Say the Pound V Dollar rises 80% then on the Dollar V Pound its fallen -44.444%

I work it out as follows:-

0.8 Divided by 1.8 = 0.444

What I can't work out is:-

If I know the Dollar V Pound as fallen -44.44%

How do I get its an 80% rise on the Pound V Dollar using -44.444?

Thanks

Gary

This mathematical confusion occurs whenever you try to compare things using using percent gains or loss based on two different bases. In your example the math works out so that the ratio of the value of pound versus dollar is the reciprocal of the value of dollar versus pound:


Pound\ v\ Doillar \ =\ \frac {1 + 0.8} 1 \ =\ 1.8 \\
Dollar\ v\ Pound\ =\ \frac {1-0.444} 1 = 0.556 \\
0.556 = \frac 1 {1.8}


So yes, your math is correct.

Here's another example of the same effect: consider whether it's better to invest money and get a flat 20% return, or make an investment that first gives you a 100% return which is then followed by an 80% loss. It may sound like the result should be the same, but it's not. If you have $100 to invest the former gives you a $20 profit, whereas the latter causes you to lose $60. That's a big difference!