Is it correct to write #1^@=2pi/360^@#? Yes or no, and also why?

Question

2418 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-02-25T17:05:37

Yes

The conversion factor between degrees and radians is

#360^@=2pi rad#.

Hence, by ratio and proportion,

#1^@=(2pi)/(360)^@rad#

Answer 2 · 2016-02-25T22:48:47

It is not correct because the units do not work.

It is true that #1^@ = 2pi/360 rad#.

In a similar way, although it is true that
#150cm=150cm xx (1m)/(100cm) = 1.5m#,

it would be incorrect to write

#150cm = 150/(100cm)#