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# Mediciones, Problemas de Conversión y Notación Científica

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### Mediciones, Problemas de Conversión y Notación Científica

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