The eighth decimal: a unit below the display
When the unit of an account is smaller than the display, the fraction stops being an accident of rounding and becomes a permanent property of every balance. This page takes eight such accounts.
- balances
- 8
- decimals
- 8
- with dust
- 5
- largest dust
- 0.00499999
In a currency with eight decimal places, the smallest unit is one hundred-millionth of a coin, far below the two places a balance is usually shown. On eight invented balances, five held a fraction smaller than the shown cent and the largest was 0.00499999, so the account held money the display could not express at all.
Eight balances, five with dust
The pattern is the balance page's disagreement with the sign reversed: where the unit is tiny, the fraction that cannot be shown is a permanent residue rather than a passing tail, and it sits in the account until something spends it or the account is closed.
| Held | Shown | Dust | Note |
|---|---|---|---|
| 0.12500000 | 0.13 | 0.00000000 | rounds up on display |
| 1.00000001 | 1.00 | 0.00000001 | one unit of dust |
| 2.34999999 | 2.35 | 0.00000001 | one unit short of the cent |
| 0.00499999 | 0.00 | 0.00499999 | shown as nothing |
| 10.00000000 | 10.00 | 0.00000000 | exact |
| 0.99999999 | 1.00 | 0.00000001 | a whole unit short |
| 7.00000001 | 7.00 | 0.00000001 | one unit of dust |
| 3.33333333 | 3.33 | 0.00000333 | a third repeated |
| 8 balances | - | 5 with dust | max 0.00499999 |
What the display can and cannot say
Two points belong here and neither is a criticism of either currency. First, a coarse display is not a coarse account. An eight-decimal account shown to two places is storing fourteen digits that a reader never sees, and every one of them can be the difference between a withdrawal clearing and being refused, which is the balance page's finding stated without a fraction to blame. Second, dust is a residue, not a fee. It is money the account genuinely holds at a precision too small to spend in that currency's chosen display, and what happens to it at the end depends on the operator's closure rules rather than on arithmetic. The fiction worth discarding is that a balance shown as 0.00 is empty: on sample I it can hold 0.00499999, which is almost half a cent, at a precision the screen will never show.
- Where an eight-decimal currency is held, ask for the balance at full precision before concluding an account is empty.
- Expect a withdrawal to leave up to one smallest unit behind, and expect the display to round it to nothing.
- Do not convert dust between currencies expecting to recover it: a conversion rounds and the unit may round it away entirely.
- Read the closure rules for residual balances in the currency in question; they differ from one operator to another.
- Remember the fraction is held even when it cannot be shown, so it is neither lost nor a charge.