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Step 1In length measurements, the prime symbol ' is used to denote minutes of arc, while the double prime symbol " is used to denote seconds of arc.
\frac{45''}{60''} = 0.75'
These units are most commonly used in the measurement of angles in degrees. To clarify, one degree can be broken down into 60 minutes of arc (also known as a minute), and each minute of arc can be further broken down into 60 seconds of arc (also known as a second). For example, an angle of 45 degrees, 30 minutes, and 15 seconds can be represented as: This means: * 45 degrees * 30 minutes (or 0.5 degrees) * 15 seconds (or 0.0025 degrees) To convert between degrees, minutes, and seconds, you can use the following conversions: 1 degree = 60 minutes = 3600 seconds So, to convert minutes to degrees, divide by 60. To convert seconds to degrees, divide by 3600. To convert seconds to minutes, divide by 60. For example, to convert 35 minutes to degrees: And to convert 45 seconds to minutes: In summary, the prime ' and double prime " symbols are used in length measurements to represent minutes and seconds of arc, which are units of angular measurement.
Final Answer
\frac{45''}{60''} = 0.75'
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