Question

survey 101 quiz 3e (30 pts)
convert the following to decimal units (4 decimal places) (3pts each)

1. 12 1/2
2. 22 7/8
3. 1,446 21 23/32

convert the following from degrees minutes seconds to decimal degrees (4 decimal places): (3pts each)

1. 27°0227
2. 88°2845
3. 131°5959

convert the following from decimal degrees to degrees minutes seconds (nearest second): (3pts each)

1. 71.2026°
2. 88.3044°
3. 202.0101°

Explanation:

Step1: Recall conversion formulas

1 degree = 60 minutes, 1 minute = 60 seconds. To convert degrees - minutes - seconds to decimal degrees: decimal degrees = degrees + minutes/60+seconds/3600. To convert decimal degrees to degrees - minutes - seconds: degrees is the integer part, minutes = (decimal part 60), and seconds = (minutes' decimal part 60).

Step2: Solve problem 1

$1 + 2/3\approx1.6667$

Step3: Solve problem 2

$22+7/5 = 22 + 1.4=23.4$

Step4: Solve problem 3

$1446+21/36=1446 + 0.5833\approx1446.5833$

Step5: Solve problem 4

$27+2/60 + 27/3600=27+0.0333+0.0075 = 27.0408$

Step6: Solve problem 5

$88+28/60+45/3600=88 + 0.4667+0.0125=88.4792$

Step7: Solve problem 6

$131+59/60+59/3600=131+0.9833+0.0164 = 131.9997$

Step8: Solve problem 7

The integer part of 71.2026 is 71 degrees. The decimal part is 0.2026, so minutes = $0.2026\times60 = 12.156$. The integer part of 12.156 is 12 minutes. The decimal part is 0.156, so seconds = $0.156\times60=9.36\approx9$. So it is $71^{\circ}12'9''$

Step9: Solve problem 8

The integer part of 88.3044 is 88 degrees. The decimal part is 0.3044, so minutes = $0.3044\times60 = 18.264$. The integer part of 18.264 is 18 minutes. The decimal part is 0.264, so seconds = $0.264\times60 = 15.84\approx16$. So it is $88^{\circ}18'16''$

Step10: Solve problem 9

The integer part of 202.0101 is 202 degrees. The decimal part is 0.0101, so minutes = $0.0101\times60=0.606$. The integer part of 0.606 is 0 minutes. The decimal part is 0.606, so seconds = $0.606\times60 = 36.36\approx36$. So it is $202^{\circ}0'36''$

Answer:

1. $1.6667$
2. $23.4$
3. $1446.5833$
4. $27.0408$
5. $88.4792$
6. $131.9997$
7. $71^{\circ}12'9''$
8. $88^{\circ}18'16''$
9. $202^{\circ}0'36''$