The display: a column that does not add up

Every number on a statement is rounded before it is shown, and a single total is rounded once from the full precision. The two are not the same, and on this page the column is larger than its own total.

Open the partner account What rounding cannot do

Sample spec

lines: 6
shown sum: 28.34
true total: 28.31
gap: 0.03

the unitThe smallest amount the currency can express. In a two-decimal currency it is 0.01; the increment a stake must take is coarser and published per market.

the directionWhich way each rounding goes: down on a stake and a return, up on a duty and down on a prize. It is a rule, published, and it decides who keeps the fraction.

the volumeOne unit per event is nothing once and a figure at scale: on the samples, two thousand events of the same size retain 60.00 from the digits alone.

Direct answer

A statement shows each line rounded to two places and computes the total from the full precision of every line before rounding it once. On an invented statement of six lines the shown column added to 28.34 while the same six numbers at full precision totalled 28.31, so the column was 0.03 larger than its own total.

One statement, six lines

The six lines are ordinary: a stake, a return, a credit, a fee, a duty and a balance. Each is shown to two places. The total is not, and that is the whole of the disagreement.

Sample J - six lines shown to two places against their full precision
Line	Full precision	Shown	Shown minus true
stake	5.0450	5.05	+0.0050
return	7.9950	8.00	+0.0050
credit	2.0050	2.01	+0.0050
fee	0.1550	0.16	+0.0050
duty	0.7650	0.77	+0.0050
balance	12.3450	12.35	+0.0050
total	28.3100	28.34	+0.0300

sample J - the column against its own total 6 lines shown: 5.05 + 8.00 + 2.01 + 0.16 + 0.77 + 12.35 = 28.34 6 lines exact: 5.0450 + 7.9950 + 2.0050 + 0.1550 + 0.7650 + 12.3450 = 28.3100 shown total: 28.3100 rounded once = 28.31 28.34 - 28.31 = 0.03 - and each line was rounded up by exactly half a unit, so six roundings moved the column six times while the total was rounded once.

Why the two methods differ

This is not an error and not a hidden charge; it is the difference between rounding each term and rounding the sum. Six lines each rounded up by half a unit move the column by three units, while the total rounded once moves by one at most. A reader who adds up the column by hand will therefore disagree with the printed total by up to half a unit for every line on the page, and on a statement with twenty lines the same method can produce a gap of a tenth. The useful habit is to treat a printed total as authoritative and the column as an approximation of it, rather than the reverse - because the total is computed from the truth and the column is computed from six roundings of it.

Compare a statement's printed total against the full-precision figures where they are available, not against the shown column.
Do not conclude that a small gap between a column and its total is a charge; it is the arithmetic of rounding each term separately.
On long statements, expect the gap to grow with the number of lines, not with the amounts.
Where a reconciliation tool uses the shown column rather than the stored values, treat a small mismatch as expected rather than as a discrepancy.
Keep the two methods apart in your own accounting: round the terms for reading, and the sum for deciding.

The display: a column that does not add up

One statement, six lines

Why the two methods differ

Read next