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°

d. 31°4
ii. choose the correct answer below.
a. 37°11
b. 11°37
c. 11°37
d. 1137
b. express the following without decimals.
i. 0.9° = □

Explanation:

Step1: Add degrees, minutes and seconds separately for 18°44'26'' + 12°19'36''

Add degrees: $18^{\circ}+ 12^{\circ}=30^{\circ}$. Add minutes: $44'+19' = 63'$. Since $60' = 1^{\circ}$, $63'=1^{\circ}3'$. Add seconds: $26''+36'' = 62''$. Since $60'' = 1'$, $62'' = 1'2''$. Combine results: $30^{\circ}+1^{\circ}3'+1'2''=31^{\circ}4'2''$.

Step2: Subtract degrees and minutes for 17°21' - 5°44'

Borrow 1° (60') from 17° to make it 16°81'. Then $16^{\circ}81'-5^{\circ}44'=(16 - 5)^{\circ}+(81 - 44)'=11^{\circ}37'$.

Step3: Convert 0.9° to degrees - minutes - seconds

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

Step4: Convert 16.62° to degrees - minutes - seconds

The whole - number part is the degree: 16°. 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. $31^{\circ}4'2''$
ii. $11^{\circ}37'$
b. i. $0^{\circ}54'$
ii. $16^{\circ}37'12''$