Asset quantities in StarkEx
In the Ethereum blockchain, token quantities are represented by a 256bit number. However, for the sake of efficiency, quantities in StarkEx are represented by a 64bit number. The largest number of digits that a 64bit number can represent is much less than that which a 256bit number can represent. So in order to support trading in significant volume, the smallest unit that StarkEx can use for an asset is larger than the smallest unit that Ethereum can use.
The inputs to all offchain transactions and some onchain requests are given in units of the offchain asset, so the code that generates the transaction signature must use the correct factor for converting 256bit quantities of onchain asset quantities to a 64bit StarkEx representation.
Converting onchain asset quantities 
This factor is called the quantization factor or quantum. The quantum represents the smallest amount of an asset that users can trade offchain, or with which they can pay offchain fees. 
You decide the value of the quantum according to the requirements of your application’s business logic.
Quantization
The quantum is the smallest unit of a token in the StarkEx system. It is similar to an exchange rate that you use to find the onchain value of a quantity of a token in StarkEx, according to the following formula:
Consider one possible quantization for ETH, which is an onchain asset:
Onchain asset 
The smallest unit of ETH is 1 WEI, which is \(10^{18}\) ETH. 
Offchain asset 
The smallest unit with which you can conduct transactions of the offchain asset that corresponds to ETH represents \(10^{11}\) onchain ETH, or \(10^{7}\) onchain WEI. 
So the operator defines the quantum for ETH to be \(10^{7}\).
This example shows how to find how many units of onchain WEI are represented by 17 units of the corresponding offchain asset.

In Ethereum, 1 WEI = \(10^{18}\)ETH.

Let \(\text{quantum}=10^7\).

Let \(\text{StarkEx_amount}=17\). This is the number of corresponding assets in a StarkEx offchain vault.
Plugging in these values to the formula above gives the following:
170,000,000 is the amount of WEI locked onchain that is associated with the corresponding StarkEx offchain vault, which is the same as \(10^{11} \cdot 17\) ETH.
The quantum is necessary for every asset that can be represented onchain. For example, in the deposit flow, the onchain deposit transaction gets an unquantized amount of tokens from the user, yet the parameter to the onchain call is a quantized amount. 