MATH PROBLEMS

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MATH PROBLEMS

• TOPIC ONE

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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

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ANSWER

• A) 14 Billion years 14,000,000,000 years ?
• 1.4 x 1010 years
• B)

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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

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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
• .

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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

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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

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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

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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

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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

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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

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QUESTION

• Express the following sum with the correct
  number of significant figures
• 1.80 m 142.5 cm 5.34 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 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.

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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

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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

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ANSWER

• Percent uncertainty Uncertainty / Measurement x
  100
• A)
• Uncertainty
• B)
• Uncertainty

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ANSWER

• Percent uncertainty Uncertainty / Measurement x
  100
• C)
• Uncertainty

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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

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ANSWER

• Express each of the following numbers to only
  three significant figures
• A. 10.072 m 10.1 m
• B. 775.4 km 775 km
• C. 0.002549 kg 2.55 x 10-3 kg
• D. 93,000,000 mi 9.30 x 107 mi

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QUESTION

• Multiplying Numbers in Scientific Notation
• Multiply 3.651023 by 4.1210154 by 1.1110-11
  and express the answer in scientific notation.
• ANSWER 1.67 x 10167
• 1st Add together exponents
• (23154(-11)) 166
• 2nd Multiply (3.65)(4.12)(1.11) 16.7
• 16.7 ? 1.67 x 101 ? 1166 167
• ANSWER ? 1.67 x 10167

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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 9.6105 kg and it experiences a
  net force of 1.5104 kgm/s2. State its
  acceleration.
• GIVEN ? F ma

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ANSWER

• Dividing Numbers in Scientific Notation
• Boat's mass 9.6105 kg
• Net force 1.5104 kgm/s2
• GIVEN ? F ma
• Acceleration ?
• ANSWER 1.6 x 10-2 m/s2

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ANSWER

• Dividing Numbers in Scientific Notation
• Boat's mass 9.6105 kg Net force 1.5104
  kgm/s2
• 1.5104 kgm/s2 / 9.6105 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

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QUESTION

• Adding and Subtracting Numbers in Scientific
  Notation
• A 3.70106 kg piece splits off an iceberg of
  mass of 5.96107 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

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QUESTION

• Adding and Subtracting Numbers in Scientific
  Notation
• A small metal chamber contains 5.63210-9 mol
  of oxygen gas at very low pressure. An additional
  4.37910-8 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

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Standard Units, Converting Units

• Which of the following is not an SI base
  quantity?
• A) Length
• B) Mass
• C) Weight
• D) Time

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Standard Units, Converting Units

• Which of the following is not an SI base
  quantity?
• A) Length
• B) Mass
• C) Weight
• D) Time

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QUESTION

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

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ANSWER

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

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QUESTION

• How many centimeters are there in a kilometer?
• Answer
• 100,000 cm

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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

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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

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ANSWER

• c) 760 mg ? Standard unit kg
• 1000 mg 1 g
• 1000 g 1 kg

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ANSWER

• d) 60.0 picoseconds ? Standard unit Second
• 1 x 10-12 s 1 ps or 1 x 1012 ps 1 s

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ANSWER

• e) 2.50 gigavolts ? Standard unit Volts
• 1 x 109 volts 1 gigavolt

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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?

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ANSWER

• ANSWER
• 100,000 tablets

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QUESTION

• Determine your own height in meters, and your
  mass in kilograms.
• Example- Height 58 (5 feet 8 inches)
• Given 1 meter 39.37 inches

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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

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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

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ANSWER

• a) Express using powers of ten
• 1 mile 1610 meters
• 93 million miles (93 x 106 miles)

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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

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QUESTION

• What is the conversion factor between
• ft2 and yd2
• 1 yard 3 feet
• b) m2 and ft2
• 1 meter 3.28 feet

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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.

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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

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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?

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QUESTION

• 11.2 meters per second is how many miles per
  hour?
• ANSWER
• 25.0 mi/h

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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?

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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
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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

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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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Dimensional Analysis

• 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

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Dimensional Analysis

• Answer
• F ma
• v2 2ax
• F/v m/t

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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

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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

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compilation of various works.