Is it correct to write $1^{\circ} = 2 \frac{π}{360^{\circ}}$ $1^@=2pi/360^@$ ? Yes or no, and also why?

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Answer 1 · 2016-02-25T17:05:37

Yes

The conversion factor between degrees and radians is

$360^{\circ} = 2 π r a d$ $360^@=2pi rad$ .

Hence, by ratio and proportion,

$1^{\circ} = \frac{2 π}{{(360)}^{\circ}} r a d$ $1^@=(2pi)/(360)^@rad$

Answer 2 · 2016-02-25T22:48:47

It is not correct because the units do not work.

It is true that $1^{\circ} = 2 \frac{π}{360} r a d$ $1^@ = 2pi/360 rad$ .

In a similar way, although it is true that
$150 c m = 150 c m \times \frac{1 m}{100 c m} = 1.5 m$ $150cm=150cm xx (1m)/(100cm) = 1.5m$ ,

it would be incorrect to write

$150 c m = \frac{150}{100 c m}$ $150cm = 150/(100cm)$

Is it correct to write 1∘=2π360∘1^@=2pi/360^@? Yes or no, and also why?