\fam 10 20 30 40 50 601 70 80 90 100 110 120 130 140 150 OXFORD Helix 13 121 141SIGNIFICANT FIGURES DATA SHEET (F2018) Name day/time PART A - AREA OF A 3 X 5 INDEX CARD Length cm # sig figs Width cm # sig figs Area = ( cm) cm) = cm 2 DO NOT ROUND-OFF ! Given (1)2 (in)2 = (2.54)2 cm2 (exactly), convert the area to square inches using sig. figs. cm 2 ) ( in2 ) = in2 # sig figs cm * * ******** * * * * ***************************************** PART B - TOTAL MASS Mass of object (triple beam balance) # sig figs Mass of object (mg scale) # sig figs Mass of object (cg scale) # sig figs Total Mass g # sig figs Given that 1.00000 g = 0.0352739 ounce, convert the mass to ounces using sig. figs. Total Weight = ( g) ( OZ ) = OZ # sig figs g PART C - COMPARING ACCURACIES AT 10 mL Mass of beaker + water #sig figs Mass of beaker #sig figs Mass of water #sig figs Mass 10 mL cylinder + water #sig figs Mass 10 mL cylinder #sig figs Mass water #sig figs Mass 100 mL cylinder + water #sig figs Mass 100 mL cylinder #sig figs Mass water #sig figs Temperature of water used OC #sig figs Density of water from graph g/ml #sig figsSIGNIFICANT FIGURES Precision refers to how close repeated measurements are to each other. Accuracy refers to how close the repeated measurements are to the true or standard value. Thus, a dart player can be precise but inaccurate, or can be imprecise but get lucky enough so that the average represents good accuracy. In this case the bulls eye was the true value. However, if we do not know the true value we cannot consider accuracy at all, but must rely upon precision. Significant figures are the number of digits necessary to express the results of a measurement to the precision with which it is made. Significant figures do not refer to accuracy but must be used to get an idea of how well we make a measurement. For example, I walk into a room and estimate, without really counting, that there are 50 students. There is only one significant figure in the number 50, the 5, and this tells me that there is uncertainty in the decimal place representing 10. Therefore, the number means 50 + 10, that the number of students is between 40 and 60. Next, I count the students and arrive at the number 49. There are two significant figures in 49 and the uncertainty occurs in the decimal place representing 1. Therefore, the number means 49 + 1, that the number is between 48 and 50. If I would have counted exactly fifty students, it would be written as 50. so that the uncertainty would be + 1. COUNTING SIGNIFICANT FIGURES 1 ) all integers (nonzeros) are significant 2) zeros between integers are significant, 909 has 3 sig figs 3) zeros after the first nonzero digit for a decimal number are significant, 909.0 and 0.09090 both have 4 sig figs 4) zeros on right of last integer when there is no decimal place are ambiguous 90900 must be considered as 3 sig figs 90900. has 5 sig fig You must use scientific notation to be unambiguous. For example, to show the above number with 4 sig figs: 9.099 x 104 5) any zero included in a number written in scientific notation is significant Exercises How many significant figures are there in each or the following numbers? a) 32 1) 56,004 () 0.00304 P) 0.00560 u) 0.001 b) 18.263 8) 1.010 x105 1) 0.003040 q) 10.0240 V) 0.0010 C) 8.0 h) 2.50 x10- 12 m) 500 0.1060 d) 10.1 i) 1.01 x 10-2 1) 500. S) 1020.00 e) 10.10 j) 0.0034 0) 1.0087 t ) 0.0260 Answers a ) 3 f) 5 k) 3 b ) 5 8 ) 4 1) 4 3 c ) 2 h ) 3 m) 1 d) 3 1 ) 3 I) n ) 3 s ) e) 4 i) 0 ) 1 ) ROUNDING OFF 1) If the number to be dropped is 5 or greater, increase the preceding number 2) If the number to be dropped is less than 5, drop the number 3) complete mathematical operations before rounding off - rounding is done after all calculations 4) exact conversion factors do not limit significant figures (12 things = 1 dozen, 2.54 cm = 1 inch)Graph the data provided on its own separate piece of graph paper and then draw the best line through the data points. Plot density on the raids and choose a scale which will provrde for a useful graph so that the density of water at a given temperature can be read from the graph. This graph will be useful in the next few experiments: mammal. Qantizrade 0.9982 20 0.9980 21 0.99% 22 0.9975 23 24 25 0.9973 0.9970 The purpose of Part A is to obtain the area of a 3 x 5 index card to the proper number of Significant Figures. 1) Obtain a 3 x 5 index card. 2) Measure its length and width in centimeters using a plastic ruler. 3) Enter the data on the Data Sheet and do the indicated calculations. 4) Convert square cm into square inches using 1 in = 2.54 cm exactly. Square both sides of the equation to get the relationship between in2 and cmz. W5 - The purpose is to obtain the total mass of three objects to the correct number of signicant figures. 1) Obtain any object. . - - ' 2) Weigh the object on three different balances (triple beam, KID-800, and A0400). 3) Calculate the total mass on the Data Sheet using signicant gures. 4) Convert grams into ounces using the given conversion factor. 1) Obtain a SOmL beaker with graduations, a 10 mL graduated cylinder, and a 100 mL graduated cylinder. ' 2) Weigh each piece of glassware to the nearest mg {1 0,001 g) on the data sheet. 3) Fill each piece of glassware with 10 ml. of distilled water as careful] , 2/ as 3'01! can using the graduations on the piece of glassware. Reweigh each and record the masses in the Data Sheet. 4) Measure the temperature of the water in one piece of glassware to $0.1 c>C. Use the graph you plotted for your prelab assignment to determine the density of this water at this temperature. ' 5} Use your calculated water density to convert g of water into mi. of water. This is your experimental volume. 6) Calculate your 9i) error using the given equation. This is an absolute value, do not bother with a negative 96 error because we are assuming that this error could be in either direction. or 3:. The actual volume is the 10 mL your were trying to measure which is considered to be a perfect number. Be sure to use signicant gures to round off 96 error. Do the math to get the unrounded answer. Then round off according to the rules for subtraction and then division. For example if the experimental volume in the beaker was 9.090g/mL, I 91390-10000 | I 0.910 I %error - | -------------- I10096 - l --------- l10096=9.1096 E 10.000 1 110.000 I SIGNIFICANT FIGURES AND UNIT CONVERSIONS (F 99) Purpose To gain a better understanding of SIGNIFICANT FIGURES To become acquainted with metric units To practice unit conversions To understand the differences in precision, accuracy, and uncertainty. Introduction Accuracy - the closeness to the standard or true value. This is usually unknown. Precision - the statistical repeatability of several measurements. Uncertainty - the variation expected in a_single measurement using a device whose precision is known. Significant Figures - a measure of the precision or uncertainty in a measured number The following illustrates good precision but poor accuracy : TARGET BULLSEYE (STANDARD OR TRUE VALUE) CLUSTER OF SHOTS Accuracy and precision depend on the skill of the experimenter, but are also limited by the measuring device used. Each has a different PRECISION or UNCERTAINTY of measure. For example, the laboratory thermometer has a precision of + 0.1 .C and a temperature of 25.0 C should be reported as 25.0 + 0.1 .C. This means that the actual temperature could be either 24.9, 25.0, or 25.1 .C when considering the uncertainty implied in the number. A trained person will look at the quantity 25.0 .C and know that it has an implied uncertainty of $ 0.1 OC. PRECISION FOR SOME MEASURING DEVICES (UNCERTAINTY, IF A SINGLE MEASUREMENT) Balance, AC-400 electronic + 0.001 g (milligram balance) Balance, XD-800 electronic + 0.01 g (centigram balance) Balance, Metler electronic + 0.0001 g (analytical balance) Balance, Triple Beam + 0.01 g (the quadruple beam is also + 0.001 g) Thermometer, 110 .C 1 0.1 Pipet, Volumetric, 15 mL $ 0.02 m L Pipet, Volumetric, 10 mL + 0.02 mL Pipet, Volumetric, 20 mL + 0.04 mL Cylinder, Graduated, 100 ml + 0.5 mL Cylinder, Graduated, 10 mL + 0.1 mL Cylinder, Graduated, 500 mL + 1 mL Flask, Volumetric, 100 mL + 0.1 mL Flask, Volumetric, 50 mL + 0.1 mL Flask, Volumetric, 250 mL 1 0.05 mL Buret, 50 mL + 0.02 mL Ruler, 15 cm + 0.01 c m Barometer + 0.1 mm Hg Hydrometer + 0.002 unitlessConvert mass of water (9) to volume of water (mL) by using the density from your graph. (Refer to Part C (5)) Volume in beaker mL #sig figs Volume in 10 mL cylinder ML #sig figs Volume in 100 mL cylinder mL #sig figs Calculate the accuracy of each piece of glassware using the following equation. Show your calculations. (Refer to Part C (6)) % error =| experimental volume -actual volume] x 100 % = actual volume % error using beaker #sig figs % error using 10 mL cylinder % #sig figs % error using 100 mL cylinder % #sig figs Which would you expect to be the most accurate and why? Which is the most accurate and why?Exercises - Round off the following numbers as indicated. Number Round To Your Answer Answer $58.921 nearest cent ($58.92) 0.1281 mm two digits (0.13 mm) $11.50 nearest dollar ($12) 4.3645 Mm one decimal place (4.4 Mm) 31,579 Mg nearest thousand (32,000 Mg) MULTIPLICATION AND DIVISION - look at the least number of sig. figs, In multiplying and dividing, the number of significant figures in the answer is the same as in the number that has the fewest significant figures. Examples 1 ) (2.11 cm)(2 cm) = 4.22 cm2 but the correct answer is 4 cm since the answer should have y one significant figure. 2) 8.2 cm / 3.194 s = 2.56713 cm/s but the correct answer is 2.6 cm/s since the answer should have only two significant figures ADDITION AND SUBTRACTION - look at the decimal place When numbers are added or subtracted the final answer cannot have more digits to the right of the decimal point than that number which has the fewest digits to the right of the decimal point. Examples 6.82 The correct answer is 251 since the number 10. has 234.0 no digits past the decimal point the answer cannot + 10. have any digits to the right of the decimal point and 250.82 the number had to be rounded off to the 'ones' place. 3 .0999 0.1 2.9999 The correct answer is 3.0 Exercises Express your answers to the correct number or significant figures. a) 0.1893 m + 1.045 m - 0.0042 m b) (9.50 x 1014 m) / (3.0 x 103 m ) c) (3.26 x 10-4 m) (8.0 x 10-2 m) / (1.04 x 10-2 m) d) ( 63.2 mm + 1.18 mm) / 15.61 s e) (3.06 x 1010 cm2 - 1.0 x 1010 cm2) / 4.51 x 106 cm Answers a) 1.230 m b ) 3.2 x 1011 c) 2.5 x 10-3 m d) 4.12 mm/s e) 4.6 x 103 cm USING RULES FOR BOTH TYPES OF OPERATIONS - apply each rule When doing sequencingroblems all rules for significant figures must be applied. Example 25.000 g - 24.990 g % error -.--100% = 0.040 % 25.000 g 25.000 The numerator is subtraction and results in a number with 2 significant figures. The final answer is the result of dividing a number with 2 significant figures by a number with 5 significant figures.IBIELE BEAM EALANQE QEEBAIING MSIBUCIIQNS Triple Beam Balance The triple beam balance is used routinely in many laboratories to obtain rough measurements. For analytical work. however, the electronic balances should be used. 1) Zero the balance by turning the ADJUSTMENT KNOB until the pointer rests on the zero mark (see Figure 1). 2) Make sure that all SLIDING RIDERS are positioned at the extreme left on the GRADUATE!) SCALE. 3) PlaCe the object to be weighed on the WEIGHING PAN. 4) Beginning with the largest GRADUATED SCALE division. the hundred gram. slide the RIDER from left to right until you are in the mass range as indicated by the POINTER. 5) Repeat this process with the ten gram and one gram RIDERS until the POINTER rest on the zero mark, 6) Read the mass to 1; 0.02 gram by estimating between the graduated sale lines. ,. .__...t_, ,_ 7~_.._-I--nH-I-l_--I._ cm Helix OXFO OVL OEL, jOZL, OIL12 13density x Measured Temperature density at Temperature measured temperature-70 60 50 40 30 20 10Graph of Water Density is Temperature density , f/ml 0.7975 0.1960 20 22 25 24 CentigradeIMG_0003.MOV Press sc | to exit full screen METTLER TOLEDO 29669 +0/T+Part A Area of a 3' x 5' Index Card Watch the following video: Significant Figures Look at the following Example 1.1: mmmmmmm mmmmmm CM Here the "ruler" markings are every 0.1-centimeter. The correct reading is 1.67 cm. The first 2 digits 1.67 are known exactly. The last digit 1.67 is uncertain. You may have instead estimated it as 1.68 cm. 1. Let's measure the length of the index card. (Click) Let us zoom in to read the scale. (Click) Make sure to read the ruler to the correct number of decimal places and write the number of sig figs for measurement. 2. Let's measure the width of the index card. (Click) Let us zoom in to read the scale. (Click)Make sure read the ruler to the correct number of decimal places and write the number of sig figs for measurement. 3. Calculate the Area and report unrounded value. 4. Take unrounded value and covert from cm to inch using the provided conversion factor. Make sure your answer is reasonable (Hint: We are using a 3" x 5" index card) and that it has the right number of significant figures. Watch the following video: Rules for Significant Figures related to multiplication and division904 40 30 20 10Distilled Water 0 2LL62 Pause (k)Distilled Water 0 0 36882 g OHilled METTLER TOLEDO MIS 385 72 g +Distilled Water METTLER TOLEDO 48.452 g +B/TE70 30 Distilled Water HO METTLER TOLEDO 0 0 1 19. 1219D 128466Convert Mass of Water to volume of water Mass of water in glassware = 9.935 g Only water! Density of water at measured temperature = 0.9965 g/ml (From Graph) D= M/V; V = M/D Volume of water = 9.935 g /0.9965 p/ml = 9.970 ml Note: I just made up the numbers. Use your measurements.Calculation % error % error = | Experimental - Actual | / Actual x 100% Using the value calculated in last step. % error = |9.970 ml - 10.000 ml| / 10.000 mL x 100% % error = |-0.030 ml | / 10.000 mL x 100% % error = 0.30% Note: 1. The two vertical lines that enclose the difference between experimental and Actual mean take absolute value (ignore the negative sign). 2. The actual should be exactly 10 mL (based upon the device reading) and so it can have an infinite number of decimal places. 3. Just ensure that the actual has the same number of decimal places as the experimental. 4. The difference has 2 significant figures (0.030 mL) and so the % error should also be 2 significant figures (0.30 %).PART B TOTAL MASS A piece of copper metal was weighed three times, for each measurement write down the mass: 1. Triple-beam balance ( click) Write down the measurement (You should be able to read mass to 3 decimal places!) In fact, we are using a Quadruple Beam Balance. Watch the following video to learn how to use and read the scale: (Click) 2. centigram scale: (click). Write down the measurement. 3. milligram scale (click) Write down the measurement. 4. Add the measurements and report the total (has no physical meaning). Using the rules for addition and subtraction underline the number you would round the total mass to. Do not round. Watch the following video: Rules for Significant Figures related to addition and subtraction 5. Use the unrounded total to convert mass from grams to ounces and report the answer to the correct number of significant figures