# Fixed-point Math

## Solidity supports integers but not decimals

Solidity scales up decimals into integers, to sidestep its ability to offer floats. The number of decimals in ERC20 determines the **factor by which decimals are scaled up.**

For instance, 18 means that the value is stored in an uint as `decimalValue * 10**18`

* 1 unit of token is represented as 1e18.
* 10 units of token is represented as 10e18.
* 0.5 units of token is represented as 5e17.
* 100.103 => stored as **uint** 100103000000000000000  *<mark style="background-color:yellow;">(100.103 \*10\*\*18)</mark>*
* 0.000340 => stored as uint 340000000000000  *<mark style="background-color:yellow;">(0.00034\*10\*\*18)</mark>*

### Converting 1 DAI to WETH (18 dp -> 18 dp)

Both DAI and WETH are of 18 decimal precision. Let us assume 1 DAI = 0.00039472576 ether.

Exchange rate on contract => DAI/ETH: 394725760000000 (0.00039472576 \* 1e18)&#x20;

**Conversion**

* 1 DAI \* DAI/ETH = Qty of Ether
* `1e18` DAI x `394725760000000` = `394725760000000...0`*(18 more '0's)*
* `1e18` x \[`0.00039472576` \* `1e18`] = `0.00039472576`` `<mark style="background-color:red;">`*1e18 *1e18`</mark>

When multiplying two integers, and the resulting value is **scaled up twice**. Which is why we **divide**, to remove the extra scaling factor, **after** multiplication.

* `1e18` x \[`394725760000000`] / decimal\_precision&#x20;
* `1e18` x \[`394725760000000`] / `1e18` = `394725760000000`&#x20;
* `394725760000000` represents `0.00039472576`&#x20;

### **Converting between different decimal representations**

* TokenA is set up with 18 decimals
* TokenB is set up with 6 decimals

If you want to convert between different representations you have to multiply or divide depending on the difference in decimals count:

```markdown
To convert valueA to valueB: (18 dp -> 6 dp)
    valueB = valueA / 10**(A.decimals - B.decimals)
    valueB = valueA / (10**(18-6))
```

**Normalize** the ***from\_token*** by stripping it of its decimal places.&#x20;

![](/files/2YXfVEaHojZrOeBvU2T6)

Then we scale up by the TokenB (to token) decimals

### Vice versa

```markdown
**To convert valueB to valueA: (6 dp -> 18 dp)
    valueA = valueB * 10**(B.decimals - A.decimals)
    valueA = valueB * (10**(18-6))

    valueA = (valueB / 10**6) * 10**18
```

![](/files/rYRS19gs8PKFThWuM4AV)


---

# Agent Instructions: Querying This Documentation

If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter:

```
GET https://calnix.gitbook.io/eth-dev/learning-solidity/module-4/fixed-point-math.md?ask=<question>
```

The question should be specific, self-contained, and written in natural language.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.