Significant Figures

PREFACE
The purpose of this web page is to tell you how we treat numbers at IonSource.Com.  We are aware that there are many great significant figure tutorials presented on the internet. We agree that this presentation doesn't necessarily add anything new to those discussions. For a list of other significant figure web pages please see the list of links at the bottom of this page, or do a web search.  The sole purpose of this presentation is to describe to the reader how we deal with significant figures, and rounding at IonSource.Com. This is our significant figure, and rounding SOP, our standard operating procedure for numbers.
The term significant figures refers to the number of important single digits (0 through 9 inclusive) in the coefficient of an expression in scientific notation . The number of significant figures in an expression indicates the confidence or precision with which an engineer or scientist states a quantity.
The table shows several examples of numbers written in standard decimal notation (first column) and in scientific notation (second column). The third column shows the number of signficant figures in the corresponding expression in the second column.
Decimal expression | Scientific notation | Sig. figs. |
1,222,000.00 | 1.222 x 10 6 | 4 |
| 1.22200000 x 10 6 | 9 |
0.00003450000 | 3.45 x 10 -5 | 3 |
| 3.450000 x 10 -5 | 7 |
-9,876,543,210 | -9.87654 x 10 9 | 6 |
| -9.876543210 x 10 9 | 10 |
-0.0000000100 | -1 x 10 -8 | 1 |
| -1.00 x 10 -8 | 3 |
Significant figures are arrived at by rounding off an expression after a calculation is executed. In any calculation, the number of significant figures in the solution must be equal to, or less than, the number of significant figures in the least precise expression or element. Consider the following product:
2.56 x 10 67 x -8.33 x 10 -54
To obtain the product of these two numbers, the coefficients are multiplied, and the powers of 10 are added. This produces the...