Significant Figures in Chemistry

Non-zero Digits: All non-zero digits are always significant (e.g., the $4$ and $5$ in a measurement).
Interior Zeros: Zeros located between two non-zero digits are significant.
Leading Zeros: Zeros to the left of all non-zero digits are not significant (e.g., the zero before the $4$ in $0.405$ \,g).
Trailing Zeros: Zeros to the right of all non-zero digits are significant only if a decimal point is explicitly written in the number.
Scientific Notation: When using scientific notation, apply sig fig rules only to the coefficient before the power of $10$ . The $10$ and its exponent are considered exact.

Multiplication and Division: Round the final result to the same number of sig figs as the value with the fewest total significant figures. * Example: $4.60\,mL$ ( $3$ sig figs) multiplied by $0.78\,g/mL$ ( $2$ sig figs) results in $3.588$ on a calculator, reported as $3.6\,g$ .
Addition and Subtraction: The result must have the same number of digits after the decimal point as the measurement with the fewest digits after the decimal point. * Example: A calculation involving $3.7\,mL$ (one decimal place) requires the answer to be reported to one decimal place.
Exact Values: Conversion factors based on definitions (e.g., $1,000\,mL = 1\,L$ ) are exact and do not impact the number of allowed sig figs in a calculation.

0.405 grams: Contains $4$ sig figs (according to the transcript, as the trailing zero after a decimal is significant).
205: This measurement contains $3$ sig figs.
402.0: This measurement contains $4$ sig figs because the decimal makes the trailing zero significant.
Subraction Example: A calculation yielding $4.5\,atm$ is restricted by the one decimal place in $0.3\,atm$ .
Division Example: Dividing using $504\,g$ ( $3$ sig figs) results in an answer reported as $8.62\,mole$ .