Question

complete parts a and b.
a. perform each of the following operations.
i. 18°4426 + 12°1936
ii. 17°21 - 5°44
b. express the following without decimals.
i. 0.9°
ii. 16.62°

a. perform each operation.
i. choose the correct answer below.
a. 4°312
b. 31°42
c. 31°2
d. 31°4

Explanation:

Step1: Add degrees, minutes and seconds separately for part a - i

Add degrees: $18^{\circ}+ 12^{\circ}=30^{\circ}$. Add minutes: $44'+19' = 63'$. Add seconds: $26''+36'' = 62''$.

Step2: Convert excess minutes and seconds to higher - units

Since $60'' = 1'$, $62''=1'2''$. Then add the extra minute to the minutes: $63'+1'=64'$. Since $60' = 1^{\circ}$, $64' = 1^{\circ}4'$. Add the extra degree to the degrees: $30^{\circ}+1^{\circ}=31^{\circ}$. So $18^{\circ}44'26'' + 12^{\circ}19'36''=31^{\circ}4'2''$.

Step3: Subtract degrees and minutes for part a - ii

Borrow $1^{\circ}$ (which is $60'$) from $17^{\circ}$ in $17^{\circ}21'$ to get $16^{\circ}81'$. Then $16^{\circ}81'-5^{\circ}44'=(16 - 5)^{\circ}(81 - 44)'=11^{\circ}37'$.

Step4: Convert decimal degrees to degrees, minutes and seconds for part b - i

Since $1^{\circ}=60'$, for $0.9^{\circ}$, $0.9\times60 = 54'$. So $0.9^{\circ}=0^{\circ}54'$.

Step5: Convert decimal degrees to degrees, minutes and seconds for part b - ii

The whole - number part is the degree: $16^{\circ}$. The decimal part is $0.62$. Since $1^{\circ}=60'$, $0.62\times60 = 37.2'$. The whole - number part of the minutes is $37'$. The decimal part of the minutes is $0.2$. Since $1' = 60''$, $0.2\times60=12''$. So $16.62^{\circ}=16^{\circ}37'12''$.

Answer:

a. i. B. $31^{\circ}4'2''$
ii. $11^{\circ}37'$
b. i. $0^{\circ}54'$
ii. $16^{\circ}37'12''$