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 B F C G D. 0.03

5. ANSWER
A Significant Figures B Significant Figures C Significant Figures D Significant Figure E Significant Figures F Significant Figures G Significant Figures .

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

7. ANSWER
A  x 100 B  2.18 x 101 C  6.8 x 10-3 D  x 101 E  2.19 x 10-1 F. 444  4.44 x 102

8. QUESTION
An electron can tunnel through an energy barrier with probability (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 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 x 104 B. 9.1 x 103 C. 8.8 x 10-1 D x 102 E x 10-5

11. ANSWER
A x ,900 B. 9.1 x 103 9,100 C. 8.8 x D x E x

12. QUESTION
Express the following sum with the correct number of significant figures: 1.80 m cm x 105 μm * To add values with significant figures, adjust all values to be added so that their units are all the same 1.80 m cm x 105 μm = 1.80 m m m = 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 / 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)

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

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

18. ANSWER
Express each of the following numbers to only three significant figures: A m 10.1 m B km 775 km C 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
( (-11)) = 166
2nd: Multiply (3.65)(4.12)(1.11) = 16.7
16.7  1.67 x 101  = 167
**ANSWER  1.67 x 10167
Q11

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
Q12

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) = ( × 10−8 mol) + (4.379 × 10−8 mol) = ( ) × 10−8 mol = * ANSWER: x 10−8 mol
Q14

25. Standard Units, Converting Units
Which of the following is not an SI base quantity? A) Length B) Mass C) Weight D) Time
Weight
SI = System international units = standard units of length (meter), mass (kg), and time (second)

26. Standard Units, Converting Units
Which of the following is not an SI base quantity? A) Length B) Mass C) Weight D) Time
Weight
SI = System international units = standard units of length (meter), mass (kg), and time (second) AKA Metric System

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

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

29. QUESTION
How many centimeters are there in a kilometer? *Answer: 100,000 cm
Kilogram
Q17

30. QUESTION
Write the following as full (decimal) numbers with standard units: a) mm b) 85 μV c) 760 mg d) 60.0 ps e) 2.50 gigavolts
Q18

31. ANSWER 1000 millivolt = 1 volt 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 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 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?
Q19

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 = inches

38. QUESTION
Determine your own height in meters, and your mass in kilograms.
* Example- Weight = 165 lbs
* Given: 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.
Q23

44. QUESTION
A typical atom has a diameter of about 1.0 x 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 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
Q25

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

51. Dimensional Analysis t time (T) v speed (L/T)
The following variables are commonly seen in equations. The name of the quantity represented by each variable, and its dimension(s), are also shown.
x distance (L) a acceleration (L/T2)
t time (T) v speed (L/T)
m mass (M) F force (ML/T2)
Using the information above, select the equations that are dimensionally correct.
F = ma v2 = 2ax v = at2 F/v = m/t

52. Dimensional Analysis
Answer F = ma v2 = 2ax F/v = m/t

53. QUESTION
The dimensions for force are the product of mass and length divided by time squared. Newton's second law states that force equals the product of mass and acceleration. What are the dimensions of acceleration? A) T2 B) T2/L C) L/T2 D) L/T

54. QUESTION
The dimensions for force are the product of mass and length divided by time squared. Newton's second law states that force equals the product of mass and acceleration. What are the dimensions of acceleration? A) T2 B) T2/L C) L/T2 D) L/T
* Disclaimer: This powerpoint presentation is a compilation of various works.