How to Fairly Split Money When Decimals Won’t Divide: 14 Rounding Strategies

1. Discount Allocation

When an order has a 10‑yuan discount that must be split among three products, 10 ÷ 3 = 3.333… cannot be divided evenly. A rule is needed to decide the final discount amount for each product.

2. Multiple Settlement

For a 100‑yuan receipt to be shared by seven people, each should receive about 14.285714… yuan. The article discusses how to handle such division in practice.

3. Payment Fee

If the fee rate is 0.38 % and the receipt is 568 yuan, the fee equals 568 × 0.38 % = 2.158 yuan. The fee must be rounded to two decimal places according to a pre‑agreed rule.

The overarching principle is to avoid over‑paying or under‑receiving any cent, aiming for exactness while ensuring fairness. When perfect equality is impossible, the goal is to reach a consensus that all parties accept.

1. Truncation (去尾法)

Simply discard extra digits after the required decimal places, yielding a slightly smaller result. Suitable for “must not exceed” constraints, such as early splits in multi‑settlement scenarios where the total must not surpass the original amount.

Example: 568 × 0.38 % = 2.159 yuan → truncation gives 2.15 yuan.

2. Ceiling (进一法)

If any non‑zero digit remains after truncation, round up, producing a slightly larger result. Suitable for “must not be lower” constraints.

Example: 568 × 0.38 % = 2.151 yuan → round‑up gives 2.16 yuan.

3. Standard Rounding (四舍五入)

The most common method: round down if the next digit is < 5, otherwise round up. Used by WeChat for transaction fees.

Example: 568 × 0.38 % = 2.158 yuan → round to 2.16 yuan.

4. Round‑Half‑To‑Even (四舍六入五成双)

When the third decimal is 5, look at the second digit: if it is even, keep it; if odd, round up. Provides a more statistically unbiased result.

Examples: 2.145 → 2.14 (even 4); 2.155 → 2.16 (odd 5).

5. Remainder Allocation (余数分配，补差法)

First allocate the integer part, then distribute the remaining cents to achieve zero overall error. Example: split 10 yuan among three items → two items get 3.33 yuan, the third gets 3.34 yuan.

6. Upward Rounding (向上取整)

Always round up any non‑zero remainder, then adjust in the final step to keep the total accurate.

Used in WeChat’s multi‑refund fee handling.

7. Downward Rounding (向下取整)

Simply drop the fractional part, similar to truncation. Combined with remainder‑allocation to correct the total.

8. Bankers Rounding (银行家舍入法)

When the third digit is 5, round to the nearest even second digit. Common in international credit‑card clearing to reduce cumulative error.

9. Rotating Allocation (轮转分配法)

Distribute the extra cent sequentially among recipients, ensuring long‑term fairness, e.g., rotating the 0.01 yuan advantage across multiple settlements.

10. Minimum‑Error Priority (最小误差优先法)

Enumerate all possible rounding combinations and choose the one with the smallest absolute total error. Suitable for high‑precision financial clearing.

11. Probabilistic Rounding (概率舍入法)

Round up with a probability proportional to the fractional part (e.g., 0.333 → 33.3 % chance to round up). Often used for virtual currency distribution in games.

12. Cumulative Remainder (累计余数法)

Accumulate remainders in a “pool” and trigger an adjustment when the pool reaches a threshold (e.g., 1 yuan).

13. Transaction Hedging (交易对冲法)

Offset over‑collected fees in one transaction with under‑collected fees in another, balancing errors across related trades.

14. Composite Strategy Optimization (组合策略优化法)

Combine several of the above methods based on specific business requirements to achieve the most fair and scientific allocation.

Ultimate Solution: Preventive Design

Design pricing or settlement rules that avoid non‑divisible numbers from the start, such as using prices that are multiples of 3 or grouping participants in sizes that divide evenly.