How do you convert $257^@30'$ to degrees?

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Answer 1 · 2017-11-16T01:24:48

There are 60 minutes in one degree, and 60 seconds in one minute of arc, aren't there?

So $30^'$ is one-half of a degree, and that would be $0.5^o$ .

$257^o$ $30^'$ , all in degrees, would be $257.5^o$ or $257$ $1/2$ degrees.

In general, to covert minutes of arc to degrees, you divide by 60,
and to go back the other way, you multiply by 60.

So $20^'$ = $20/60 = 1/3 = 0.33^o$ and $50^' = 50/60 = 5/6 = 0.83^o$ .

(These are actually repeating decimals: $1/3 = 0.333333333$ forever and $5/6 = 0.83333333$ forever. I've rounded them to two places.)

In the other direction, $1^o = 60^'$ ; $15^o = 15 * 60 = 900^'$ , though I don't think you'd be expressing a measurement of arc all in minutes.

Arc is curvature, like the curve of the Earth or of a circle in geometry.

How do you convert 257^@30'257^@30' to degrees?