Convert each angle measure to decimal degrees. If applicable, round to the nearest thousandth of a degree. 112° 15'

Verified step by step guidance

1. Identify the components of the angle: 112° (degrees) and 15' (minutes). Remember that 1 degree = 60 minutes.
2. Convert the minutes to decimal degrees by dividing the number of minutes by 60. Use the formula: \(\text{Decimal degrees from minutes} = \frac{\text{minutes}}{60}\).
3. Calculate the decimal degrees from the minutes: \(\frac{15}{60}\).
4. Add the decimal degrees obtained from the minutes to the whole degrees to get the total angle in decimal degrees: \(112 + \frac{15}{60}\).
5. If required, round the final decimal degree value to the nearest thousandth.

Key Concepts

Degrees, Minutes, and Seconds (DMS) Notation

Angles can be expressed in degrees (°), minutes ('), and seconds ("), where 1 degree equals 60 minutes and 1 minute equals 60 seconds. This notation is commonly used in navigation and surveying to represent precise angle measures.

Conversion from Minutes to Decimal Degrees

To convert minutes to decimal degrees, divide the number of minutes by 60 since there are 60 minutes in one degree. For example, 15 minutes equals 15/60 = 0.25 degrees, which can then be added to the whole degrees.

Rounding Decimal Degrees

After converting the angle to decimal degrees, rounding to the nearest thousandth means keeping three digits after the decimal point. This ensures a precise yet manageable representation of the angle for practical use.