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Math Unit Welcome to Chemistry! 1. Scientific Notation • Exponential notation from math class • Example: 12,500,000 • Example: 0.000368 • Example: 2.3 x 10-2 • Example: 5.6 x 103 2. Density • 1 mL = 1 cm3 • Example: An unknown liquid has a mass of 42 g and occupies a volume of 102 cm3. What is its density? Could this unknown be a salt water solution that has a density of 0.40 g/mL? • What is the mass of a substance that occupies 250 mL and has a density of 0.698 g/cm3? 3. Metric Base Units • • • • gram (g) – mass liter (l) – volume meter (m) – length second (s) – time 4. Metric Prefixes • • • • • • • • mega (M) 1Mg = 1,000,000 g = 1 x 106 g kilo (k) 1 kg = 1000 g deci (d) 1 g = 10 dg centi (c) 1 g = 100 cg milli (m) 1g = 1000 mg micro (u) 1 g = 1 x 106 ug nano (n) 1 g = 1 x 109 ng pico (p) 1 g = 1 x 1012 pg 5. Dimensional Analysis • Brittany wants to know her height in meters. She knows that her height is 1.86 km. • During a lab, Becca poured 4.2 x 102 mL of hydrochloric acid into a beaker. How many liters is this? • Owen needed to obtain 5.3 x 10-1 g of sodium chloride for his experiment. How many nanograms did he need? • A chemist needs 5.6 x 1014 pg of iron. How many kilograms is this? • A student runs 0.26 Mm. How many centimeters did this student run? 3 cm • Ben needs 420 of water. How many microliters does he need? • 2.54 cm = 1 inch • How many meters are in 1 yard? • How many feet are in 1.2 x 105 mm? 6. Velocity calculations • Garrett drives his truck 114 km/hr down Cavalier Drive. How fast is he driving in meters per second? • Shamyra’s speed in the 400m run was 14 km/hr. What would her speed be in inches per second? • Mrs. Fulks was late to work this morning and got a speeding ticket for driving 92 mph down King William Rd. How fast was she going in kilometers per minute? 7. Mass conversions • How many grams of apples did I buy at Food Lion if I purchased 2.75 lbs? (Hint: 1 pound = 454 g) 8. Significant Figures • All nonzero digits ARE significant • All “trapped” zeros are significant • Trailing zeros in the decimal portion ONLY are significant • Any number before the “x 10” is significant • 56 • 301 • 1000 • 0.00500 • 5.6 x 10-20 9. Sig Fig Calculations • 2.0014 + 5.36 + 1.2597423 = • (3.642)(1.02)(8.9) = 10. Accuracy • Getting the right (or accepted) value 11. Precision • Getting the same data (value) over and over even if it is NOT the correct value 12. Percent Error • In a lab experiment, you find the density of aluminum to be 3.14 g/mL. If the accepted value for the density of aluminum is 2.70 g/mL, what is your percent error?