**Significant Figures**is a method of determining propogation of error in a scientific experiment that is often taught in high school science classes. It is often reffered to as "sig figs" or as "sig digs" (significant digits).

## Measuring with Significant Figures

The significant figures method teaches that when measuring using a non-electronic instrument, the observer should estimate within the nearest tenth of a division marked on the insturment. For example, if a graduated cylinder was marked off at every mililiter, the observer should measure the amount of volume contained in the cylinder to the nearest tenth of a mililiter. In order to express the degree of percision to which a value was measured, decimals are used. When using significant figures rules, it should be assumed that the last significant digit of every value was estimated. Using the previous example, if the observer read the amount of liquid in the cylinder to be exactly 12 mililiters, he would write the value as 12.0, which would indicate that the tenths place was an estimation. If the cylinder was marked off to every tenth of a milimeter, he would write the value as 12.00. Note that exact numbers obtained by counting should not be subject to the rules of significant figures.

## Counting Significant Figures

- Each non-zero number is a significant figure
- All zeroes between two non-zero numbers are significant figures
- All zeroes at the end of a number after a decimal point are significant figures
- The number of significant figures is then totaled

## Multiplying and Dividing using Significant Figures

## Adding and Subtracting using Significant Figures

When adding and subtracting numbers together, the sum or differences is rounded to the place farthest to the right of the decimal point of the number with the least amount of digits after the decimal point. The number of significant figures in each number is irrelevant. For instance, using significant figures rules:

- 1m + 1.1m = 2 m
- 1.0m + 1.1m = 2.1m
- 100m + 110m = 100m
- 1.0 x 102m + 111m = 210m

## Even-Odd Rule

As with all rounding procedures, if the number directly to the right of the digit to be rounded to is less than five, the digit stays the same; if more than five, the digit is rounded up. However, to always round up or down if the digit is equal to exactly five would skew data in one direction or the other. Thus, when using the significant figures system and rounding in such situation, the even-odd rule is used: round in whichever direction would make the last digit of the final product even. For example:

- 6m x 0.75m must be rounded to one significant figure
- 4.5m2 should be rounded to 4, since 4 is even

- 14m / 4m must be rounded to one significant figure
- 3.5 should be rounded to 4, since 4 is even

- 3.5 should be rounded to 4, since 4 is even