If you can understand significant figures, you can understand the difference between precise and imprecise information.

The accepted use of significant figures can be found in various on line sources such as MathWorld or the Reference.com, where the following logical rule is specified:

Ignoring any decimal point in a number, start at the left end of it and move right; when a non-zero digit is found, that digit and all digits to its right are significant.

Reference.com offers a number of examples and a few exceptions to the rule (and is, unsurprisingly, less mathematical than MathWorld). They also suggest that numbers with multiple trailing zeros be expressed in scientific notation if they are supposed to be meaningful. This makes sense for scientific documents and technical publications, but it violates the style manuals of most (if not all) newspapers. This creates a lot of confusion in newspaper accounts: readers have a hard time discerning precise from imprecise information.

To give a simple example, the number 50,000 reported in a newspaper could mean any one of the following ranges of values (as well as many others):

50,000, following the definition above | 49,999.5 to 50,000.4 |

5.0 x 10^4 rounded to the nearest 0.1 x 10^{4} |
49,000 to 51,000 |

5 x 10^4 rounded to the nearest 1 x 10^{4} |
40,000 to 60,000 |

If the exponent is increased even less precision is implied. For example:

0.5 x 10^5 rounded to the nearest 0.1 x 10^{5} |
0 to 100,000 |

And if that’s not enough, sometimes numbers have precision that is based on a logarithmic base other than 10, such as the natural logarithm(e=2.718…) Here’s a good three-part rule of thumb to follow when reading numbers that reflect measurements or estimates of something:

- All numbers are uncertain. It’s the only thing that’s certain about them.
- A clear statement of how many digits are significant is an essential first step in figuring out what a number means. The statement tells you how much precision there is in the measurement or estimate. The amount of precision that matters depends on what you are going to do with the number.
- Any number that does not include a clear statement of how many digits are significant is inherently imprecise. It’s perfectly reasonable to admit that you don’t know what such a number means. In fact, it’s the only reasonable thing to do.