Vocabulary | |
scientific notation significant digit |
If you're not in the Americas, you may prefer the following less colorful way to say the same thing:
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:
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 × 10^{1} mm = 2.0 × 10^{4} 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 × 10^{2}. 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 × 10^{7}. 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. |
Copyright © 1997-2010 by Fred Senese
Comments & questions to fsenese@frostburg.edu
Last Revised 08/17/15.URL: http://antoine.frostburg.edu/chem/senese/101/measurement/faq/print-simple-sigfig-rules.shtml