Significant Figures

Significant Figures, also called Significant Digits, are a way to limit how much accuracy is given in an answer, so that you don't give an extremely exact measurement when your measuring tool's accuracy is mediocre.

Pure Numbers
Pure numbers have infinite significant figures, meaning they are exact. If you have 12 eggs, then 12 is a pure number. You don't have 12.01 eggs, or 11.9 eggs.

Physical Numbers
Physical numbers have finite significant figures. For example, the measured length of a pencil.

Estimating Digit
The estimating digit is digit in a measurement where unsurety starts. If you are measuring the length of an object with a normal ruler, you can be pretty sure that the measurement is 13.1 cm, but you are not as sure that it is 13.12 cm. Thus, the estimating digit is 2.

Reading the number of significant figures in other people's measurements
The following rules can be used to determine the number of significant figures in another person's measurement.


 * All non-zero numbers count as significant figures.
 * Zeroes placed between significant figures are always significant; 4009 kg has four significant figures.
 * Zeroes placed after a decimal point a non-zero number are significant; 4.00 kg has three significant figures and 0.0400 has three significant figures.
 * Digits with bars over them are always significant. Keep in mind that since they are significant zeroes between them are significant.
 * All other digits are insignificant.

Information source.

Addition and Subtraction
When adding or subtracting two physical numbers, you first line up the numbers by their decimal points. You then draw a vertical line to the right of the estimating digit the shortest distance from the decimal point. That line is where you round off your answer.

1.01| +

2.01|3

=

3.02|3

Answer: 3.02.

Multiplication and Division
When multiplying or dividing two physical numbers, the answer will have the same number of significant figures as the number with the least number of significant figures.

2.10 * 3.607 = 7.5747

Answer: 7.57

Events that involve Significant Figures
Simple Machines

Compound Machines

Metric Mastery

Experimental Design (C Division)

Technical Problem Solving