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Scientific Notation Scientific Notation Very large or small numbers can be written in scientific notation. Scientific notation uses decimals and a power of 10 to represent the original number. To write a number is scientific notation, the number must be written with a decimal point after the first digit. Converting to Scientific Notation Write out the entire number. 2. Count the number of places you move the decimal point so that the number is after the first digit. 3. If you moved the decimal to the LEFT, write 10 raised to the positive of the number of places you moved the decimal. 4. If you moved the decimal to the RIGHT, write 10 raised to the negative of the number of places you moved the decimal. 1. Write In Scientific Notation 1025000 0.00257 9810000 0.2365 Measuring Accurately Accuracy vs. Precision Accuracy The extent to which a measured value agrees with the accepted value Percent error between experimental or calculated numbers and accepted number Precision Degree of exactness to which a quantity is measured. Measurements may be precise, but may not be accurate. Based on the scale of the measuring devise. Recording and Reporting Measurements When recording a measurement, always record all values given by the devise and the “guess” at the last place value. For example, if you measure a strip of paper to be 5.6 cm, you would want to add one more digit to the end of your number based on where you think the paper ends. If it ends right on the 0.6 mark, then your value would be 5.60 cm. If it appears to go halfway between 0.6 and 0.7 your value would be 5.65 cm. Liquid Measurements- Meniscus • Water is a “sticky” molecule. • Water will climb the sides of the glass. • This is called the Meniscus. The Metric System Space Station Issues The International Space Station (ISS) is regularly populated with Russians, Americans, Japanese, and Europeans. Language is a problem. So math is not a problem, one system of units has been adopted. Measure out 5 feet. How many meters is that? The Metric System Mass (how heavy things are) is measured in grams. Volume (how much space something takes up) is measured in liters. Length (how far, long, wide something is) is measured in meters. Examples of Mass A Penny weighs 2.5 grams 1 gram of pure gold is worth ~$100 Examples of Volume A Bottle of Soda 2 Liters Gallon of Milk 3.8 Liters http://www.doobybrain.com/2008/07/24/new-coca-cola-2-liter-contour-bottle/ http://www.citysackers.com/product_info.php?products_id=370 Examples of Length A stride is approximately meter 1 A car is approximately 4 meter Importance of Prefixes Which is easier to report? .000000003 grams or 3 nanograms Prefixes King Henry Died from drinking chocolate milk Kilo = 1000 100 Deca = 10 Hecto = Free = grams, liters, meters .1 Centi = .01 Milli = .001 Deci = http://www.fanpop.com/spots/chocolate-milk/images/1297950/title/choco-milk-photo OR…. King Have Diamonds but diamonds cost money Kilo = 1000 100 Deca = 10 Hecto = Base unit= grams, liters, meters .1 Centi = .01 Milli = .001 Deci = http://www.fanpop.com/spots/chocolate-milk/images/1297950/title/choco-milk-photo Convert 5000 grams to kilograms K H D f d c m 5000.g Convert 5000 millimeters to meters Convert 15 deciliters to hectoliters Practice Conversions 9000 mL to DL .006 Km to m 54 cg to g .408 L to dL 905 Hm to cm 9 g to Kg Importance of the Metric System Chemists work across the globe to further our understanding. We need to be able to share our information so that we can make discoveries more quickly. Conversions Conversions Simplify Life Conversions allow you to represent the same amount in different units. http://www.fiftybucksaweek.com/tag/eggs/ Consider Eggs Eggs are not sold individually.You buy eggs or 1 dozen. 1dozen = 12 eggs. http://www.reuters.com/article/idUSTRE67J34H20100820 Units Setting Up A Converson… Make sure you have the same units on the top and the same units on the bottom 1 dozen = 3x dozen __________ __________ 12 eggs 36 eggs 1 dozen = 2x dozen _________ 12 eggs ____________ 24 eggs 1 dozen = x? dozen _________ 12 eggs __________ 15 eggs 1 dozen = x dozen ___________ 12 eggs _____________ 15 eggs Step One: Cross Multiply Step Two: Divide Step Three: Check Units 1 dozen = x dozen _____________ ________________ 12 eggs 30 eggs = =x Pressure Conversions 1 atm = 760 Torr 4 atm = ??? 1 atm 4 atm = 760 Torr X Torr In chemistry we don’t use dozens. We use Moles. A mole is a number of particles. Number of Particles 23 10 1 Mole = 6.02 x Particles 60,200,000,000,000,0 00,000,000,000 Particles Mole Conversions One mole of an element has a specific mass. We can convert between moles and grams. 1 mole of Carbon = 12 grams 1 mole of Carbon = 12 grams How many moles is 30 grams of Carbon? 1 mole of Oxygen = 32 grams How many moles is 59 grams of Oxygen? Math Review You have 20 beads; 6 of them are red. What is the percentage of red beads? How much is 13% of 54? How much is 54% of 120? How much is 98% of 6? 35 = 70 5 + 6 = 26 50 = + 70 5 − 10 = 10 25 = 75 3 14 = 2 2 = 64 2 + 3 = 39 5 − 2 = 10 25 + 50 = 55 + 3=5 60 1 mole = 40 grams. How many moles is 60 grams? 1 mole = 22.4 liters. How many liters is 3 moles? 12 Eggs = 1 dozen eggs. How many eggs is 4.66 dozen? 100 cents = 1 dollar. How many dollars is 14,000 cents? 1 mole = 32 grams. How many grams does 2.5 moles weigh? 1 atm = 760 Torr. How many Torr is 3.4 atms? Significant Figures Significant Figures When using a measuring device, the last digit is always an estimate. To make sure all calculations with measurements are accurate, we have to make sure our answers do not have more digits than the original measurements. Scientists use significant figures to help solve this issue. The more sig figs a measurement has the more precise it is. What Numbers are Significant? All digits other than zero are significant numbers. Zeros are significant if: It is surrounded by two non-zero digits If more than one zero is surrounded by non-zero numbers, all the surrounded zeros are significant If a decimal is present, all the zeros after the first non-zero number are significant All numbers written in scientific notation are significant Steps to Counting Sig Figs Step 1: Is the decimal point present or absent? Present: start from left Absent: start from right Step 2: Start counting with the first number that isn’t zero Step 3: Once you start counting, count everything, including zeros The Rules of Zero How many significant figures? Pacific Present Left 0.554 Atlantic Absent Right 3 Sig Figs The Rules of Zero How many significant figures? Pacific Present Left 8004 Atlantic Absent Right 4 Sig Figs The Rules of Zero How many significant figures? Pacific Present Left 1.0450 Atlantic Absent Right 5 Sig Figs The Rules of Zero How many significant figures? Pacific Present Left 60650 Atlantic Absent Right 4 Sig Figs The Rules of Zero How many significant figures? Pacific Present Left 900.0 Atlantic Absent Right 4 Sig Figs The Rules of Zero How many significant figures? Pacific Present Left 733 Atlantic Absent Right 3 Sig Figs Identify the number of significant figures: 1.03690 100000 900.0 0.000002369 0.00450 10679.0 Do Now: Solve for x: x2 – 5 = 29 How many significant figures: 0.00150 18% of 105 is how much? What units would you measure the volume of a pool in? Convert from scientific notation: 2.3 x 10-4 Calculations with Sig Figs When you multiply or divide the answer must have has many sig figs as the least precise number. When you add or subtract the answer must have the same number of digits after the decimal place as the number with the fewest digits after the decimal place. Perform each operation: 103 x 2.0 684.9 x 42.3 300 / 50.00 2369 / 3 462.7 + 82.697 945.0526 + 1 695.336 – 452.2214 6547.9999 – 4521.0 Graphing Graphing Remember to SLAP IT Scale- does your scale cover all data? Label- did you label each axis with units? Axis- is your independent variable on the x-axis and your dependent variable on the y-axis? Plot Points- are all points properly plotted? Investigate- have you looked for trends and relationships between the variables graphed? Title!- does your graph have an appropriate title? Reference Table Graphs There are two graphs you need to be familiar with in your reference table. They are in Table G: Solubility Curves at Standard Pressure and Table H: Vapor Pressure of Four Liquids. To be able to read these graphs, you need to first identify which graph will give you the information you need. The title and axis labels will tell if the graph has the information you need. Now you need to identify the scale used on each axis. Once these steps are done, use the given information in the problem to determine your missing information. Example What is the solubility of NH3 at 55C? At which temperature does NaNO3 have a solubility of 100 g solute/100g H20? Which liquid has a vapor pressure of 150 kPa at 90 C? At what temperature does water have a water vapor of 101.3kPa? Using Graphs One important piece of information you can use from a linear graph is the slope. To find slope, use the formula: Slope = y2 – y1 x2 – x1 Example: Find the slope of this graph: