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Mediciones, Problemas de Conversión y Notación Científica

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  • 1. 1
    Chapter 2 Measurements
    2.1
    Units of Measurement
    Copyright © 2008 by Pearson Education, Inc.
    Publishing as Benjamin Cummings
  • 2. 2
    Measurement
    You make a measurement
    every time you
    • Measure your height.
    • 3. Read your watch.
    • 4. Take your temperature.
    • 5. Weigh a cantaloupe.
    Copyright © 2008 by Pearson Education, Inc.
    Publishing as Benjamin Cummings
  • 6. 3
    Measurement
    In a measurement
    • A measuring tool is used to compare some dimension of an object to a standard.
    • 7. Of the thickness of the skin fold at the waist, calipers are used.
    Copyright © 2008 by Pearson Education, Inc.
    Publishing as Benjamin Cummings
  • 8. 4
    Stating a Measurement
    In a measurement, a number is followed by a unit.
    Observe the following examples of measurements:
    Number Unit
    35 m
    0.25 L
    225 kg
    3.4 hr
  • 9. 5
    The Metric System (SI)
    The metric system or SI (international system) is
    • A decimal system based on 10.
    • 10. Used in most of the world.
    • 11. Used everywhere by scientists.
  • 6
    Units in the Metric System
    In the metric (SI) system, one unit is used for each
    type of measurement:
    Measurement Metric SI
    length meter (m) meter (m)
    volume liter (L) cubic meter (m3)
    mass gram (g) kilogram (kg)
    time second (s) second (s)
    temperature Celsius (C) Kelvin (K)
  • 12. 7
    Volume Measurement
    Volume
    • Is the space occupied by a substance.
    • 13. Has the unit liter (L) in metric system.
    • 14. Uses the unit m3(cubic meter)in the SI system.
    • 15. Is measured using a graduated cylinder.
    Copyright © 2008 by Pearson Education, Inc.
    Publishing as Benjamin Cummings
  • 16. 8
    Mass Measurement
    The massof an object
    • Is the quantity of material it contains.
    • 17. Is measured on a balance.
    • 18. Has the unit gram(g)in the metric system.
    • 19. Has the unit kilogram(kg)in the SI system.
    Copyright © 2008 by Pearson Education, Inc.
    Publishing as Benjamin Cummings
  • 20. 9
    Temperature Measurement
    Thetemperature of a substance
    • Indicates how hot or cold it is.
    • 21. Is measured on the Celsius (C) scale in the metric system.
    • 22. In the SI system uses the Kelvin(K) scale.
    Copyright © 2008 by Pearson Education, Inc.
    Publishing as Benjamin Cummings
  • 23. 10
    Time Measurement
    Time measurement
    • Has the unit second(s) in both the metric and SI systems.
    • 24. Is based on an atomic clock that uses a frequency emitted by cesium atoms.
    Copyright © 2005 by Pearson Education, Inc.
    Publishing as Benjamin Cummings
  • 25. 11
    For each of the following, indicate whether the unit describes 1) length, 2) mass, or 3) volume.
    ____ A. A bag of onions has a mass of 2.6 kg.
    ____ B. A person is 2.0 m tall.
    ____ C. A medication contains 0.50 g aspirin.
    ____ D. A bottle contains 1.5 L of water.
    Learning Check
  • 26. 12
    For each of the following, indicate whether the unit describes 1) length, 2) mass, or 3) volume.
    2 A. A bag of onions has a mass of 2.6 kg.
    1 B. A person is 2.0 m tall.
    2 C. A medication contains 0.50 g aspirin.
    3 D. A bottle contains 1.5 L of water.
    Solution
  • 27. 13
    Learning Check
    Identify the measurement with an SI unit.
    A. John’s height is
    1) 1.5 yd 2) 6 ft 3) 2.1 m
    B. The race was won in
    1) 19.6 s 2) 14.2 min 3) 3.5 hr
    C. The mass of a lemon is
    1) 12 oz 2) 0.145 kg 3) 0.6 lb
    D. The temperature is
    1) 85C 2) 255 K 3) 45F
  • 28. 14
    Solution
    Identify the measurement with an SI unit.
    A. John’s height is
    3) 2.1 m
    B. The race was won in
    1) 19.6 s
    C. The mass of a lemon is
    2) 0.145 kg
    D. The temperature is
    2) 255 K
  • 29. 15
    STEP 1 State the given and needed units.
    STEP 2 Write a plan to convert the given unit to the
    needed unit.
    STEP 3 Write equalities/conversion factors that connect the units.
    STEP 4 Set up problem with factors to cancel
    units and calculate the answer.
    Unit 1 x Unit 2 = Unit 2
    Unit 1
    Given Conversion Needed
    unit factor unit
    Guide to Problem Solving (GPS)
  • 30. 16
    Setting up a Problem
    How many minutes are 2.5 hours?
    given unit = 2.5 hr
    needed unit = ? min
    plan= hr min
    Set up problem to cancel units (hr).
    given conversion needed
    unit factor unit
    2.5 hr x 60 min = 150 min
    1 hr
    Copyright © 2008 by Pearson Education, Inc.
    Publishing as Benjamin Cummings
  • 31. 17
    A rattlesnake is 2.44 m long. How long is the snake
    in centimeters?
    1) 2440 cm
    2) 244 cm
    3) 24.4 cm
    Learning Check
  • 32. 18
    A rattlesnake is 2.44 m long. How long is the
    snake in centimeters?
    2) 244 cm
    given conversion needed
    unit factor unit
    2.44 m x 100 cm = 244 cm
    1 m
    Solution
  • 33. 19
    • Often, two or more conversion factors are required to obtain the unit needed for the answer.
    Unit 1 Unit 2 Unit 3
    • Additional conversion factors can be placed in the setup to cancel each preceding unit
    Given unit x factor 1 x factor 2 = needed unit
    Unit 1 x Unit 2 x Unit 3 = Unit 3
    Unit 1 Unit 2
    Using Two or More Factors
  • 34. 20
    How many minutes are in 1.4 days?
    Given unit: 1.4 days Needed unit: min
    Plan: days hr min
    Equalties: 1 day = 24 hr
    1 hr = 60 min
    Set up problem:
    1.4 days x 24 hr x 60 min = 2.0 x 103 min
    1 day 1 hr
    Example: Problem Solving
  • 35. 21
    • Be sure to check your unit cancellation in the setup.
    • 36. The units in the conversion factors must cancel to give the correct unit for the answer.
    What is wrong with the following setup?1.4 day x 1 day x 1 hr
    24 hr 60 min
    Units = day2/min is Not the needed unit
    Units don’t cancel properly.
    Check the Unit Cancellation
  • 37. More units
    Area m2 = m x m
    Volume m3 = m x m x m
    Density mass/volume
    g/mL or Kg/L
    22
  • 38. K = oC + 273
    Ex
    23 oC = _______ K
    135 K = ________ oC
    1L = 1 dm3
    1 m3 =1000L
    Ex 27 m3 = ________ L
    23
  • 39. 24
    Osmium is a very dense metal. What is its
    density in g/cm3 if 50.0 g of osmium has a
    volume of 2.22 cm3?
    1) 2.25 g/cm3
    2) 22.5 g/cm3
    3) 111 g/cm3
    Learning Check
  • 40. 25
    Given: mass = 50.0 g volume = 2.22 cm3
    Plan: Write the density expression.
    D = mass
    volume
    Express mass in grams and volume in cm3mass = 50.0 g volume = 2.22 cm3
    Set up problem using mass and volume.
    D = 50.0 g = 22.522522 g/cm3
    2.22 cm3
    = 22.5 g/cm3
    Solution
  • 41. 26
    Volume by Displacement
    • A solid completely submerged in water displaces its own volume of water.
    • 42. The volume of the solid is calculated from the volume difference.
    45.0 mL - 35.5 mL
    = 9.5 mL = 9.5 cm3
    Copyright © 2008 by Pearson Education, Inc.
    Publishing as Benjamin Cummings
  • 43. 27
    Density Using Volume Displacement
    The density of the object is
    calculated from its mass and
    volume.
    mass = 68.60 g = 7.2 g/cm3
    volume 9.5 cm3
    Copyright © 2008 by Pearson Education, Inc.
    Publishing as Benjamin Cummings
  • 44. 28
    Sink or Float
    Copyright © 2008 by Pearson Education, Inc.
    Publishing as Benjamin Cummings
    • Ice floats in water because the density of ice is less than the density of water.
    • 45. Aluminum sinks because its density is greater than the density of water.
  • 29
    Which diagram correctly represents the liquid layers in the cylinder? Karo (K) syrup (1.4 g/mL), vegetable (V) oil (0.91 g/mL,) water (W) (1.0 g/mL)
    1 2 3
    K
    W
    V
    V
    W
    K
    W
    V
    K
    Learning Check
  • 46. 30
    1)
    vegetable oil 0.91 g/mL
    water 1.0 g/mL
    Karo syrup 1.4 g/mL
    V
    W
    K
    Solution
  • 47. 31
    Chapter 2 Measurements
    2.2
    Scientific Notation
    Copyright © 2008 by Pearson Education, Inc.
    Publishing as Benjamin Cummings
  • 48. 32
    Scientific Notation
    Scientific notation
    • Is used to write very large or very small numbers.
    • 49. For the width of a human hair of 0.000 008 m is written as
    8 x 10-6m
    • For a large number such as 2 500 000 s is written as
    2.5 x 106s
    Copyright © 2008 by Pearson Education, Inc.
    Publishing as Benjamin Cummings
  • 50. 33
    Scientific Notation
    • A number written in scientific notation contains a coefficient and a power of 10.
    coefficient power of ten coefficient power of ten
    1.5 x 102 7.35 x 10-4
    • To write a number in scientific notation, the decimal point is moved after the first digit.
    • 51. The spaces moved are shown as a power of ten.
    52 000. = 5.2 x 1040.00378 = 3.78 x 10-3
    4 spaces left 3 spaces right
  • 52. 34
    Some Powers of Ten
    Copyright © 2008 by Pearson Education, Inc. Publishing as Benjamin Cummings
  • 53. 35
    Comparing Numbers in Standard and Scientific Notation
    Number in
    Standard Format Scientific Notation
    Diameter of the Earth
    12 800 000 m 1.28 x 107 m
    Mass of a human
    68 kg 6.8 x 101 kg
    Mass of a hummingbird
    0.002 kg 2 x 10-3 kg
    Length of a pox virus
    0.000 000 3 cm 3 x 10-7 cm
  • 54. 36
    Learning Check
    Select the correct scientific notation for each.
    A. 0.000 008
    1) 8 x 106 2) 8 x 10-6 3) 0.8 x 10-5
    B. 72 000
    1) 7.2 x 104 2) 72 x 103 3) 7.2 x 10-4
  • 55. 37
    Solution
    Select the correct scientific notation for each.
    A. 0.000 008
    2) 8 x 10-6
    B. 72 000
    1) 7.2 x 104
  • 56. 38
    Learning Check
    Write each as a standard number.
    A. 2.0 x 10-2
    1) 200 2) 0.00203) 0.020
    B. 1.8 x 105
    1) 180 000 2) 0.000 0183) 18 000
  • 57. 39
    Solution
    Write each as a standard number.
    A. 2.0 x 10-2
    3) 0.020
    B. 1.8 x 105
    1) 180 000

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