Final answer:
To convert 12°26'5'' to decimal degrees, divide the minutes and seconds by 60 and 3600, respectively, and add these to the degrees. The result, rounded to the nearest thousandth, is 12.434°.
Step-by-step explanation:
To convert the angle of 12°26'5'' to a decimal number of degrees, we first recognize that there are 60 minutes in a degree (°) and 60 seconds in a minute ('). Thus, we can convert the minutes and seconds to a fractional part of a degree.
Firstly, we convert the minutes to degrees by dividing by 60:
26' ÷ 60 = 0.433°.
Secondly, we convert the seconds to degrees by dividing by 3600 (since there are 60 minutes in a degree and 60 seconds in a minute):
5'' ÷ 3600 = 0.0014°.
Finally, we add these to the original 12 degrees to get the total in decimal:
12° + 0.433° + 0.0014° = 12.4344°.
Round this to the nearest thousandth as requested:
12.434°.