Significant figures (significant digits)

Basic rules for counting

• All nonzero digits are significant (e.g., 123 has three significant figures).
• Zeros between nonzero digits are significant (e.g., 2004 has four significant figures).
• Leading zeros are not significant; they only locate the decimal point (e.g., 0.0052 has two significant figures).
• Trailing zeros in a number with a decimal point are significant (e.g., 2.300 has four significant figures).
• Trailing zeros in a number without an explicit decimal point can be ambiguous; scientific notation clarifies significance (e.g., 2300 may be two, three, or four significant figures unless written as 2.300×10^3 or 2.3×10^3).
• Exact counts and defined constants (for instance, 12 eggs or 1 meter = 100 centimeters by definition) are considered to have infinite significant figures for calculation purposes.

Arithmetic with significant figures

When multiplying or dividing, the result is rounded to the same number of significant figures as the least precise factor. When adding or subtracting, align decimals and round the result to the least precise decimal place among the operands. These rules are practical conventions to avoid suggesting greater precision than the data support, but for rigorous uncertainty handling, use formal error propagation instead.

Uses, examples, and importance

Scientists, engineers, and technicians use significant figures to report measurements, calibrations, and computed values so that readers understand the implied precision. Examples:

• 2300 — often interpreted as two significant figures unless additional notation indicates otherwise.
• 2.300 × 10^3 — clearly four significant figures because scientific notation removes ambiguity.

History and notable distinctions

The concept grew out of needs in measurement science and error analysis: as instruments and methods were refined, conventions developed to communicate precision clearly. Significant figures are a helpful shorthand but differ from the statistical notion of uncertainty; they do not replace explicit uncertainty estimates or confidence intervals when detailed error information is required.

Common pitfalls

Be cautious about trailing zeros and assumed precision from calculators. Use scientific notation to avoid ambiguity and prefer explicit uncertainty statements when precision matters for decisions or further calculations.