Every time a measurement is taken, we must be aware of significant figures! Define significant figures.

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1 SCHM 103: FUNDAMENTALS OF CHEMISTRY Ch. 2: Numerical Side of Chemistry Types of data collected in experiments include: Qualitative: Quantitative: Making Measurements Whenever a piece of data is collected, it is important to keep in mind that EVERY MEASUREMENT HAS A DEGREE OF UNCERTAINTY! THEY ARE NEVER EXACT. First: Familiarize yourself with any measuring device you use! Determine the units to use and the limit of certainty (an indicator of how many decimal places to report your measurement). Second: Make sure your recorded measurement reflects the greatest precision of the instrument! Ruler I Smallest division (cm) Object A Object B Ruler II Every time a measurement is taken, we must be aware of significant figures! Define significant figures. The digit in a number associated with a measuring device is uncertain or (least significant)! When we record a number in science, we must indicate the degree of uncertainty in the measurement by using the correct number of significant figures. The general rule is to record all the certain digits plus one estimated place. Looking at the close-up of the graduated cylinder: The decimal place associated with the smallest gradations on the measuring device is. Therefore ANY measurement taken from this measuring device MUST be reported to the place. The volume in the cylinder is

2 ACCURACY VS. PRECISION Define Accuracy. Define Precision: Think of a bull s-eye. Thinking of the definitions for accuracy and precision, describe each condition below. Example: Student A Student B Student C Trial g 9.78 g g Trial g 9.82 g 9.99 g Trial g 9.75 g g Trial g 9.80 g 9.98 g Average g 9.79 g g The actual mass of the object was g. Which student was most accurate? Which student was most precise? Least accurate? Least precise? Counting significant figures Significant figures deal with precision. The number of significant figures associated with a measuring device indicates how close replicate measurements will be to each other. RULES FOR SIGNIFICANT FIGURES RULE 1: All non-zero digits are significant. (1-9) RULE 2: Zeroes located between non-zero digits are significant. (205) RULE 3: Leading zeroes (zeroes preceding the first non-zero integer) are insignificant. ( )

3 RULE 4: Trailing zeroes (zeroes after the last non-zero integer) are significant if the number contains a decimal point. (9.070) not significant if the number does not contain a decimal point. (5600) PRACTICE PROBLEM 1: State how many significant figures each number has and its assumed uncertainty. Number of Significant Figures Assumed uncertainty Scientific Notation 1, ,213, SCIENTIFIC NOTATION AND SIGNIFICANT FIGURES Mantissa (A) is between 1 and 10 A 10 x Exponent (x) must be a + or - whole number. The same rules for significant figures apply to scientific notation. PRACTICE PROBLEM 2: In the last column of the above table, express each number in scientific notation showing only significant digits. PRACTICE PROBLEM 3: Determine how many significant figures each scientific notation value has and the place of least significant digit. Convert to standard notation Number of Significant Figures Assumed uncertainty Standard Notation

4 ROUNDING RULES Let x be defined as the number to be dropped. There are three scenarios Case 1: If x < 5 The preceding number remains the same. Example: Round 6.3 to one significant figure. Answer: 6 Case 2: If x > 5 The preceding number is increased by one unit (round up) Example: Round 6.8 to one significant figure. Answer: 7 Case 3: x = 5 Proceed so the resulting number is even. Example: Round 6.5 to one significant figure. Answer: 6 Special note: Case 3 is applied only if 5 is the last non-zero digit! If a non-zero number(s) follow 5, then you should always round up! Example: Round 6.51 to one significant figure. Answer: 7 PRACTICE PROBLEM 4: Round the following to three significant figures ,896, Number of Significant Figures Rounded Result 693, SIGNIFICANT FIGURES AND ALGEBRAIC OPERATIONS I. Addition and Subtraction: Round the final result to the same place as the number with the least number of decimal places extending to the right.

5 Example: Given the following measurements, report the sum in the proper number of significant figures in 1.2 in in How many decimal places to the right of the decimal place should there be in the answer? Let s solve the example, reporting the sum with the proper significant figures: How many significant figures does the sum have? PRACTICE PROBLEM 5: Given the measurements below, report the sum or the difference in the proper number of significant figures. a g g g = b. 12 L L L = II. Multiplication and Division: Determine the number of significant figures in each number to be multiplied or divided in a step. The smallest number determined is the number of significant figures in the answer. Let s solve the example, reporting the product of the three numbers with the proper significant figures:

6 PRACTICE PROBLEM 6: Given the measurements below, report the quotient in the proper number of significant figures. a. (1.460 ml ml) / ml = b. ( kg)( kg) / (0.258 kg) = III. Exact Numbers Exact numbers have an infinite number of sig figs and therefore are not considered when determining how many sig figs your final answer should have. Exact numbers fall into two categories a. Example: There are 23 students in this class. b. Example: 12 inches = 1 foot PRACTICE PROBLEM 7: What is the average of the following measurements: in, 1.2 in, in? Be sure to report your answer with the proper significant figures! IV. SI Units Define SI Units: What advantage does the Metric system have over the English system?

7 Complete the table below. English SI Metric Unit Length Base Unit Volume Base Unit Mass Base Unit Some of the units in the table above have prefixes. The definitions of these prefixes are provided in Table 2.3 in your textbook. You are expected to memorize these! V. Generating Conversion Factors for SI Metric Units Let s apply this to remaining prefixes in Table 2.3. There are two versions of the metric conversion factors. Either one is acceptable! VERSION I

8 Version II What is the mathematical relationship between Version 1 and Version 2? VI. Units & Conversion CONVERSION OF UNITS WITHIN THE METRIC SYSTEM: DIMENSIONAL ANALYSIS Dimensional Analysis (also called factor-label method or the unit factor method or unit conversion) is a problem-solving method that uses the fact that any number or expression can be multiplied by one without changing its value. You have done dimensional analysis many times! Let s take an example we are familiar with How many days are in a hours? The first step in the conversion is to determine the following: hours = 1 day. Now two conversion factor can be written. Answer 1: Answer 2:

9 The basic set up in dimensional analysis is First we start with what is given, i.e, Next we use one of our conversion factors. Which one? So, the proper way to set up the problem is How many significant figures must our answer have? Explain. In conclusion, whenever we want to get rid of units, what do we need to do? Another problem! using dimensional analysis. How many inches are in 5.6 yards? Be sure to report your answer in the correct number of sig fig. The same process is applied when converting metric units Example: Convert 29.4 cl to liters (L). Write a conversion factor between cl and L. 1 L = cl The conversion factors are or. Which one should be used?

10 PRACTICE PROBLEM 8: Make the following conversions a mm to m b dg to µg c nl to cl CONVERSION OF UNITS: ENGLISH METRIC AND METRIC ENGLISH Dimensional analysis can be used for these problems as well. PRACTICE PROBLEM 2: Perform the following conversions a. 7.4 L to gal

11 b tons to g c µm to miles DENSITY, TEMPERATURE, AND UNIT CONVERSION PRACTICE PROBLEMS: a. Convert 3.30 cm 3 to pl b. Convert cm 3 to m 3 c. The mass of a piece of silver is 12.4 g. The density of silver is 10.5 g/cm 3. What is the volume of this piece of silver in dl? d. The volume of a piece of aluminum is m 3. The density of aluminum is 2.70 g/ml. What is the mass of the aluminum block?

12 e. Convert 62 C to Kelvin f. Convert F to Kelvin g. Convert 86.5 K to Fahrenheit h. Convert 686 ft 2 to cm 2 i. 225 ml to cm 3 j. 186,000 mi/sec to km/hr