# Price of an ERC20 token¶

Similar to amount, there are two different representations for a token price: decimal price and undecimal price.

## Decimal price¶

**Decimal price** is the price in the sense of natural language, and decimal price is the price based on decimal amount

we continue taking use of example USDT and BNB.

Suppose we need to pay 300 usdt for 1 bnb or need to pay 0.0033 bnb for 1 usdt during the trade, we say the price of bnb by usdt is 300 usdt/bnb or the price of usdt by bnb is 0.0033 bnb/usdt. Here, the price 300 usdt/bnb or 0.0033 bnb/usdt is called decimal price in our sdk

Generally, for tokenA and tokenB ERC20 tokens, assume that we need to pay 3.3 tokenB to acquire 1.0 tokenA, where 3.0 and 1.0 are decimal amounts of tokenB and tokenA during this trade.

Then the decimal price of A by B is 3.3 (tokenB / tokenA), where A by B stands for value of tokenA counted by tokenB. And the decimal_price_BNB_by_USDT is 300 usdt/bnb.

```
1decimal_amount_A * decimal_price_A_by_B = decimal_amount_B
21.0 (tokenA) * 3.3 (tokenB/tokenA) = 3.3 (tokenB),
```

where A_by_B correspond to (tokenB / tokenA) and B_by_A correspond to (tokenA / tokenB).

## Undecimal price¶

**Undecimal Price** is the price used in EVM, and is based on undecimal amount.

As mentioned in the undecimal amount section, there is no decimal amount on block chain, we can only see undecimal amount. We need undecimal price which describe price based on undecimal amount.

In the bnb/usdt example, replace decimal amount to undecimal amount and we can see that we pay 300,000,000 undecimal-amount of usdt for 1,000,000,000,000,000,000 undecimal-amount of bnb (trade1), or we pay 3,300,000,000,000,000 undecimal-amount of bnb for 1,000,000 undecimal-amount of usdt (trade2).

The undecimal price of trade1 is 300,000,000 / 1,000,000,000,000,000,000 (usdt/ bnb).

The undecimal price of trade2 is 3,300,000,000,000,000 / 1,000,000 (bnb / usdt).

Generally, from the decimal price formula of tokenA and tokenB in code block decimal price

We can get

```
1decimal_amount_A * (10 ** decimalA) * decimal_price_A_by_B * (10 ** decimalB / 10 ** decimalA) = decimal_amount_B * (10 ** decimalB)
```

which equals to

```
1undecimal_amount_A * (decimal_price_A_by_B * (10 ** decimalB / 10 ** decimalA)) = undecimal_amount_B
```

And finally we have:

```
1undecimal_price_A_by_B = decimal_price_A_by_B * (10 ** decimalB / 10 ** decimalA)
```

Similar to decimal price, we use A by B stand for value of tokenA counted by tokenB.

In the example of usdt and bnb, decimal_price_BNB_by_USDT is 300 usdt/bnb and undecimal_price_BNB_by_USDT is ` 3 * 10**(-10)`.

Now a problem has arisen. Since undecimal price usually is a float number, check the next section point to find how to describe them in contract.