Q: Is there any term to differentiate a percentage of 0 to 100 from a percentage of 0 to 1? Take, for instance, that case:

t . p where t is the total price and p is the percentage.

Is there any term to explicitly tell that the percentage represented by p is in a ratio of 0 to 1, rather than a ratio of 0 to 100?

A: I would normally identify a percentage as a representation of a fractional value based on the fact that the fraction is represented numerically as a ratio between 0 and 1. One would then take the value of the ratio and multiply it by 100 to get that expression as a percentage. I know of no such case where a percentage would be represented as a ratio other than what was described.

A: When you see $77\%$ you can replace it by $0.77$. The percent sign means "divide by $100$". So $0.5\%$ is $0.005$.

t . p where t is the total price and p is the percentage.

does not make sense as written.

A: Answering the question, I think just specifying it is fine,
$t\cdot p$ where $t$ is the price and $p$ between $0$ and $1$ defines the percentage.
Though most of anything will do $0$ to $1$ by default since actual percentages from $0\%$ to $100\%$(generally translated to their $0$ to $1$ counterpart) don't have much meaning in actual calculations but rather just a good way to interpret results.
