Write a formula for converting a measure of degrees in degrees, minutes, and seconds to a decimal number of degrees. The formula should convert, for example, 39º 5’ 34” to 39.093º.
The model includes the assumption that a full degree equals 60 minutes and one minute equals 60 seconds. Use the following symbols:
D = decimal number of degrees
d = whole number of degrees
m = number of minutes
s = number of seconds
A.) D = d + m(60) + s (60)
B.) D = d + m(1/60) + s (1/60)
C.) D = d + m(60) + s (3600)
D.) D = d + m(1/60) + s (1/3600)
D+1/60+1/3600
The correct formula for converting a measure of degrees in degrees, minutes, and seconds to a decimal number of degrees is:
D = d + m/60 + s/3600
Let's break down the formula:
- d represents the whole number of degrees. Since degrees are already in their decimal form, there is no need for any conversion.
- m represents the number of minutes. To convert minutes to degrees, we divide m by 60 (since 60 minutes make up 1 degree).
- s represents the number of seconds. To convert seconds to degrees, we divide s by 3600 (since 3600 seconds make up 1 degree).
Therefore, the correct formula is D = d + m/60 + s/3600, which corresponds to option B:
D = d + m(1/60) + s(1/60)