Currency Conversion Question

[DFF]

Ok...if you convert 1.00 Euro into U.S. dollars, it equals 1.56955 -- an increased difference of 57%.

However...

If you convert 1.00 U.S. dollar into Euros, it equals 0.637125 -- a decreased difference of 36%.

These differences, percentage wise, should be equivalent to one another, but they aren't.

Why is this?

BTW -- to further clarify, these are the two specific answers I'm looking for:

1 Euro is _____ percent greater than 1 dollar.

1 U.S. dollar is _____ percent less than 1 Euro.

For reference, here's a link to a currency converter.

http://www.xe.com/ucc/convert.cgi

 

[AceNZ]

Why is this?

It's called "math": basic "fractions" or "algebra".

E = 1.56D, or E/D = 1.56

take the reciprocal of both sides:

D/E = 0.64

 

[DFF]

I understand that part.

What I'm trying to wrap my brain around is why the Euro is worth 57% more than the dollar, yet the dollar is worth 36% less than the dollar.

It seems they should be equal. If one is worth 57% more than the other should be worth 57% less.

 

[theseus51]

It's like why is a quarter worth 500% more than a nickel, but a nickel is worth 80% less than a quarter. 25/5 and 20/25.

Or if you have $80 and $100. $80 is worth 20% less than $100. But $100 is 25% more than $80. 20/100, 20/80.

 

[Corydoras]

The important thing to remember is, percent OF WHAT?
A percentage is always a portion of something.

One quarter is worth 500% OF a nickel, while one nickel is worth 20% OF a quarter.

One euro is worth 157% OF a dollar, while one dollar is worth 64% OF a euro.