Convert 0.001 arcseconds to radians.

[ZedCar]

Homework Statement

Convert 0.001 arcseconds to radians.

I believe the correct solution is 4.85 x 10^-9 radians.

Homework Equations

2∏rad = 360° = 60' = 3600''

The Attempt at a Solution

The way I was trying to achieve this solution is by setting my calculator to radian mode, typing in {2Pi/(60x60)} x 0.001 which gives 1.74x10^-6.

So I was wondering what I'm doing wrong?

Thank you!

 

[Doc Al]

2π radians = 360 degrees
1 degree = 60 arcminutes
1 arcminute = 60 arcseconds

 

[ZedCar]

2π radians = 360 degrees
1 degree = 60 arcminutes
1 arcminute = 60 arcseconds

That's great. Thanks very much.

(2∏ / (360x60x60)) x 0.001 = 4.85x10^-9

 

[CWatters]

Not everyone knows but Google can also do sums...

https://www.google.co.uk/#hl=en&tbo...ef9f3f538eb70d&bpcl=40096503&biw=1194&bih=671

 

[Nickie]

Your calculation is correct, but you have to remember that 0.001 arcseconds is a very small unit of measurement. It is equivalent to 1/3600000 of a degree, which is why the resulting value in radians is also very small (1.74x10^-6). However, the correct solution is actually 4.85 x 10^-9 radians, as you mentioned in your initial response. This is because 1 arcsecond is equal to 4.85 x 10^-6 radians, and 0.001 arcseconds is 1/1000 of 1 arcsecond. Therefore, to convert 0.001 arcseconds to radians, you simply need to divide 4.85 x 10^-6 by 1000, which gives you 4.85 x 10^-9 radians.