> ## Documentation Index
> Fetch the complete documentation index at: https://docs.openfiskal.com/llms.txt
> Use this file to discover all available pages before exploring further.

# Decimal precision

> Submit decimal amounts as strings; tax_amount is checked at 8 decimal places against the inclusive-tax formula.

Send every monetary amount as a **decimal string** (`"100.00"`, `"-19.00"`, `"0.19"`). There is no wire-level cap on fractional digits.

## `tax_amount` consistency

For each `line_items[].taxes[]` on a `sale` / `return` / `exchange`, OpenFiskal recomputes the expected `tax_amount` from the line's `total_amount` (gross) and the rates on the same line, and rejects with `422 tax_amount_precision_invalid` if it disagrees.

```
expected_tax_i = total_amount × rate_i / (1 + Σ rate_j)
```

The divisor sums every rate on the line. Single-tax lines collapse to `gross × rate / (1 + rate)`; multi-tax stacking (e.g. US state + municipal) checks every row against the full rate set.

Comparison is strict at 8 decimal places: expected is rounded half-up to 8 dp and compared by numeric equality. **Submit `tax_amount` rounded to 8 dp.**

| `total_amount` | `rate`                       | Submit                | Why                                                                                         |
| -------------- | ---------------------------- | --------------------- | ------------------------------------------------------------------------------------------- |
| `"119.00"`     | `"0.19"`                     | `"19.00"`             | Math is exact (`19.00000000`); trailing zeros are equal.                                    |
| `"7.00"`       | `"0.19"`                     | `"1.11764706"`        | `7 × 0.19 / 1.19 = 1.117647058…` half-up at 8 dp. Truncating to `"1.11764705"` is rejected. |
| `"107.50"`     | `"0.05"` + `"0.025"` stacked | `"5.00"` and `"2.50"` | `107.50 / (1 + 0.05 + 0.025) = 100` net, then `net × rate_i`.                               |

The operation-level identity `pretax_amount + tax_amount + tip_amount = total_amount` is enforced separately and exactly.