>>That depends on the context. If the context is currency, you will mostly only consider two decimals
>>
>>In your tax problem
>>
>>

>>base for federal tax = 500.00
>>round(500.00 * .05, 2) = 25.00 && federal tax
>>
>>base for  provincial tax = 500.00 + 25.00 = 525.00
>>
>>round( ( 500.00 + 25.00) * 9.5 / 100, 2) = 49.88 && provincial tax
>>
>>Total = 500.00 + 25.00 + 49.88 = 574.88
>>

>>
>>So, if you want to reverse the process, you have to apply the steps backwards - one at a time - do not combine them - this is no algebra
>>After each division you have to round to 2 decimals
>>
>>

>>Total = 574.88
>>(1) 
>>Base for provincial tax = round( 574.88 / 1.095, 2) = 525.00
>>
>>provincial tax = 574.88 -  525.00 = 49.88
>>
>>(2) 
>>base for federal tax = Base for provincial tax / 1.05
>>base for federal tax = round( 525.00 / 1.05, 2)  = 500.00
>>federal tax = 525.00 - 500.00 = 25.00
>>
>>

>>
>>iow, you need two decimals since the taxes were calculated with two decimals
>>
>>You apply the steps backwards
>> - dividing and rounding to 2 decimals to obtain the base
>> - subtracting to obtain the tax ( do not use a division here )
>
>Thanks, this sums it all assuming you have the original amount. In the other thread, where I am looking for the formula, we do not have the original amount. We only have the total tax amount and we need to collect each tax from that total tax amount.


I don't think that is possible - due to rounding scenarios

Take this for example

Provincial tax on  $1.74 is round(1.74 * .095, 2) or $0.17

What amount is the base of $0.17 tax ?

round($.017 / .095,2)  = $1.79  (see how this compares to the original $1.74)

iow, you need the Total including all taxes, and knowing the two percentages and the order in which they were applied, you work your way back