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

# Precision Handling

> Understanding decimal precision bridging between Cosmos and EVM

## The Precision Challenge

Cosmos SDK and Ethereum use different decimal precisions for their native tokens:

* **Cosmos SDK**: 6 decimals (1 ATOM = 10^6 uatom)
* **Ethereum**: 18 decimals (1 ETH = 10^18 wei)

This 12-decimal difference creates challenges when bridging the two ecosystems. Simply scaling values would lose precision or create rounding errors.

## PreciseBank Solution

The [PreciseBank module](/evm/next/documentation/cosmos-sdk/modules/precisebank) solves this by decomposing balances into integer and fractional components:

```
Total Balance (18 decimals) = Integer Part (6 decimals) × 10^12 + Fractional Part
```

For any account with balance `a(n)` in smallest units:

```
a(n) = b(n) × 10^12 + f(n)
```

Where:

* `a(n)` = Total balance in 18-decimal units (atest)
* `b(n)` = Integer balance in 6-decimal units (uatom) - stored in x/bank
* `f(n)` = Fractional balance (remainder) - stored in x/precisebank
* Constraint: `0 ≤ f(n) < 10^12`

### Example

Balance of 1,234,567,890,123,456,789 atest decomposes to:

```
1,234,567,890,123,456,789 = 1,234,567 × 10^12 + 890,123,456,789

Where:
- b(n) = 1,234,567 uatom (stored in x/bank)
- f(n) = 890,123,456,789 atest (stored in x/precisebank)
- Total = 1.234567890123456789 ATOM
```

## Reserve Backing

A module reserve account maintains supply consistency:

```
Reserve Balance × 10^12 = Sum of All Fractional Balances + Remainder
```

This ensures the fundamental invariant:

```
Total Supply (18-decimal) = Bank Supply (6-decimal) × 10^12
```

The reserve holds integer units to back all fractional amounts in circulation.

## Implementation

**Storage**:

* 6-decimal amounts stored in existing bank module
* Only fractional remainders stored separately in precisebank
* Full 18-decimal precision reconstructed on query

**Query Performance**:

```go theme={"system"}
fullBalance = bankBalance × 10^12 + fractionalBalance
```

**Operations**: Transfer, mint, and burn operations automatically handle carry/borrow between integer and fractional parts.

## Why This Approach

**Backward Compatibility**: Existing bank module continues to work unchanged for non-EVM operations.

**Storage Efficiency**: Only stores fractional amounts when needed, not full 18-decimal balances for every account.

**Precision Guarantee**: No rounding or precision loss - every atest is tracked accurately.

**Performance**: Single multiplication and addition reconstructs full precision without expensive arbitrary-precision math.

## Related Documentation

* [PreciseBank Module Reference](/evm/next/documentation/cosmos-sdk/modules/precisebank) - Full implementation details
* [VM Module Configuration](/evm/next/documentation/cosmos-sdk/modules/vm) - Extended denomination setup