Precentance differerence on and off?

Question

When calculating VAT on a number and off a number there is a difference, why is that? For example when putting a 24% VAT on 532.647 the VAT is 127.835 if you then ad the two numbers you get 660.483. When calculating the VAT off that number we are told to use the number 19,35 and when that is applied to the number 660.482 you get the VAT of 127.803 and there is a 32 difference in the calculations. Why is that and does this increase when numbers get higher? When applying the same calculations to the number 1.000 you get olmost the same VAT when you put on 24% and when you calculate 19,35% of 1.240 you get 240 and 239,94 with 19,35. Kind regards, Björn Styrmir

Answer 1

This is just a rounding issue. If VAT is $v$, as a decimal, then your computation computes $\frac {v}{1+v}$. If $v=.24$ as in your example, you get $0.193548387...$, so to avoid the discrepancy they should have said "use $19.3548387...\%$".