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Significant FiguresRules for determining the number of significant figures in a measured quantity:What is an "exact number"?Normally, the number of digits in your answer (in the calculator display) must be decreased to the correct number of significant figures. Follow the rules below.So, how do you determine the proper number of significant figures for your answer?Physical Science PHS 112 Significant Figures The number of significant figures in a result is simply the number of figures that are known with some degree of reliability. The number 12.3 is said to have 3 significant figures. The number 12.30 is said to have 4 significant figures. Rules for determining the number of significant figures in a measured quantity: (1) All nonzero digits are significant: 1.874 cm has 4 significant figures 3.4 kg has 2 significant figures. (2) Zeroes between nonzero digits are significant: 2005 kg has 4 significant figures 4.08 LB has 3 significant figures (3) Zeroes to the left of the first nonzero digits are not significant; such zeroes merely indicate the position of the decimal point: 0.005 m has only 1 significant figure 0.069 g has 2 significant figures (4) When a number ends in zeroes, the zeroes are not necessarily significant: 280 miles may be 2 or 3 significant figures 82,400 Calories may be 3, 4, or 5 significant figures There are several methods in common use that deal with the problem mentioned in (4) above. One method requires the use of a bar over the last significant digit in a number. For example, 89 500 kg denotes that the five is the last digit that is intended to be significant. So, this number is written to 3 significant figures. Whereas 89 500 kgis written to 5 significant figures. The drawback is this method requires using a “mark” that can easily get lost in poor penmanship (which describes about 95% of people in science). Another method uses a decimal to indicate that zeroes are significant. For example, 89 500. kg with the decimal means 5 significant figures and 89 500 kg without the decimal means 3 significant figures. This method is worse than the one above. In order to convey your meaning, you must insure that the reader sees the decimal. That brings up the penmanship problem again. The method that seems to be almost foolproof is writing numbers using powers of ten and only including the digits that are significant. For example, depending on whether 3, 4, or 5 significant figures is correct, we could write 82,400 Calories as: 8.24 (10 4 ) Calories (3 significant figures) 8.240 (10 4 ) Calories (4 significant figures) 8.2400 (10 4 ) Calories (5 significant figures)What is an "exact number"? Some numbers are exact because they are known with complete certainty. Most exact numbers are integers: exactly 12 inches are in a foot; there might be exactly 23 students in a class (assuming we do not have a partial student). Exact numbers are often found as conversion factors or as counts of objects (one student, two student, etc). Exact numbers can be considered to have an infinite number of significant figures. Thus, number of apparent significant figures in any exact number can be ignored as a limiting factor in determining the number of significant figures in the result of a calculation. For example, if you count cars in the parking lot you might have 35 cars. That would be 35.0000000 iiiand as many zeroes as you care to write because the number is exact. Normally, the number of digits in your answer (in the calculator display) must be decreased to the correct number of significant figures. Follow the rules below. ! If the first 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 first 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. ! If the first digit to be dropped is 5, the last remaining digit is rounded to the nearest even number. For example, 11.5 is rounded to 12 12.5 is rounded to 12 ! The rationale is to avoid bias in rounding. Half of the time we round up, half the time we round down. So, how do you determine the proper number of significant figures for your answer? Unless you are working in an environment that requires extreme accuracy (for example, calibrating very sensitive electronic measuring equipment), you may use a procedure that will yield reasonable results in many real-world calculations. Look at the values given in the problem and any other numbers used to derive the answer such as measurements you make or unit conversions used. Any numbers used in the calculation of the answer must be considered. The least accurate of these numbers (least number of significant figures) will determine the accuracy of your answer. That is, the answer can be no more accurate than the least accurate number used in calculating the answer. For example: d = 125 mi [3 S.F.] t = 2.0 Hr [2 S.F.] 125 . . .62.5 622.0dmi mimivtHr HrHr== = ≈ The answer is given to 2 S.F. because 2 was the least number of S.F. we had to work


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NW-SCC PHS 112 - Significant Figures

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