The Atlantic-Pacific Rule says:
"If a decimal point is Present, ignore zeros on the Pacific (left) side. If the decimal point is Absent, ignore zeros on the Atlantic (right) side. Everything else is significant."
If you're not in the Americas, you may prefer the following less colorful way to say the same thing:
- Ignore leading zeros.
- Ignore trailing zeros, unless they come after a decimal point.
- Everything else is significant.
The rule is easy to use and to remember, but it lets you count significant digits without having the slightest idea what they really are.
If you feel comfortable with scientific notation, the simplest rule for counting significant digits is:
"Convert the number into scientific notation.
Any leading or trailing zeros the decimal point bumps past in the conversion will vanish. Everything else is significant."
Writing measurements in scientific notation shows that the significant part of the measurement doesn't change when you change units. For example, 2.0 cm = 2.0 × 10-2 m = 2.0 × 101 mm = 2.0 × 104 µm, all with 2 significant digits.
Here are some examples that apply both rules. The nonsignificant zeros are colored blue.
|Number||Atlantic-Pacific rule||Scientific notation rule|
|0.001010||decimal point Present: ignore zeros on the Pacific side. 4 sig. digits.||In scientific notation: 1.010 × 10-3. 4 sig. digits. The decimal point moved past the three leading zeros; they vanished.|
|0.30000||decimal point Present: ignore zeros on the Pacific side. 5 sig. digits.||In scientific notation: 3.0000 × 10-1. 5 sig. digits. The decimal point bumped past the leading zero; it vanished.|
|100.0000||decimal point Present: ignore zeros on the Pacific side (none!) 7 sig. digits.||In scientific notation: 1.000000 × 102. The decimal point moved past two zeros, but they aren't trailing zeros; they're in the middle of the number. 7 sig. digits.|
|12303000||decimal point Absent: ignore zeros on the Atlantic side. 5 sig. digits.||In scientific notation: 1.2303 × 107. The decimal point moved past the trailing three zeros; they vanished. It moved past the zero between the threes, too, but that's not a trailing or leading zero; it stays. 5 sig. digits.|
- H. M. Stone, "Atlantic-Pacific sig figs (INS)", J. Chem. Educ., 66, 829 (1989).
Author: Fred Senese firstname.lastname@example.org