Significant digits or figures reveal the precision to which something has been measured. If you traveled 212.5 miles in your car after your last fill-up, and then filled the tank with 12.87 gallons of gas, it would be ridiculous to claim that you got 16.51126651 mpg on a tank of gas. Most of those digits are just random junk. The number should be rounded to a number of digits equal to the number of digits in the least precise number used in the calculation, in this case 4. So the correct claim would be 16.51 mpg. All digits presented in an answer are assumed to be accurate, with the exception of the last, which may be assumed to be approximate due to rounding.

The rules for significant digits can be confusing, so here are the rules we will following in this class:

• All non-zero digits are significant
• Zeros between two non-zero digits are significant
• Zeros on the end of decimal numbers are significant

Here are some examples.

3,500 contains 2 significant digits
3,050 contains 3 significant digits
3,005 contains 4 significant digits
3.011 contains 4 significant digits
3.010 contains 4 significant digits
0.001 contains 1 significant digit
0.010 contains 2 significant digits
1.001 contains 4 significant digits

Granted this can be confusing, so here is an alternate rule you can follow: All non-zero digits are significant, period. The rules for determining how many significant digits you are allowed to have in an answer can also be confusing, so here is the rule we will following in this class: Do what I tell you to do! If I tell you to give me 4 significant (non-zero) digits in an answer, then give me 4, even if that would offend your chemistry teacher.

See scientific notation for more on significant digits.