7 1,000100kilok10hectoh1decadc0.1MeterLiterGramStaircase Rule:The direction you slide your finger is the direction the decimal place goes!0.01decid0.001centicmillim
8 Derived Units A unit that is defined by a combination of base units VolumeDensity
9 Density A ratio that compares the mass of an object to its volume The units for density are often g/cm3Formula:
10 Example ProblemSuppose a sample of aluminum is placed in a 25-mL graduated cylinder containing 10.5mL of water. The level of the water rises to 13.5mL. What is the mass of the sample of aluminum?Volume: final-initial13.5mL-10.5mL= 3.0mLDensity: 2.7 g/mL (Appendix C)Mass: ????
14 Using and Expressing Measurements A measurement is a quantity that has both a number and a unit.Measurements are fundamental to the experimental sciences. For that reason, it is important to be able to make measurements and to decide whether a measurement is correct.
15 Dimensional Analysis *Very Important* A method of problem solving that focuses on the units to describe matterConversion factor- a ratio of equivalent values used to express the same quantity in different unitsExample: 9.00 inches to centimetersConversion factor: 1 in = 2.54 cm
16 Scientific notationWe often use very small and very large numbers in chemistry. Scientific notation is a method to express these numbers in a manageable fashion.Definition: Numbers are written in the form M x 10n, where the factor M is a number greater than or equal to 1 but less than 10 and n is a whole number.= 5 x 103= 5 x (10 x 10 x 10)= 5 x 1000=Numbers > one have a positive exponent.Numbers < one have a negative exponent.
17 ExampleEx. 602,000,000,000,000,000,000,000 Ex In scientific notation, a number is separated into two parts.The first part is a number between 1 and 10.The second part is a power of ten.6.02 x10231.775 x10-3
20 Accuracy and precision Your success in the chemistry lab and in many of your daily activities depends on your ability to make reliable measurements. Ideally, measurements should be both correct and reproducible.Accuracy: a measure of how close a measurement comes to the actual or true (accepted) value of whatever is being measured.Precision: a measure of how close a series of measurements are to one another
21 Good AccuracyPoor PrecisionPoor AccuracyPoor PrecisionPoor AccuracyGood PrecisionGood AccuracyGood Precision
22 Determining error Error - the difference between the accepted value and the experimental valueAccepted Value: referenced/true valueExperimental Value: value of a substance's properties found in a lab.
23 ExampleA student takes an object with an accepted mass of 150 grams and masses it on his own balance. He records the mass of the object as 143 grams. What is his percent error?
25 Significant FiguresThe significant figures in a measurement include all of the digits that are known, plus the last digit that is estimated.Measurements must always be reported to the correct number of significant figures because calculated answers often depend on the number of significant figures in the values used in the calculation.Instruments differ in the number of significant figures that can be obtained from their use and thus in the precision of measurements.
26 Rules for Determining Sig Fig’s Every nonzero digit in a reported measurement is assumed to be significant.The measurements 24.7 meters, meter, and 714 meters each express a measure of length to 3 significant figures.Zeros appearing between nonzero digits are significant.The measurements 7003 meters, meters, and meters each have 4 significant figures.
27 3. Leftmost zeros appearing in front of nonzero digits are NOT significant. They act as placeholders.The measurements meter, and 0.42 and meter each have only 2 significant figures.By writing the measurements in scientific notations, you can eliminate such place holding zeros: in this case 7.1 x10-3 meter, 4.2x10-1 meter, and 9.9x10-5 meter.
28 4. Zeros at the end of a number to the right of a decimal point are always significant. The measurements meters, meters, and meters each have 4 significant figures.5. Zeros at the rightmost end of a measurement that lie to the end of an understood decimal point are NOT significant if they serve as placeholders to show the magnitude of theThe zeros in the measurements 300 meters, 7000 meters, and 27,210 meters are NOT significant.
29 6. There are two situations in which numbers have unlimited number of significant figures. The first involves counting. If you count 23 people in the classroom, then there are exactly 23 people, and this value has an unlimited number of significant figures.The second situation involves exactly defined quantities such as those found within a system of measurement. For example, 60 min= 1 hour, each of these numbers have unlimited significant figures.
33 Rounding Rules: Addition/Subtraction When you add/subtract measurements, your answer must have the same number of digits to the RIGHT of the decimal point as the value with the FEWEST digits to the right of the decimal pointExample: cmcmcmcmRounded to cmFewest Decimal places
34 Rounding Rules: Multiplication/Division When you multiply or divide numbers, your answer must have the same number of significant figures as the measurements with the FEWEST significant figuresExample: 3.20cm x 3.65cm x 2.05cm== cm3Rounded = 23.9 cm3Each has 3 sig fig’s
35 HOMEWORK Finish #2 and #3 from previous worksheet Page 29 #1-3, Pages #14-16Page 38 #29-30Pages #31-38