I would distinguish between accounting accuracy and useful personal budgeting.
For bank accounts, credit cards, loans, investments, etc., I recommend recording the exact amounts. If your statement says $27.43, record $27.43 rather than $30. Otherwise small rounding errors accumulate and eventually your records will no longer reconcile with the actual account.
Cash is different because tracking every coin can require more effort than the information is worth. You have several reasonable choices.
If you want completely accurate records, record every cash transaction exactly. If that becomes burdensome, keep a “Cash” account and periodically count the cash you actually have. If your records say $84.32 but you really have $81.75, enter a $2.57 adjustment, perhaps categorized as “Cash adjustment” or “Uncategorized expense.”
I would not recommend deliberately rounding every transaction to the nearest $10. Ten dollars is a fairly large rounding interval. Ten purchases of $14, for example, could be recorded as only $100 instead of the actual $140. Your spending analysis could become substantially distorted.
A good compromise is therefore:
Electronic transactions → record exactly.
Important cash transactions → record exactly.
Tiny cash discrepancies/coins → periodically reconcile and enter an adjustment.
The objective of personal finance software is to give you useful information for decisions, not to make bookkeeping so tedious that you stop doing it. Your accounts should be accurate enough to reconcile and to show where your money is going, while your method should also be simple enough to maintain consistently.
If you find yourself spending more time accounting for pennies than analyzing hundreds or thousands of dollars of spending and saving, the additional precision probably has very little practical value.
