Significant Figures: Introduction and Example

Rounding of numbers is done so that one can concentrate on the most important or significant digits. For example, consider a flat price at 285500. A rich man might think in hundreds of thousands of dollars. To a rich man, it is easier to think in terms of 1 significant figure, the “3” in 300,000. A wage might e worried about the hundreds of dollars. To him, there may be four significant figures, the ‘2’, ‘8’, ‘5’, ‘5’ in 285500.

Consider an example: A wight recorded as 8426kg is correct to 3 decimal places. Reporting this weight in grams, the 8425g is nearest to the whole number. Recording the weight as 8.426kg correct to 4 significant figures and converting the weight to 8426g, the number of significant figures is still 4. Thus, sometimes it is more useful to express a result in terms of numbers of significant figures rather than the number of decimal places.

There are some rules for writing significant figures:

Rule 1: Include one extra figure for consideration. Simply drop the extra figure if it is less than 5. If it is 5 or more, add 1 to the previous figure before dropping the extra figure.

Rule 2: All non-zero digits are significant wherever they are recorded. For example, 7.22 is correct to 3 significant figures.

Rule 3: Zeros that lies between non-zero digits are significant. For example, 2003 is correct to 4 significant figures.
Rule 4: Zeros which are not preceded by a non-zero digit (leading zeros) are not significant. For example, 0.000325 is correct to 3 significant digits.

Rule 5: Zeros that appear after the decimal points (trailing zeros) but are not followed by a non-zero digit are significant. For example, there are 5 significant digits in 22.300.

Rule 6: The final zeros in a whole number may or may not be significant. It depends on how the estimation is made.

A point to remember is that the number of digits is used to denote an exact value to a specified degree of accuracy. For example, 6084.324 is a value accurate to 7 significant figures. If written as 6080 it is accurate to 3 significant digits. The final 0 is not significant because it is used to show the order of magnitude of the number.

Significant Figures

Muhammad Imdad Ullah

Currently working as Assistant Professor of Statistics in Ghazi University, Dera Ghazi Khan. Completed my Ph.D. in Statistics from the Department of Statistics, Bahauddin Zakariya University, Multan, Pakistan. l like Applied Statistics, Mathematics, and Statistical Computing. Statistical and Mathematical software used is SAS, STATA, GRETL, EVIEWS, R, SPSS, VBA in MS-Excel. Like to use type-setting LaTeX for composing Articles, thesis, etc.

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