Measurement and Vectors - Theory & Concepts - Significant Figures

Fundamental principles of measurements, SI units, dimensional analysis, and vector algebra in physics for engineers.

Interactive engineering simulation

Significant Figures & Measurement Lab

Learn the fundamental rules of significant digits. Compare real vs. measured values in the Lab, or parse complex arithmetic in the Sig-Fig Engine.

Interactive Expressions

Operand A

Operation

Operand B

Significant Figure Guidelines

Non-zero digits are always significant ( $4.7$ has $2$ sig figs).
Captive zeros between non-zeros are significant ( $503$ has $3$ sig figs).
Leading zeros are never significant ( $0.02$ has $1$ sig fig).
Trailing zeros are significant only if a decimal point is explicitly shown ( $15.0$ has $3$ sig figs; $150$ is ambiguous).

Step-By-Step Parse Logic

Operand A (14.50):

Decimal present. Non-zero digits and trailing zeros are significant. Zeros before the first non-zero digit () are leading zeros and not significant. Total significant figures: 4. Decimal places: 2.

Operand B (3.2):

Decimal present. Non-zero digits and trailing zeros are significant. Zeros before the first non-zero digit () are leading zeros and not significant. Total significant figures: 2. Decimal places: 1.

Multiplication/Division Rule: Round to the least number of significant figures.

Operand A has 4 sig figs. Operand B has 2 sig figs. The least is 2 sig figs. Rounding the raw result (46.4) to 2 sig figs yields: 46.

Operand A Sig Figs

Operand B Sig Figs

Least Sig Figs

Raw Mathematical Output

46.4

Significant Figure Rounded

Model scope and verification

Use the displayed units and idealizations, then verify the governing balance or compatibility equation before interpreting the result.

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