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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.
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.
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.
Why is rounding to significant figures important? It lets us express answers with appropriate precision, matching the context: Measurements & science: Equipment has its limits – overstating accuracy in a result is misleading. Huge quantities: 3 significant figures make big numbers like populations easier to compare quickly.
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.
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.
1) Round the numbers in the table. Number Nearest 10 Nearest 100 423 420 482 535 799 [1] 2) Round the numbers in the table. Number Nearest unit Nearest tenth 3.41 3 7.27 1.82 7.95 [1] 3) Round the numbers in the table. Number 1 decimal place 2 decimal places 0.474 0.5 4.945 0.6138 88.7057 [1] Rounding, Decimal Places and Significant Figures ...
