Question

1° = 60, 1 = 60
a. perform the following operation, showing and justifying all steps: 13°22 - 6°48
b. express the following without decimals: 17.24°

Explanation:

Step1: Borrow 1 degree for subtraction

Since \(22'<48'\), we borrow 1 degree from \(13^{\circ}\). So \(13^{\circ}22' = 12^{\circ}82'\). Then \(12^{\circ}82'-6^{\circ}48'=(12 - 6)^{\circ}+(82 - 48)'=6^{\circ}34'\)

Step2: Convert decimal - degree to degrees, minutes and seconds

For \(17.24^{\circ}\), the whole - number part is the degree, so \(17^{\circ}\). The decimal part \(0.24\) is converted to minutes: \(0.24\times60 = 14.4'\). The whole - number part of the minutes is \(14'\). The decimal part of the minutes \(0.4\) is converted to seconds: \(0.4\times60=24''\). So \(17.24^{\circ}=17^{\circ}14'24''\)

Answer:

a. \(6^{\circ}34'\)
b. \(17^{\circ}14'24''\)