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Rules for rounding off numbers. If the digit to be dropped is greater than 5, the last retained digit is increased by one. For example, 12.6 is rounded to 13. If the digit to be dropped is less than 5, the last remaining digit is left as it is. For example, 12.4 is rounded to 12.
Rounding a lone 5 (A 5 without following digits). Some instructors prefer the simple “round 5 up” rule. Others prefer a slightly more precise “engineer’s rule” described as follows. a. If the number in front of the 5 is even, round down by dropping the 5. Example: 1.45 = 1.4 b. If the number in front of the five is odd, round it up.
Significant Figures and Rounding – Explanations and Examples Read pages 18-22 in your Lab Manual for a more thorough discussion of the meaning of significant figures and how it relates to accuracy, precision, and error.
SIGNIFICANT FIGURES. The amount of approximation required in a number may be described in another way by saying how many significant figures are required. To find how many significant figures a number contains count all figures in the number except zeros at the beginning or end of the number.
There are three rules on determining how many significant figures are in a number: Non-zero digits are always significant. Any zeros between two significant digits are significant. A final zero or trailing zeros in the decimal portion ONLY are significant. Focus on these rules and learn them well.
Use the order of mathematical operations to determine which order to apply the rules for addition/subtraction (determine the number of sig figs for that step) or the rules for multiplication/division.
Scientific notation, significant figures and rounding . Scientific or Standard Notation is best used to express very large or very small numbers in a compact, easy to read form, but can be used on any numbers. Simply, the basic format of the notation is + n-> a positive index indicates a large number. a 10× n
