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.