Computing profits from fractional stock trading

For fractional shares, people normally express the number of shares as a decimal rather than as a percentage of one share. For example, instead of saying "10 shares and 12.5% of one share", we say 10.125 shares.

If I buy $1 fraction of a share that's worth $25 per share, I own 4% of one share.

In other words, you bought 0.04 shares, and you paid $1 for it.

Now, suppose that a share from said company is now worth $35 dollars.

When the price per share increases to $35, your 0.04 shares will be worth $1.40 (35 * 0.04 = $1.40).

Do I still own 4% of that share?

If you haven't sold your 0.04 shares, you will still be owning those shares. Is there any particular reason why you think that the number of shares you own will be changed by an increase in stock price?

so my growth is 40%, correct?

Yes. (1.40 - 1) / 1 = 0.4. (35 - 25) / 25 = 0.4