How do you read currency exchange rates in terms of domestic and foreign currency?

Question

I am having some issues understanding how to read exchange rates. E is the exchange rate

I read online that if we have for example E\$/€, then the base currency in this case is the dollar and the quote currency is the euro . In this case , if E\$/€ = 1.50, this would mean that 1$ would buy 1.50€.

However, in my textbook i am having some miss understandings. In my textbook , the domestic currency is the EURO and the foreign currency is the DOLLAR.

It states : The exchange rate can be defined in two ways, the first one being

1) The price of the domestic currency (euro) in terms of the foreign currency (dollar). If 1€ =$1.50 , then E=\$/1€=1.50.

If i look at E=\$/1€=1.50 , i see E\$/€.

This implies how in this case, the base currency , orelse 1€, is written as a the second currency , and E\$/€= 1.50 . With one euro you can buy 1.50 dollars.

2) The second way of writing the exchange rate is the price of the foreign currency in terms of the domestic currency . In this case E=€/\$= €0.65 . In this case, the base currency is also written as the second currency , with 1 dollar being able to buy 0.65 euros.

Then my questions is that i'm not sure why there are different ways of writing the exxhange rate. On internet E\$/€=1.50 means that with one dollar you can buy 1.50 euros. In my textbook, E=\$/1€=1.50. , which i assume is the same thing as E=\$/€= 1.50 means that with 1 euro you can buy 1.50 dollars.

What am i misenterpeting ?

Answer 1

The currency in the denominator is always the currency that is being priced. For example $\$/€=x$ means that the price of euros is $x$ dollars. That is, if you want $1$ euro, you have to pay $x$ dollars (Keep in mind that in practice the euro will have a bid and an ask price, but in both cases, the euro will be in the denominator). In fact, the notation $\$/€$ should be read "dollars per euro". In contrasts, $€/\$$ reads "euros per dollar", so the currency that is being priced now is the dollar (of course in terms of euros).

With this in mind, the statement online that says "E$\$/€ = 1.50$, [...] would mean that $1\$$ would buy $1.50€$". was either misunderstood or simply wrong. Such notation means that $1.50\$$ is equivalent to $1€$.

Finally, keep in mind that, in practice, countries decide to write their exchange rate in terms of the dollar according to convenience of the numbers. For example, the exchange rate for the Mexican peso is almost always written as peso/dollar. Technically speaking such notation is giving the price of dollars, but note that it is more convenient to say that E$(peso/dollar)=24$ pesos rather than saying E$(dollar/peso)=0.041666$ dollars. This creates no problem since both quotes are equivalent.