Distribute Value by Row Percentage in SQL

I have a category, percentage table in SQL (the table itself has been obtained by the following query:

SELECT p.category, 
       sum(p.sales) * 100 / sum(sum(p.sales)) OVER () AS percentage
FROM product p
GROUP BY p.category;

Category	Percentage
Books	20.51%
Clocks	9.49%
Pens	60.2%
Desks	9.8%

How can I spread $100 (whole dollars, no cents) across the categories by percentage keeping in mind the GROUP BY and windows functions already in the query.

Intended Solution:

Category	Percentage	Amount
Books	20.51%	21
Clocks	9.49%	9
Pens	60.2%	60
Desks	9.8%	10

I have been googling but I can't seem to find a similar scenario.

Solution

You could just round() the percentages you already have because they already sum up nicely to a 100 when rounded, but that's because Books round up and Clocks round down, balancing each others' rounding errors out. If you lose that balance, you'll get Amounts summing up to less than a 100 or more than a 100: demo

SELECT category
    ,p::numeric(5,2) AS percentage
    ,(sum(p%1)over()::int >= row_number()over() )::int + trunc(p) AS amount
FROM ( SELECT category, 
              sum(sales)*100/sum(sum(sales))over() AS p
       FROM product
       GROUP BY category) a;

This distributes the rounding remainders evenly. You can also round all values until the last one and make the last one catch the remainders. Some banks and insurance companies prefer to set up installments this way:

SELECT category
      ,percentage::numeric(5,2)
      ,case when lead(percentage)over() is null
            then (sum(percentage%1)over()+floor(percentage))::int
            else floor(percentage)::int
       end AS amount 
FROM ( SELECT p.category, 
              sum(p.sales)*100/sum(sum(p.sales))over() AS percentage
       FROM product p
       GROUP BY p.category) a

Use of floor() keeps the remainder sum positive to avoid that last one dropping below 0.