Units and Measurements - Significant Figures

Significant figures in a measurement are those digits that are known reliably plus one digit that is uncertain.

Rule 1: All non-zero digits are significant. For example, $123.45$ has $5$ significant figures.

Rule 2: All zeros occurring between two non-zero digits are significant, regardless of the decimal point (e.g., $100.05$ has $5$ significant figures).

Rule 3: Leading zeros (zeros to the left of the first non-zero digit) are not significant. They only indicate the position of the decimal point (e.g., $0.0025$ has $2$ significant figures).

Rule 4: Trailing zeros in a number with a decimal point are significant (e.g., $3.500$ has $4$ significant figures; $0.060$ has $2$ significant figures).

Rule 5: Trailing zeros in a number without a decimal point are ambiguous and are generally not considered significant unless specified. To avoid this, use scientific notation ($a imes 10^b$).

Arithmetic Rule (Addition/Subtraction): The final result should retain as many decimal places as are present in the measurement with the least number of decimal places.

Arithmetic Rule (Multiplication/Division): The final result should retain as many significant figures as are present in the measurement with the least number of significant figures.

Rounding Off: If the digit to be dropped is $5$ followed by zeros, the preceding digit is increased by $1$ if it is odd, and left unchanged if it is even (e.g., $2.735$ becomes $2.74$ while $2.745$ becomes $2.74$).