有效数字Significant figures

非零数字都是有效数字；数字中间的“0”是有效数字（1.05 为 3 位）；首位非零数字前面的“0”只起定位作用，不是有效数字（0.0052 为 2 位）；小数末尾的“0”是有效数字（2.50 为 3 位）；整数末尾的 0 不确定，应用科学计数法表示（2.5 × 10³ 为 2 位，2.500 × 10³ 为 4 位）；pH、lgK 等对数值的有效数字只看小数部分（pH = 10.28 为 2 位）。纯数字和定义值（如 1 L = 1000 mL、化学计量数）视为无限多位。

All non-zero digits are significant; zeros between them are significant (1.05 has three); leading zeros only locate the decimal point (0.0052 has two); trailing zeros after a decimal point are significant (2.50 has three); trailing zeros in an integer are ambiguous and should be written in scientific notation (2.5 × 10³ has two, 2.500 × 10³ four); for logarithms such as pH and lgK only the decimal part counts (pH 10.28 has two). Exact numbers and defined values, such as 1 L = 1000 mL and stoichiometric coefficients, have unlimited figures.

加减运算：结果保留的小数位数与小数位数最少的数相同（以绝对误差最大者为准）；乘除运算：结果的有效数字位数与有效数字位数最少的数相同（以相对误差最大者为准）；修约采用“四舍六入五成双”：尾数 ≤ 4 舍去，≥ 6 进位，等于 5 时若后面还有非零数字则进位，否则使保留的末位为偶数。计算过程中可多保留一位，最后再修约。

For addition and subtraction, keep as many decimal places as the number with the fewest (the largest absolute uncertainty decides); for multiplication and division, keep as many significant figures as the number with the fewest (the largest relative uncertainty decides). Round by 'round half to even': drop a final digit of 4 or less, round up 6 or more, and for exactly 5 round up if any non-zero digits follow, otherwise make the retained last digit even. Carry one extra digit through intermediate steps and round only at the end.

仪器精度决定可记录的位数：万分之一分析天平称量记到 0.0001 g（如 0.2035 g，4 位），50 mL 滴定管读到 0.01 mL（如 22.45 mL），移液管和容量瓶按其精度记录（25.00 mL）。写成 25 mL 和 25.00 mL 含义不同，前者暗示精度只有 ±1 mL。

The instrument sets the digits you may record: an analytical balance reads to 0.0001 g (0.2035 g, four figures), a 50 mL burette to 0.01 mL (22.45 mL), and pipettes and volumetric flasks to their precision (25.00 mL). Writing 25 mL rather than 25.00 mL implies a precision of only ±1 mL.