Question

Convert each angle to \(D^{\circ} M^{\prime} S^{\prime \prime}\) form. Round your answer to the nearest second. \(44.01^{\circ}\)

Short answer

44.01° = 44° 0' 36''

Step-by-step solution

- Separate the Degrees

Identify the whole number part of the angle, which represents the degrees. For the angle \(44.01^{\text{°}}\), the degrees part is \(44^{\text{°}}\).

- Calculate the Minutes

Subtract the degrees from the original angle to get the decimal part: \[ 44.01^\text{°} - 44^\text{°} = 0.01^\text{°} \] Convert this decimal part to minutes by multiplying by 60 (since 1 degree = 60 minutes): \[ 0.01 \times 60 = 0.6^\text{'} \]So, we have 0 minutes and 0.6 minutes remaining.

- Calculate the Seconds

Convert the remaining minutes to seconds by multiplying by 60 (since 1 minute = 60 seconds): \[ 0.6 \times 60 = 36^{\text{''}} \]So, we have 36 seconds.

- Round to the Nearest Second

Since there are no decimal places in our seconds calculation, the seconds are already rounded to the nearest whole number, which is 36 seconds.

- Compile the Answer

Combine the degrees, minutes, and seconds to form the final answer. Thus, \(44.01^\text{°}\) is equal to \(44^\text{°} 0^\text{'} 36^\text{''}\)

Key concepts

Degrees

Degrees are the primary unit for measuring angles. They represent a division of a circle into 360 equal parts. When converting an angle to degrees, minutes, and seconds (DMS) form, start by identifying the degrees portion. For instance, in the angle 44.01°, the whole number part, which is 44, represents the degrees. Consider degrees as the largest unit in angle measurement, just like hours in time.
Understanding degrees helps make conversions easier and ensures accurate angle measurements in fields such as astronomy, navigation, and engineering.

Minutes

Minutes are the next smaller unit in angle measurement, with 60 minutes in one degree, similar to how there are 60 minutes in an hour. To find the minutes part of an angle, subtract the degrees from the original angle to get the decimal portion. For the angle 44.01°, subtract 44° to get 0.01°. Then, multiply this decimal by 60 to convert it into minutes:
\(0.01 \times 60 = 0.6'\)
In our example, this gives us 0 minutes and 0.6 minutes remaining. This detailed understanding of minutes is crucial in accurately breaking down and converting angles.

Seconds

Seconds are the smallest unit in angle measurement in the DMS system. There are 60 seconds in one minute, analogous to time measurement. To convert remaining minutes to seconds, multiply by 60. From our example, we have 0.6 minutes remaining:
\(0.6 \times 60 = 36''\)
Therefore, 0.6 minutes equals 36 seconds. Often, you may need to round the seconds to the nearest whole number, especially if dealing with more complex decimal values. Remembering this conversion can help in various applications, such as precise scientific calculations and detailed geographic mapping.

Angle Measurement

Angle measurement plays a vital role in many disciplines like geometry, astronomy, and navigation. The DMS (degrees, minutes, seconds) form is a common representation for precise angular measurements. Converting between different units involves clear steps:

• Identify the degrees (whole number part of the angle).
• Calculate the minutes by isolating the decimal part and multiplying by 60.
• Convert any remaining minutes to seconds (by multiplying the remaining decimal by 60).
• Compile the results to get the final angle in DMS form.

The example given, 44.01°, converted to 44° 0' 36'', demonstrates these steps elegantly. Being adept at these conversions ensures accuracy and clarity in projects requiring precise measurements.