# Price of ERC20 token¶

here, we describe concepts about price

etc, decimal price and undecimal price point

## decimal price¶

we continue to take use of example USDT and BNB

suppose on a centralized dex, we need to pay 300 usdt for 1 bnb or need to pay 0.0033 bnb for 1 usdt,

then we say the price of bnb by usdt is 300 usdt/bnb or we say 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, tokenA and tokenB as 2 erc20-token, and we assume that we need to pay 3.3 tokenB to acquire 1.0 tokenA. here, 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), here we use A by B stand for value of tokenA counted by tokenB, it means how much tokenB to acquire one tokenA , and in the above example 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)
```

notice: in above formula , A_by_B correspond to (tokenB / tokenA), B_by_A correspond to (tokenA / tokenB)

decimal price is price based on decimal amount

## undecimal price¶

as mentioned in 1.2 undecimal amount, there is no decimal amount on block chain, we can only see undecimal amount so we need undecimal price which describe price based on undecimal amount

see the bnb/usdt example in 2.1 and 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)

more generaly, from decimal price formular 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 is

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

and we can get

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

also, like decimal price, here we use A by B stand for value of tokenA counted by tokenB

and in the example of usdt and bnb decimal_price_BNB_by_USDT is 300 usdt/bnb

undecimal_price_BNB_by_USDT is ` 3 * 10**(-10)`

there is a problem, undecimal price usually is a float number, how to describe them in contract

see next section point.