Mathematics Review final

Mathematics Review final - Mathematics Review Scientific...

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1 Mathematics Review Scientific notation • Examples – Activity •C u r ie s • 3.7 x 10 10 dis s -1 • 3.7 E10 Bq – Avogadro’s number •N A • 6.02 x 10 23 atoms/mole • 6.02 E23 atoms/mole – Nuclear diameter •1 x 10 -14 m • 1 E-14 m Significant Figures • Example – a recorded value should not contain more “significant figures” than that provided by the instrument • Calculators can lend themselves to “blurring” of this point • Some rules have been developed for significant figures
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2 Determining the Number of Significant Figures • The number of significant figures in a measurement, such as 2.531, is equal to the number of digits that are known with some degree of confidence (2, 5, and 3) plus the last digit (1), which is an estimate or approximation. – 3 - 1 significant figure – 2.53 - 3 significant figures – 2.531 - 4 significant figures Determining the Number of Significant Figures • Rules for counting significant figures are: – Zeros within a number are always significant. Both 4308 and 40.05 contain four significant figures. – Zeros that do nothing but set the decimal point are not significant. Thus, 470,000 has two significant figures. – Trailing zeros that aren't needed to hold the decimal point are significant. For example, 4.00 may have three significant figures. – If you are not sure whether a digit is significant, assume that it isn't. For example, if the directions for an experiment read: "Add the sample to 400 mL of water," assume the volume of water is known to one significant figure. Addition and Subtraction with Significant Figures • When combining measurements with different degrees of accuracy and precision, the accuracy of the final answer can be no greater than the least accurate measurement. • This principle can be translated into a simple rule for addition and subtraction: When measurements are added or subtracted, the answer can contain no more decimal places than the least accurate measurement. • 150.0 + 0.507 = 150.5
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3 Multiplication and Division With Significant Figures • Same principle applies in multiplication and division: – The final result can be no more accurate than the least accurate measurement. – Count the significant figures in each measurement, not the number of decimal places: When measurements are multiplied or divided, the answer can contain no more significant figures than the least accurate measurement. •E x am p l e : – Calculate the cost of copper in a penny. – Assume a mass of 2.531 grams per penny – Price of copper is 67 cents per pound. Multiplication and Division With Significant Figures • Use the price of a lb of copper to calculate the cost of cu metal • Significant figures – Four in the penny wt (2.531) and conversion factor (453.6 g/lb).
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This note was uploaded on 09/24/2011 for the course PCS 229 taught by Professor Pejovic-milic during the Fall '11 term at Ryerson.

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Mathematics Review final - Mathematics Review Scientific...

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