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Honors Chemistry Name__________________________ period____Significant Figures ws 3– Mathematical Computations“A chain is no stronger than its weakest link”. An answer is no more precise than the least precise number used to get the answer.Addition and Subtraction – For addition and subtraction, look at the decimal portion (i.e., to the right of the decimal point) of the numbers ONLY. Here is what to do: 1) Count the number of significant figures in the decimal portion of each number in the problem. (The digits to the right of the decimal place. Digits to the left of the decimal are not used to determine the number of decimal places in the final answer.) 2) Add or subtract in the normal fashion. 3) Round the answer to the LEAST number of places in the decimal portion of any number in the problem. EXAMPLES: ? 1. 2.3. 4.Multiplication and Division - The following rule applies for multiplication and division: The LEAST number of significant figures in any number of the problem determines the number of significant figures in the answer. Examples: 2.5 x 3.42 = The answer is 8.6 (which was rounded from the calculator reading of 8.55). Why? 2.5 has two significant figures while 3.42 has three. Two significant figures is less precise than three, so the answer has two significant figures. 3.10 / 4.520 = The answer is 0.686 The answer has 3 sig figs because 3.10 has 3 sig figs and that is less than the sig figs in 4.520 which is 4 sig figs. (All trailing zeros in the decimal portion are considered significant.) Note: A common error is to think that 14 and 14.0 are the same thing. THEY ARE NOT. 14.0 is ten times more precise than 14. The two numbers have the same value, but they convey different meanings about how trustworthy they are. Examples: Determine the answer and report it with the proper number of sig figs :2.33 x 6.085 x 2.1. ______________(4.52 x 10?4) ÷ (3.980 x 10?6) _____________WARNING: the rules for add/subtract are different from multiply/divide. A very common error is to swap the two sets of rules. Another common error is to use just one rule for both types of operations. Practice Problems Identify the number of significant figures: 1) 3.0800 ______2) 0.00418 ______3) 7.09 x 10?5 ______4) 91,600 ______5) 0.003005 ______6) 3.200 x 109 ______7) 250 ______8) 780,000,000 ______9) 0.0101 ______10) 0.00800 ______Use your calculator to determine the answer to the problems below and report the answers with the correct sig figs11) 3.461728 + 14.91 + 0.980001 + 5.2631 = _________________________12) 23.1 + 4.77 + 125.39 + 3.581 = _________________________13) 22.101 - 0.9307 = _________________________14) 0.04216 - 0.0004134 = _________________________15) 564,321 - 264,321 = _________________________16) (3.4617 x 107) ÷ (5.61 x 10?4) = _________________________17) [(9.714 x 105) (2.1482 x 10?9)] ÷ [(4.1212) (3.7792 x 10?5)]. Watch your order of operations on this problem. = _________________________18) (4.7620 x 10?15) ÷ [(3.8529 x 1012) (2.813 x 10?7) (9.50)] = _________________________19) [(561.0) (34,908) (23.0)] ÷ [(21.888) (75.2) (120.00)] = _________________________Answers: 1-10: 5, 3, 3, 3, 4, 4, 2, 2, 3, 3 11) 24.6112) 156.8 13) 21.170 14) 0.04175. 15) 300,000. or 3.00000 x 105 16) 6.17 x 1010 17) The calculator shows 1.3398 x 101 which then rounds to 13.40 - four significant figures. In this problem pay attention to order of operations, since division is not commutative. The best way to do this problem in the calculator is to multiply the first two numbers then do two divisions. 18) Three significant figures 19) The calculator shows 2280.3972, which rounds off to 2280, three significant figures. In scientific notation, this answer would be 2.28 x 103. ................
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