Question

1. convert 45° 32 55\ into decimal degrees to the nearest two decimal places. (2 points)

Explanation:

Step1: Convert minutes to degrees

We know that \(1^\circ = 60'\), so to convert \(32'\) to degrees, we divide by 60. So \(32'=\frac{32}{60}\) degrees.
\[
\frac{32}{60}\approx0.5333^\circ
\]

Step2: Convert seconds to degrees

We know that \(1^\circ = 3600''\), so to convert \(55''\) to degrees, we divide by 3600. So \(55''=\frac{55}{3600}\) degrees.
\[
\frac{55}{3600}\approx0.0153^\circ
\]

Step3: Add all the parts together

We have the whole number of degrees as \(45^\circ\), then we add the degrees from minutes and seconds. So the total decimal degrees is \(45 + 0.5333+ 0.0153\).
\[
45+0.5333 + 0.0153=45.5486\approx45.55
\]

Answer:

\(45.55^\circ\)