Significant Figures Calculator

1. All non-zero digits are significant. In 345.6, all four digits are significant. This is the most basic rule and applies in every case.
2. Zeros between non-zero digits are significant. In 4005, all four digits are significant because the zeros are "sandwiched" between 4 and 5.
3. Leading zeros are never significant. In 0.00450, the three leading zeros just show the magnitude. Only 4, 5, and the trailing 0 are significant, giving 3 sig figs.
4. Trailing zeros after a decimal point are significant. In 3.40, the trailing zero is significant, so there are 3 sig figs. In 3.40×10³, same rule applies.
5. Trailing zeros without a decimal point are ambiguous. The number 1200 might have 2, 3, or 4 sig figs. Write 1.200×10³ to make clear all four are significant.

For addition and subtraction: the result has the same number of decimal places as the least precise number. For 12.11 + 18.0 = 30.11, rounded to 1 decimal place = 30.1.

For multiplication and division: the result has the same number of significant figures as the input with the fewest sig figs. For 4.56 × 1.4 = 6.384, rounded to 2 sig figs = 6.4.

Rules for counting significant figures:

Number       Sig Figs   Reason
---------    --------   ------
345.6        4          All non-zero digits
4005         4          Zeros between non-zeros count
0.00450      3          Leading zeros do not count; trailing zero after decimal counts
1200         2 (ambiguous) Trailing zeros, no decimal point
1.200×10³    4          Scientific notation makes it unambiguous
100.         3          Decimal point after 100 makes trailing zero significant
0.1          1          Leading zeros not significant

Rounding to 3 sig figs:
  12345   → 12300
  0.012345 → 0.0123
  1.2345  → 1.23

Addition rule (decimal places):
  12.11 + 18.0 = 30.1   (1 decimal place)
  1.002 + 3.5  = 4.5    (1 decimal place)

Multiplication rule (sig figs):
  4.56 × 1.4 = 6.4      (2 sig figs)
  2.000 × 3.1 = 6.2     (2 sig figs)