Tax inclusive pricing I have a system where is user can enter a price (without tax) and a tax rate. I then calculate the total cost of the item.
Example:
Price:100.00
Tax percent: 10%
Final price: 110.00 = (100 + (100* (10/100))
I have got a request to work backwards and start with the final price and tax and determine the price without tax.
In my system I store only price without tax and tax percent.
For example if a user wants a final price of 30.00 and a tax percent of 8.25
The starting price in this case has more than 2 decimals.
How many decimals do I need to store to allow for tax inclusive pricing for all possibilities?

As you've shown, given a initial price $p_i$ and tax percentage $t$, we directly have that the final price $p_f$ is $p_f=p_i\left(1+\frac{t}{100}\right)$.
Given that, can you solve $p_i$ in terms of $p_f$ and $t$?
