The 5 Rules of Significant Figures

• 1
  All non-zero digits are significant. In 284, all three digits (2, 8, 4) are significant → 3 sig figs.
• 2
  Zeros between non-zero digits are significant. In 3007, the two zeros between 3 and 7 are significant → 4 sig figs.
• 3
  Leading zeros are NOT significant. In 0.0042, the three leading zeros are not significant. Only 4 and 2 are → 2 sig figs.
• 4
  Trailing zeros after a decimal point ARE significant. 1.500 has 4 sig figs; the two trailing zeros indicate precision to the thousandths place.
• 5
  Trailing zeros in a whole number are ambiguous. 1200 could have 2, 3, or 4 sig figs. Use scientific notation (1.2 × 10³ = 2 sig figs) to be unambiguous.

Rounding Examples

Original	Rounded	Sig Figs
0.003407	0.00341	3
12345	12300	3
0.10500	0.105	3
9876.54	9880	3
0.000598	0.000600	3
1,234,567	1,230,000	3

Why Do Significant Figures Matter?

Significant figures communicate the precision of a measurement. If a scale reads 12.3 g, you know the mass to the nearest tenth of a gram — writing 12.300 g would falsely imply precision to the nearest milligram. In science and engineering, misrepresenting precision can lead to errors in calculations, reports, and real-world applications.

When multiplying or dividing measurements, your answer should have the same number of sig figs as the measurement with the fewest sig figs. When adding or subtracting, round to the same number of decimal places as the least precise measurement.

Sig Figs in Scientific Notation

Scientific notation removes all ambiguity. The coefficient always shows exactly how many digits are significant:

1.20 × 10⁴ → 3 sig figs (the trailing zero after the decimal is significant).

1.2 × 10⁴ → 2 sig figs.

If you need to express 12000 with exactly 3 sig figs, write it as 1.20 × 10⁴.