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MATH PROBLEMS

MATH PROBLEMS. TOPIC ONE. Measurement, Uncertainty, Significant Figures. The age of the universe is thought to be about 14 billion years. Assuming 2 significant figures, write this in powers of ten in a) Years b) Seconds. ANSWER. A) 14 Billion years = 14,000,000,000 years 

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MATH PROBLEMS

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  1. MATH PROBLEMS TOPIC ONE

  2. Measurement, Uncertainty, Significant Figures The age of the universe is thought to be about 14 billion years. Assuming 2 significant figures, write this in powers of ten in a) Years b) Seconds

  3. ANSWER A) 14 Billion years = 14,000,000,000 years  1.4 x 1010 years B)

  4. QUESTION How many significant figures do each of the following numbers have: A. 214 E. 0.0086 B. 81.60 F. 3236 C. 7.03 G. 8700 D. 0.03

  5. ANSWER A. 214 3 Significant Figures B. 81.60 4 Significant Figures C. 7.03 3 Significant Figures D. 0.03 1 Significant Figure E. 0.0086 2 Significant Figures F. 3236 4 Significant Figures G. 8700 2 Significant Figures .

  6. QUESTION Write the following numbers in powers of ten notation (Scientific Notation): A. 1.156 F. 444 B. 21.8 C. 0.0068 D. 27.635 E. 0.219

  7. ANSWER A. 1.156  1.1.56 x 100 B. 21.8  2.18 x 101 C. 0.0068  6.8 x 10-3 D. 27.635  2.7635 x 101 E. 0.219  2.19 x 10-1 F. 444  4.44 x 102

  8. QUESTION An electron can tunnel through an energy barrier with probability 0.0000000000375. (This is a concept used in quantum mechanics.) Express this probability in scientific notation. * Answer: 3.75 x 10−11

  9. QUESTION Sara has lived 18.0 years. How many seconds has she lived? Express the answer in scientific notation. Use 365.24 days per year for your calculations. * Answer: 5.68 x 108 s

  10. QUESTION Write out the following numbers in full with the correct number of zeros: A. 8.69 x 104 B. 9.1 x 103 C. 8.8 x 10-1 D. 4.76 x 102 E. 3.62 x 10-5

  11. ANSWER A. 8.69 x 104 86,900 B. 9.1 x 103 9,100 C. 8.8 x 10-1 0.88 D. 4.76 x 102 476 E. 3.62 x 10-5 0.0000362

  12. QUESTION Express the following sum with the correct number of significant figures: 1.80 m + 142.5 cm + 5.34 x 105μm * To add values with significant figures, adjust all values to be added so that their units are all the same 1.80 m + 142.5 cm + 5.35 x 105 μm = 1.80 m + 1.425 m + 0.534 m = 3.759 m  3.76 m * When adding, the final result is to be no more accurate than the least accurate number used. In this case, that is the first measurement, which is accurate to the hundredths place.

  13. QUESTION What is the percent uncertainty in the measurement 3.76 +/- 0.25 m? PERCENT UNCERTAINTY: Percent Uncertainty = Uncertainty /Measurement x 100% * Measurement = 3.76 m * Uncertainty = 0.25 m

  14. QUESTION Time intervals measured with a stopwatch typically have an uncertainty of about 0.2s, due to human reaction time at the start and stop moments. What is the percent uncertainty of a handtimed measurement of A) 5 s B) 50 s C) 5 min

  15. ANSWER Percent uncertainty = Uncertainty / Measurement x 100% A) % Uncertainty = B) % Uncertainty =

  16. ANSWER Percent uncertainty = Uncertainty / Measurement x 100% C) % Uncertainty =

  17. QUESTION Express each of the following numbers to only three significant figures: A. 10.072 m B. 775.4 km C. 0.002549 kg D. 93,000,000 mi

  18. ANSWER Express each of the following numbers to only three significant figures: A. 10.072 m 10.1 m B. 775.4 km775 km C. 0.002549 kg 2.55 x 10-3 kg D. 93,000,000 mi 9.30 x 107 mi

  19. QUESTION * Multiplying Numbers in Scientific Notation Multiply 3.65×1023 by 4.12×10154 by 1.11×10−11 and express the answer in scientific notation. *ANSWER: 1.67 x 10167 1st: Add together exponents (23+154+(-11)) = 166 2nd: Multiply (3.65)(4.12)(1.11) = 16.7 16.7  1.67 x 101  1+166 = 167 **ANSWER  1.67 x 10167

  20. QUESTION *Dividing Numbers in Scientific Notation Newton's second law states that the net force equals the product of mass and acceleration. A boat's mass of is 9.6×105 kg and it experiences a net force of 1.5×104 kg∙m/s2. State its acceleration. * GIVEN  F = ma

  21. ANSWER *Dividing Numbers in Scientific Notation Boat's mass = 9.6×105 kg Net force = 1.5×104 kg∙m/s2 * GIVEN  F = ma * Acceleration = ? ANSWER: 1.6 x 10−2 m/s2

  22. ANSWER *Dividing Numbers in Scientific Notation Boat's mass = 9.6×105 kg Net force = 1.5×104 kg∙m/s2 1.5×104 kg∙m/s2 / 9.6×105 kg 1st: Subtract the exponents 4 – 5 = -1 2nd: Divide 1.5/9.6 = 0.16  1.6 x 10-1 3rd: Add together the exponents (-1) + (-1) = -2 ** ANSWER: 1.6 x 10-2 m/s2

  23. QUESTION * Adding and Subtracting Numbers in Scientific Notation: A 3.70×106 kg piece splits off an iceberg of mass of 5.96×107 kg. Calculate the mass of the remaining iceberg and express the answer in scientific notation. (5.96 × 107 kg) – (3.70 x 106 kg) = (5.96 × 107 kg) – (0.370 x 107 kg)= (5.96 – 0.370) × 107 kg = 5.59 x 107 kg * ANSWER: 5.59 x 107 kg

  24. QUESTION * Adding and Subtracting Numbers in Scientific Notation: A small metal chamber contains 5.632×10−9 mol of oxygen gas at very low pressure. An additional 4.379×10−8 mol of oxygen gas are added. Find the total amount of gas in the chamber. (5.632 × 10−9 mol) + (4.379 × 10−8 mol) = (5.632 × 10−9 mol) + (4.379 × 10−8 mol) = (0.5632 × 10−8 mol) + (4.379 × 10−8 mol) = (0.5632 + 4.379) × 10−8 mol = * ANSWER: 4.942 x 10−8 mol

  25. Standard Units, Converting Units Which of the following is not an SI base quantity? A) Length B) Mass C) Weight D) Time

  26. Standard Units, Converting Units Which of the following is not an SI base quantity? A) Length B) Mass C) Weight D) Time

  27. QUESTION Which of the following is the SI unit of mass? a) pound b) gram c) kilogram d) ton

  28. ANSWER Which of the following is the SI unit of mass? a) pound b) gram c) kilogram d) ton

  29. QUESTION How many centimeters are there in a kilometer? *Answer: 100,000 cm

  30. QUESTION Write the following as full (decimal) numbers with standard units: a) 286.6 mm b) 85 μV c) 760 mg d) 60.0 ps e) 2.50 gigavolts

  31. ANSWER a) 286.6 mm  Standard Unit = Meter 1000 mm = 1 m b) 85 μV  Standard Unit = Volt 1000 microvolt (μV) = 1 millivolt 1000 millivolt = 1 volt

  32. ANSWER c) 760 mg  Standard unit = kg 1000 mg = 1 g 1000 g = 1 kg

  33. ANSWER d) 60.0 picoseconds  Standard unit = Second 1 x 10-12 s = 1 ps or 1 x 1012 ps = 1 s

  34. ANSWER e) 2.50 gigavolts  Standard unit = Volts 1 x 109 volts = 1 gigavolt

  35. QUESTION A drug company has just manufactured 50.0 kg of acetylsalicylic acid for use in aspirin tablets. If a single tablet contains 500 mg of the drug, how many tablets can the company make out of this batch?

  36. ANSWER * ANSWER: 100,000 tablets

  37. QUESTION Determine your own height in meters, and your mass in kilograms. * Example- Height = 5’8” (5 feet 8 inches) * Given: 1 meter = 39.37 inches

  38. QUESTION Determine your own height in meters, and your mass in kilograms. * Example- Weight = 165 lbs * Given: 0.456 kg = 1 lb * Technically, pounds and mass measure 2 separate properties. To make this conversion, we have to assume that we are at a location where the acceleration due to gravity is 9.8 m/s2

  39. QUESTION The Sun, on average, is 93 million miles from Earth. How many meters is this? Express a) Powers of ten notation (Scientific Notation) b) Using a metric prefix

  40. ANSWER a) Express using powers of ten… 1 mile = 1610 meters 93 million miles = (93 x 106 miles)

  41. ANSWER b) Express using a metric prefix… 1.5 x 1011 m  150 x 109 m = 150 gigameters OR 1.5 x 1011 m  0.15 x 1012 m = 0.15 terameters

  42. QUESTION What is the conversion factor between… • ft2 and yd2 1 yard = 3 feet b) m2 and ft2 1 meter = 3.28 feet

  43. QUESTION An airplane travels at 950 km/h. How long does it take to travel 1.00 km? * Use the speed if the airplane to convert the travel distance into a time.

  44. QUESTION A typical atom has a diameter of about 1.0 x 10-10 m. A) What is this in inches? Given: 1 m = 3.28 ft

  45. QUESTION A typical atom has a diameter of about 1.0 x 10-10 m. B) Approximately how many atoms are there along a 1.0-cm line?

  46. QUESTION 11.2 meters per second is how many miles per hour? * ANSWER: 25.0 mi/h

  47. QUESTION A light-year is the distance light travels in one year (at speed = 2.998 x 108 m/s). A) How many meters are there in one light year? Know  1 light year = 2.998 x 108 m/s * How many seconds are in one year?

  48. ANSWER A light-year is the distance light travels in one year (at speed = 2.998 x 108 m/s). A) How many meters are there in one light year? Know  1 light year = 2.998 x 108 m/s *Answer = 9.46 x 1015 meters

  49. QUESTION A light-year is the distance light travels in one year (at speed = 2.998 x 108 m/s). B) An astronomical unit (AU) is the average distance from the Sun to Earth, 1.50 x 108 km. How many AU are there in 1.00 light-year? Know  1 light year = 9.46 x 1015 meters 1 AU = 1.50 x 108 km

  50. QUESTION A light-year is the distance light travels in one year (at speed = 2.998 x 108 m/s). C) What is the speed of light in AU/h? Know  1 light year = 6.31 x 104 AU 1 AU = 1.50 x 1011 m 1 light year = 2.998 x 108 m/s

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