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Significant Figures In chemistry it is often impossible to obtain the exact value of the quantity under investigation. For this reason, it is important Significant Figures to indicate the margin of error in a measurement by indicating the number of significant figures. Significant figures are the meaningful digits in a measured or calculated quantity up to and including the first uncertain digit. A graduated cylinder reads 6.0 mL. 6.0 mL implies 6.0 ± 0.1 mL so the actual volume is somewhere between 5.9 mL and 6.1 mL. The number of significant figures in a measurement ensures that calculations involving the data will reflect the precision of the measuring device. In all cases the last digit is always uncertain and amount of this uncertainty depends on the particular measuring device used. Suppose that three people were told to determine the length of a piece of tile and were given a ruler whose smallest markings were at 0.1 cm intervals. They report the following values: Student 1 Student 2 Student 3 1.35 1.3 1.354 Who is right? Who has reported a value of the proper accuracy?" Rules for Significant Figures Any digit that is not zero is significant, 725 m has 3 significant figures Zeros between nonzero digits are significant (captive zeros), 40,703 kg has 5 significant figures Zeros to the left of the first nonzero digit (leading zeros) are not significant. 0.000045 g contains 2 significant figures. The zeros simply indicate the placement of the decimal point If a number does not contain a decimal point and trailing zeros, the zero may or may not be significant. 500 cm may have 1 (5), 2 (50), or 3 (500) significant figures. More info is needed to know which one is correct. Adding and Subtracting The number of sig figs to the right of the decimal point in the final sum or difference is determined by the smallest number of decimal places in any of the original numbers. 89.432 + 1.1 = 90.532 round to 90.5 2.097 - 0.12 = 1.977 round to 1.98 Multiplication and Division The number of sig figs in the final product or quotient is determined by the original number that has the smallest number of significant figures. 2.8 x 4.5039 = 12.61092 round to 13 6.85/112.04 = 0.0611388789 round to 0.0611 One more wrinkle… Exact numbers obtained from definitions or by counting numbers of objects have an infinite number of significant figures. Let’s assume a brick weighs 5.372 lbs. Then the weight of 5 bricks is 5.372 lbs x 5 = 26.86 You do not round off this product to one sig fig. because 5 is 5.00000…. by definition