4 Precision and Accuracy Errors in Scientific Measurements Precision - Refers to reproducibility or how close themeasurements are to each other.Accuracy - Refers to how close a measurement is to the‘true’ value.Systematic Error - produces values that are either all higheror all lower than the actual value.Random Error - in the absence of systematic error, producessome values that are higher and some thatare lower than the actual value.
6 Rules for Determining Which Digits Are Significant All digits are significant, except zeros that are used only toposition the decimal point.1. Make sure that the measured quantity has a decimal point.2. Start at the left of the number and move right until youreach the first nonzero digit.3. Count that digit and every digit to its right as significant.Zeros that end a number and lie either after or before thedecimal point are significant; thus mL has foursignificant figures, and L has four significant figuresalso. Numbers such as 5300 L have 2 sig. figs., but5.30x103 L has 3. A terminal decimal point is often used toclarify the situation, but scientific notation is clearer (best).
7 Examples of Significant Digits in Numbers Number Sig digits Number Sig digitsL x 107 nm six18.00 g four ngkg two ,000 L twoL six ,002.3 ng sixg four g four875,000 oz x 10–6 L30,000 kg one oz fivem five kg sixlbs seven mL nineg kg eight1,470,000 L three ,000,000,000 g
8 Examples of Significant Digits in Numbers Number Sig digits Number Sig digitsL two x 107 nm six18.00 g four ng twokg two ,000 L twoL five ,002.3 ng sixg four g four875,000 oz three x 10 -6L four30,000 kg one oz fivem five kg six23, lbs seven mL nineg three kg eight1,470,000 L three ,000,000,000 g one
9 Rules for Significant Figures in answers 1. For multiplication and division. The number with theleast certainty limits the certainty of the result. therefore, theanswer contains the same number of significant figures asthere are in the measurement with the fewest significantfigures. Multiply the following numbers:9.2 cm x 6.8 cm x cm =2. For addition and subtraction. The answer has the samenumber of decimal places as there are in the measurementwith the fewest decimal places. Example, adding two volumes83.5 mL mL =Example subtracting two volumes:865.9 mL mL =
10 Rules for Significant Figures in answers 1. For multiplication and division. The number with theleast certainty limits the certainty of the result. therefore, theanswer contains the same number of significant figures asthere are in the measurement with the fewest significantfigures. Multiply the following numbers:9.2 cm x 6.8 cm x cm = cm3 = 23 cm32. For addition and subtraction. The answer has the samenumber of decimal places as there are in the measurementwith the fewest decimal places. Example, adding two volumes83.5 mL mL = mL = mLExample subtracting two volumes:865.9 mL mL = mL = mL
11 Rules for Rounding Off Numbers (1) In a series of calculations*, carry the extra digits through to the final result, then round off. **(2) If the digit to be removedis less than 5, the preceding digit stays the same. For example, 1.33 rounds to 1.3.is equal to or greater than 5, the preceding digit is increased by one. For example, 1.36 rounds to 1.4.(3) When rounding, use only the first number to the right of the last significant figure. Do not round off sequentially. For example, the number when rounded to two significant figures is 4.3, not 4.4.Notes:* Your TI-93 calculator has the round function which you can use to get the correct result. Find round by pressing the math key and moving to NUM. Its use is round(num, no of decimal places desired), e.g. round(2.746,1) =2.7.** Your book will show intermediate results rounded off. Don’t use these rounded results to get the final answer.
12 Rounding Off Numbers – Problems (3-1a) Round to three significant figuresAns:(3-1b) Round to two significant figuresWe used the rule: If the digit removed is greater than or equal to 5, the preceding number increases by 1.(3-2a) Round to three significant figures(3-2b) Round to two significant figuresWe used the rule: If the digit removed is less than 5, the preceding number is unchanged
14 Sample Problem – 3-3Lithium (Li) is a soft, gray solid that has the lowest densityof any metal. If a slab of Li weighs 1.49 x 103 mg and hassides that measure 20.9 mm by 11.1 mm by 12.0 mm, whatis the density of Li in g/ cm3 ?Lengths (mm)of sidesMass (mg)of LiLengths (cm)of sidesMass (g)of LiVolume (cm3)Density (g/cm3) of Li
15 Sample Problem – 3-3(cont.) Mass (g) of Li = 1.49 x 103 mgLength (cm) of one side = 20.9 mmSimilarly, the other side lengths are:Volume (cm3) =Density = mass/volumeDensity of Li =
17 Problem 3-4: Volume by Displacement Problem: Calculate the density of an irregularly shaped metalobject that has a mass of g if, when it is placed into a2.00 liter graduated cylinder containing mL of water,the final volume of the water in the cylinder is mL ?Plan: Calculate the volume from the different volumereadings, and calculate the density using the mass thatwas given.Solution:Volume =massDensity =volume
18 Definitions - Mass & Weight Mass - The quantity of matter an object containskilogram - ( kg ) - the SI base unit of mass, is aplatinum - iridium cylinder kept inParis as a standard!Weight - depends upon an object’s mass and the strengthof the gravitational field pulling on it, i.e.w = f = ma.
19 Problem 3-5: Computer Chips Future computers might use memory bits which require anarea of a square with 0.25 mm sides. (a) How many bits couldbe put on a 1 in x 1 in computer chip? (b) If each bit requiredthat 25 % of its area to be coated with a gold film 10 nm thick,what mass of gold would be needed to make one chip?Approach:use Achip =(b) use r = m/V
24 Temperature Scales and Interconversions Kelvin ( K ) - The “Absolute temperature scale” begins atabsolute zero and only has positive values.Celsius ( oC ) - The temperature scale used by science,formally called centigrade and mostcommonly used scale around the world,water freezes at 0oC, and boils at 100oC.Fahrenheit ( oF ) - Commonly used scale in America forour weather reports, water freezes at 32oF,and boils at 212oF.T (in K) = T (in oC)T (in oC) = T (in K)T (in oF) = 9/5 T (in oC) + 32T (in oC) = [ T (in oF) - 32 ] 5/9
25 Problem 3-6:Temperature Conversions (a) The boiling point of Liquid Nitrogen is oC, what isthe temperature in Kelvin and degrees Fahrenheit?T (in K) = T (in oC)T (in K) =T (in oF) = 9/5 T (in oC) + 32T (in oF) =(b)The normal body temperature is 98.6oF, what is it in Kelvinand degrees Celsius?T (in oC) = [ T (in oF) - 32] 5/9T (in oC) =T (in K) = T (in oC)T (in K) =
26 Answers to Problems in Lecture #3 (a)5.38; (b) 5.4(a) 0.241; (b) 0.240.536 g/cm3g / mL31 mg gold(a) 77.4 K; oF; (b) 37.0 oC; K