Here is what we do. We use YNAB to do our budgeting and track our expenses. Anything that gets paid electronically is tracked to the penny. It really needs to be, because you want your transaction records to match your bank's transaction records.
However, for cash spending, we only count the paper money, not the coins. Here is how it works:
If I want a Coke out of a vending machine for 75 cents, and I put a dollar bill in and get a quarter back as change, I record that as a $1.00 expense.
If, instead, I put 3 quarters in to get the Coke, I don't record that expense at all. Spending coins is "free money."
We do this mainly because it is just easier to keep track of. I can quickly count the cash in my wallet and verify that it matches the amount that YNAB thinks I have in my wallet, and I don't need to worry about the coins. Coins that are in my car to pay for parking meters or coins in the dish on my dresser don't need to be counted.
This works for us mainly because we don't do a whole lot of cash spending, so the amount we are off just doesn't add up to a significant portion of our spending. And, again, bank balances are exact to the penny.