Rounding & Cents
Money divides unevenly. Ten dollars across three people is $3.333… each, and no till can charge that. This page explains how Pratham ResPOS places the leftover cents, and why the answer is always right even when two customers pay amounts that differ by a cent.
The rule
When an amount has to be shared - a discount across items, a delivery charge across a bill, an item across its units - the POS:
- Works out each share exactly.
- Gives everyone their whole cents.
- Hands the leftover cents, one at a time, to whoever was owed the most of a part-cent.
The result always adds back to the original amount exactly.
Why not just round each share?
Because rounding each share on its own loses or gains money.
$10.00 shared three ways:
| Method | Shares | Total |
|---|---|---|
| Round each share | $3.33, $3.33, $3.33 | $9.99 ✗ |
| The POS | $3.34, $3.33, $3.33 | $10.00 ✓ |
A cent short does not sound like much, but it means the parts of a bill no longer match the bill. On a receipt it shows up as a total that does not add up.
A $10.00 discount over three items at $33.33, $33.33 and $33.34:
Rounding each gave $3.33 three times - $9.99 printed against an order that said $10.00. The three receipts contradicted the order they came from. The POS now gives $3.34, $3.33, $3.33.
INFO
The same cart with a coupon drifted the other way - up a cent - while the delivery charge drifted down. A fix in one direction only would have missed one of them, which is why every shared amount goes through the same rule.
Where the odd cent lands
The leftover cent goes to the largest share. Two reasons:
- On the biggest line, a cent is proportionally the least visible.
- Two identical items are never split apart by it.
Example - a $10.00 delivery charge across items of $0.01, $0.01 and $99.98:
Almost the whole charge lands on the $99.98 item - over $9.90 of it. The two one-cent items are not each handed a third of the delivery.
Splitting an item across its units
An item with a quantity of 3 is divided into three units so that people can take one each. The same rule applies, so the three unit prices add back to the line exactly.
A line of 3 at $13.34 becomes $4.45, $4.45, $4.44 - not an impossible $4.4466 each.
TIP
This is why two people can pay a cent apart for what looks like the same item. Neither is wrong. The unit price shown under an item is the line divided evenly and is indicative only - the amounts actually charged always add back to the line total.
Items sold by weight - a fractional quantity like 0.75 kg - are not divided. They are claimed whole, by one person.
What this guarantees
Because every shared amount follows the same rule:
- Each item's share of the bill adds back to the order total, exactly.
- Any grouping of items adds up correctly - so a bill split four ways comes to the same as the bill paid by one person.
- A person paying cash gets the same discount whether they pay alone or as part of a split.
WARNING
Before this rule was applied everywhere, a split customer could pay up to 9 cents more than the same bill paid by one person. Small, but it meant splitting a bill cost the customer money - which is why every shared figure now goes through the same calculation.
Common questions
Two customers paid a cent apart for the same item. Is that a bug?
No. When a line is divided across units, the units can differ by a cent - $4.45 and $4.44 rather than an impossible $4.445 each. The amounts always add back to the line total.
Why is one person's share of the delivery charge so much bigger?
Shared amounts are split in proportion to what each person is buying, not equally. Someone with $100 of food carries far more of a delivery charge than someone with a $2.00 drink.
The discount on three receipts adds to a cent more than the order discount. Should I worry?
That should not happen now - the shares are calculated so they add back exactly. If you see it, note the order number and report it, because it means a figure somewhere is being rounded on its own.