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Today’s Do Now 8/11/2014 1) Five different individuals measured the volume of a sample of sulfuric acid. Their data is in the table to the right: Individual Measurement 1 2 3 4 5 2.85 2.87 2.84 2.85 2.86 Today’s Do Now 8/11/2014 Write each of the following numbers in scientific notation: 2. 1,490,000,000 3. 0.00000832 1.49 x 109 8.32 x 10-6 Write the following number in standard notation. 4. 5.36 x 10-2 0.0536 Our first objective… By the middle of this class period, I will be able to… convert between units of measure using dimensional analysis. Take a minute… Mark Cuban has decided that he wants to leave his position as general manager and open a bracelet shop. Before he leaves, he needs to confiscate 4 dozen bracelets from his players to start his shop. How many bracelets total is Mr. Cuban going to confiscate? Dimensional Analysis Dimensional Analysis: a problem solving method used to convert between units. To change from one unit to another we will use a conversion factor. Unit1 x conversion factor = Unit2 When you solved the Cuban mystery you used a conversion factor 4 dozen bracelets x 12 bracelets 1 dozen = 48 bracelets This is a conversion factor! Equivalence statement Equivalence statement: two measurements with the exact same value Example: 1 dozen = 12 Conversion factor Conversion factor: ratio of the two parts of an equivalence statement Example: 1 dozen = 12 2 Possible conversion factors: 12 OR 1 dozen 1 dozen 12 GaGa for Dimensional Analysis Example problem: Lady GaGa’s hat for her meat dress is 10.5 inches long. What is the length in centimeters? Step 1 and 2 1) Identify your given. Circle it in the problem and write it down. 2) Identify your unknown. Circle it in the problem and write it down. Example problem: Lady GaGa’s hat for her raw meat dress is 10.5 inches long. What is the length in centimeters? Step 3 3) Find the equivalence statement(s) that relates the two units. 1 inch = 2.54 cm Step 4 4) Choose the correct conversion factor based upon your given and unknown. ( 1 inch/2.54 cm) OR (2.54cm/1 inch) Step 5 5) Multiply your given by your conversion factor; cross off the units that cancel! Step 6 6) Round your answer to the correct number of significant figures Way to go!! The lizard Mr. Pope found was 5.62 cm long. What was the length of the lizard in inches? What are the steps? 1. 2. 3. 4. Identify given and unknown Find an equivalence statement to relate the two The denominator’s units must match the given. The numerator’s units must match the unknown. Next objective: By the end of this class period, I will be able to… determine the number of significant figures in an integer to perform calculations reporting the correct number of significant figures. UNCERTAINTY IN MEASUREMENT Because Nothing in chemistry is ever certain… Measuring Volume in the Lab Volume is measured from the bottom of the meniscus Uncertainty in Measurement Any measurement involves an estimate and thus is uncertain to some extent Let’s get up and move… There are 6 graduated cylinders around the room. Go find at least 2 and take the measurement you think a scientist would take. YOU HAVE 1 MINUTE. Were you correct? Number 1 2 3 4 5 6 Volume Certain vs. Uncertain Numbers Certain numbers are all of the numbers that can be said for sure. They will be the same even if 5 different people made a measurement. Uncertain numbers are any numbers that require an estimate. Rules for counting Significant Figures Rules for counting Significant Figures 1. Nonzero numbers always count Ex: 1457 has 4 sig figs Rules for counting Significant Figures 1. 2. Nonzero numbers always count Leading zeros never count Ex: 0.0025 has 2 sig figs 5 sig figs 15,677 3 sig figs 0.0391 Rules for counting Significant Figures 1. 2. 3. Nonzero numbers always count Leading zeros never count Captive zeros always count Ex: 1.008 has 4 sig figs 3 sig figs 506 4 sig figs 0.06002 Rules for counting Significant Figures 1. 2. 3. 4. Nonzero numbers always count Leading zeros never count Captive zeros always count Trailing zeros only count if the number contains a decimal point Ex: 100 has only 1 sig fig 100. has 3 sig figs 4 sig figs 0.4700 3 sig figs 2.40 x 3 10 1 sig figs 5,000 Rules for counting Significant Figures 1. 2. 3. 4. 5. Nonzero numbers always count Leading zeros never count Captive zeros always count Trailing zeros only count if the number contains a decimal point Exact numbers (have an unlimited number) What is an exact number?? Numbers that are determined by counting: 10 experiments 8 molecules Definitions 1 inch = 2.54 cm Significant Figures and Rounding If the digit to be removed: A. is less than 5, the preceding digit stays the same (1.33 1.3) B. is equal to or greater than 5, the preceding digit is increased by 1 (1.36 1.4) Round to 3 significant figures! 0.02345 0.023 5 Round to 3 significant figures! 5012 5010 Round to 3 significant figures! 0.07415 0.074 2 Round to 3 significant figures! 10,001 1.00 x 4 10 Round to 3 significant figures! 567.8 568 Bonus Practice! Use your number cards to decide how many significant figures each number has 1,000.1 5 sig figs 0.004050 4 sig figs 0.000405 3 sig figs Last Step … back to your notes Significant Figures in Calculations For multiplication & division The limiting term is the one with the smallest number of significant figures 4.56 x 1.4 = 6.384 3 sig figs 2 sig figs Round to 6.4 2 sig figs Significant Figures in Calculations Multiplication & Division Smallest number of significant figures Work it Out! Swivel Style Work out the following 4 problems with your lab partner on the back of your notes sheet: 8.6 0.027 x 0.000556 155 9 x 0.0998 x 286 1. 2.45 x 3.5 2. 8.315 ÷ 298 3. 135 x 246 4. (3.60 x 10-3) x (8.123) ÷ 4.3 0.0068 Significant Figures in Calculations For addition & subtraction The limiting term is the one with the smallest number of decimal places 12.161 + 3.12 = 15.281 3 decimal places 2 decimal places Round to 15.28 2 decimal places Significant Figures in Calculations Addition & Subtraction Smallest number of decimal places Work it Out! Swivel Style Work out the following 4 problems with your lab partner on the back of your notes sheet: 31.1 1. 12.11 + 18.0 + 1.013 = 2. 29.63 + 24.798 + 1.263 = 3. 1081 – 7.25 = 55.69 1074 8.44 x 4. 8.445 x 105 – 9.44 x 102 = 5 10