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Imagine I want to buy a piece of clothing. The price is €20. I want to tell my American friend about how much it costs in dollars.

So my question is: How do native people say this?

I may use several sentences like:

€20 is worth $23.

€20 is equal to $23.

The value of €20 is equal to $23.

Do native people use a similar sentence? If not, How do they talk about currency exchange?

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The most common way to say this is, "is about $23". Saying "is equal to" also makes sense since you're comparing two measurements.

Currencies are used two different ways. "$20" can mean twenty instances of a dollar. A dollar is a thing you can have some number of. But more commonly, "$20" is used as a measurement of value. It isn't twenty of any particular discrete thing, it's a measurement of the amount of value.

That's why saying "is worth" doesn't really make sense, because the phrase "is worth" is used to describe the value of things and "€20" is a measurement of value, not a thing. We don't talk about the value of currency amounts because currency amounts is how you measure value. It's almost like saying something's length is 20 feet long. No, it's length is 20 feet and it's 20 feet long, but it's length is not 20 feet long because lengths don't have lengths. $20 is already a value, and values don't have values.

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    In informal everyday conversation, tourists are very likely to say that x amount of the local currency is worth y dollars. It's idiomatic and grammatically correct although not the proper way of expressing the comparative values. If you want to express them formally, X local currency is equivalent to Y dollars. – Ronald Sole Sep 2 '18 at 23:31
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    It is correct because "20 dollars" can also mean 20 instances of a thing with a particular value. That's not what we usually mean by "20 dollars", we mean a measurement of worth. A measurement of worth isn't worth anything, it's a measurement. A think is worth twenty dollars because twenty dollars is a measurement of worth. But twenty dollars (as a measurement of worth) isn't worth anything. – David Schwartz Sep 2 '18 at 23:59
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In an informal conversation I would simply tell your friend

"That dress is (about) twenty dollars."
"That would be $20"

I use "about" since exchange rates are calculated to 4 decimal places.
Your wording seems to want to explain what the FX rate is instead of how much something is.

Since I am an American, I'm interested to know what a dollar is worth, for example

The Pound is one thirty (130)

meaning that a British Pound costs $1.30, so I immediately know that the price of my £10 GAP shirt in London is 30% more than my $10 GAP shirt in New York City.

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