You have a certain amount of leeway as to what kind of material you wish to include in your CV. I have seen things on CVs that were of little or no interest to me: high school honors, nonmathematical awards, etc. It doesn't make me think less of the person.

I would say that it's within reason to include a grant that you have applied for but not yet heard back from. You are inviting the reader to compute an expected value, which will presumably turn out to be positive. This cannot be said for grants that you have definitely not received, and I wouldn't normally recommend that someone put that on their CV. Still, I could imagine cases where that might be appropriate: for instance, at many research universities, given that you don't have a grant, the information that you have at least applied for one every time you had the opportunity might be looked upon favorably: ask a trusted mentor about this.

You have a certain amount of leeway as to what kind of material you wish to include in your CV. I have seen things on CVs that were of little or no interest [edit: here I actually meant "of interest to me as a potential hirer", not personal interest]: high school honors, nonmathematical awards, etc. It doesn't make me think less of the person.

I would say that it's within reason to include a grant that you have applied for but not yet heard back from. You are inviting the reader to compute an expected value, which will presumably turn out to be positive. This cannot be said for grants that you have definitely not received, and I wouldn't normally recommend that someone put that on their CV. Still, I could imagine cases where that might be appropriate: for instance, at many research universities, given that you don't have a grant, the information that you have at least applied for one every time you had the opportunity might be looked upon favorably: ask a trusted mentor about this.