Significant Figures

Significant figures: indicate the precision of the measured quantity

Rules

• Nonzero Digits → SIGNIFICANT

  • ex) 111 → 3 SF

• Interior Zeros → SIGNIFICANT

  • ex) 101→ 3 SF

• Leading Zeros → NOT SIGNIFICANT

  • 000001355 → 4 SF

• Trailing Zeros BEFORE a decimal point and AFTER a nonzero number → SIGNIFICANT

  • 4000. → 4 SF

• Zeros at the end of a number without a written decimal point are ambiguous and should avoided using scientific notation

  • ex) 1.23 x 10³ → 3 SF

Calculations

• ADDITION/SUBTRACTION: the answer should have the same # of decimal places as the measurement with the fewest

• MULTIPLICATION/DIVISION: same # of sig figs as the measurement with the fewest

• Follow PEMDAS and associated rules when doing multiple calculations

Rounding (after last sig fig)

• 0-4: drop it

• 5-9: round up the last sig fig by 1

• ROUND AT THE END OF CALCULATIONS