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Answer :
Final answer:
To write 29 degrees 6'6'' as a decimal to the nearest thousandth, convert the minutes and seconds into decimal form. Add these decimals to the original measure of 29 degrees. Round to the nearest thousandth.
Explanation:
To write 29 degrees 6'6'' as a decimal to the nearest thousandth, we need to convert the minutes and seconds into decimal form. There are 60 minutes in a degree and 60 seconds in a minute, so the conversion factor is:
1 degree = 60 minutes = 60 x 60 = 3600 seconds
Therefore, the decimal equivalent of 6 minutes is 6/60 = 0.1 and the decimal equivalent of 6 seconds is 6/3600 = 0.001667.
Adding these decimals to the original measure of 29 degrees:
29 degrees + 0.1 minutes + 0.001667 seconds = 29.101667 degrees
Rounding this decimal to the nearest thousandth, we get:
29.102 degrees
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