Question

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

Answer 1

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

Explanation:

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.