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# sigfig - 3.7 Significant Figures 20 3.7 Significant Figures...

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Unformatted text preview: 3.7 Significant Figures 20 3.7 Significant Figures I A significant figure is one that is reliably known I Zeros may or may not be significant l Those used to position the decimal point are not significant I To remove ambiguity, use scientific notation I In a measurement, the significant figures include the first estimated digit 21 3.7 Significant Figures I Examples... I 0.0075 m has 2 significant figures I The leading zeros are placeholders only I Can write in scientific notation to show more clearly: 7.5 x 10 ‘3 m for 2 significant figures I 10.0 m has 3 significant figures I The decimal point gives information about the reliability of the measurement I 1500 m is ambiguous I Use 1.5 x 103 m for 2 significant figures I Use 1.50 x 103 m for 3 significant figures I Use 1.500 x 103 m for 4 significant figures 22 3.7 Significant Figures I Operations with Significant Figures - Multiplying or Dividing I When multiplying or dividing, the number of significant figures in the final answer is the same as the number of significant figures in the quantity having the lowest number of significant figures. I Example: 25.57 m x 2.45 m = 62.6 m2 - The 2.45 m limits your result to 3 significant figures 23 3.7 Significant Figures I Operations with Significant Figures - Adding or Subtracting I When adding or subtracting, the number of decimal places in the result should equal the smallest number of decimal places in any term in the sum. l Example: 135 cm + 3.25 cm = 138 cm - The 135 cm limits your answer to the units decimal value 24 3.7 Significant Figures I Summary I The rule for addition and subtraction are different than the rule for multiplication and division I For adding and subtracting, the number of decimal places is the important consideration I For multiplying and dividing, the number of significant figures is the important consideration 25 3.7 Significant Figures I Rounding... I Last retained digit is increased by 1 if the last digit dropped is 5 or above I Last retained digit remains as it is if the last digit dropped is less than 5 I Ifthe last digit dropped is equal to 5, the retained digit should be rounded to the nearest even number I Saving rounding until the final result will help eliminate accumulation of errors 26 ...
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