Question

1. convert 119°0803 into decimal degrees. round to the nearest thousandth of a degree.

Explanation:

Step1: Convert seconds to minutes

We know that \(1' = 60''\), so to convert \(03''\) to minutes, we do \(3\div60 = 0.05'\).

Step2: Add to the existing minutes

Now we have the minutes part as \(08' + 0.05' = 8.05'\).

Step3: Convert minutes to degrees

Since \(1^{\circ}=60'\), we convert \(8.05'\) to degrees by doing \(8.05\div60\approx0.134167^{\circ}\).

Step4: Add to the existing degrees

The original degree is \(119^{\circ}\), so we add the converted minutes: \(119^{\circ}+ 0.134167^{\circ}=119.134167^{\circ}\).

Answer:

\(119.134^{\circ}\) (rounded to the nearest thousandth of a degree)