\) degrees