Scenario 1
Let’s assume, we have a farmer named Chirag. Chirag booked a spraying service for one acre. Our spraying rate per acre is 10000 cents and we are offering a discount of 10.66 percent.
So, he gets the following bill.
| Spraying Cost | Discount | Total | Final after Rounding off |
| 10000 cents | 10.66% | 8934 cents | 89 $ |
He pays the bill before spraying, it’s prepaid.
Now, when spraying happens on his farm, it’s actually 2 acres and not 1 acre that he told before. So, we give him another bill for his extra acre.
| Spraying Cost | Discount | Total | Final after Rounding off |
| 10000 cents | 10.66% | 8934 cents | 89 $ |
So, How much does Chirag pay total for 2 acres?
89 + 89 = 178 $.
Scenario 2
But what if, Chirag had booked for 2 acres in the first go itself?
What would the bill look like?
| Spraying Cost | Discount | Total | Final after Rounding off |
| 20000 cents | 10.66% | 17868 cents | 179 $ |
What?
179 $.
That’s one dollar more than the previous case.
Where did the magic happen?
It’s in rounding.
Assume we have new denomination called unit where 10^4 units = 1 $
Now, if we use 10^4 as storage instead of cents, the problem will still persist but it will have negligible practical effect. Let’s see how. We will replay both scenarios that we discussed above again.
So now, 10^4 units = 1 $
Scenario 1:
When he booked 1 acre farm:
| Spraying Cost | Discount | Total | Final after Rounding off |
| 1000000 units | 10.66% | 893400 units | 89 $ |
When he later booked for one more acre:
| Spraying Cost | Discount | Total | Final after Rounding off |
| 1000000 units | 10.66% | 893400 units | 89 $ |
Total paid till now: 178 $
Scenario 2:
If he would have booked 2 acres:
| Spraying Cost | Discount | Total | Final after Rounding off |
| 2000000 units | 10.66% | 1786800 units | 178 $ |
Here, in both cases, we have paid 178 $.
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