How many arcseconds are in a degree?

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Solution

Answer:
There are 3600 arcseconds in 1 degree.
Explanation:
We can use dimensional analysis to convert from degrees to arcminutes, then from arcminutes to arcseconds:
$1^{\circ}$
$= 1^{\circ} . \frac{60 a r c m i n u t e s}{1^{\circ}}$
$= 60 a r c m i n u t e s$
$= 60 a r c m i n u t e s . \frac{60 a r c s e c o n d s}{1 a r c m i n u t e}$
$= 60 . \frac{60 a r c s e c o n d s}{1}$
$= 60 \cdot 60 a r c s e c o n d s$
$= 3600 a r c s e c o n d s \cdot$

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