Diffraction Grating and Maximums

[majormaaz]

Homework Statement

A grating has 728 lines per centimeter. Find the angles of the first three principal maxima above the central fringe when this grating is illuminated with 680 nm light.

Homework Equations

Our teacher briefly told us that N = # of slits / cm
and that d sin θ = mλ, and that d = 1/N

The Attempt at a Solution

I substituted d=1/N into the d sin θ = mλ so it became sin θ / N = mλ.
I then rearranged for θ to get arcsin(mNλ) = θ, and I plugged in values:
first order --> arcsin(1 * 728 * 680e-9) and so on for m = 2, 3.
However, I got it wrong.
I tried converting N into lines / m instead of cm, but I still got it wrong.

I know our teacher started to tell us this before class ended, but I feel that I am missing something

 

[majormaaz]

never mind, I converted from cm into m in the opposite direction.
my bad. don't answer this.

 

[Emilyjoint]

In the equation d should be in metres