1/1.001 - 1*0.999 is non zero. But whats the difference between multiplying by 0.999 and dividing by 1.001?
If say I was doing some foreign exchange at the airport and they wanted a 0.5% transaction fee, and I wanted to exchange $100 USD for AUD at a rate of 2. Would I divide the result by 1.005 or multiply it by 0.995?
I feel like if they "take 0.5% commission" it would mean:
AUD/2=x AUD=(USD)*2 AUD= (x+0.005x)*2 where 1.005x= 1USD
we take away the commision and so:
AUD= x*2 AUD=(USD*2)/1.005
However, multiplying by 0.995 also makes sense, when they say, we take 0.5% of what you get as comission, leaving you with 0.995 of what you had originally.
Does one interpretation actually make more sense than another when talking about taking comissions or is one chosen over the other by convention? would you always rather they divide by (1+commission) rather than multiply by (1-commission)?