Convert each angle measure to decimal degrees. If applicable, round to the nearest thousandth of a degree. - 70° 48'

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Identify the components of the angle: 70° (degrees) and 48' (minutes). Recall that 1 degree = 60 minutes.

Convert the minutes to decimal degrees by dividing the minutes by 60: calculate \(\frac{48}{60}\) degrees.

Add the decimal degrees obtained from the minutes to the whole degrees: \(70 + \frac{48}{60}\).

Perform the addition to express the angle entirely in decimal degrees.

If necessary, round the final decimal degree value to the nearest thousandth.

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주요 개념

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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 an angle from DMS to decimal degrees, minutes are divided by 60 since there are 60 minutes in a degree. For example, 48 minutes is converted by calculating 48 ÷ 60 = 0.8 degrees, which is then added to the degrees part.

Rounding Decimal Degrees

After converting the angle to decimal degrees, the result is often rounded to a specified precision, such as the nearest thousandth. This involves rounding the decimal portion to three decimal places to ensure clarity and consistency in measurements.