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# Mediciones, Problemas de Conversión y Notación Científica

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### Transcript

• 1. 1
Chapter 2 Measurements
2.1
Units of Measurement
Publishing as Benjamin Cummings
• 2. 2
Measurement
You make a measurement
every time you
• 5. Weigh a cantaloupe.
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.
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.
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.
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.
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.
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
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
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
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
Publishing as Benjamin Cummings
• 44. 28
Sink or Float
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
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
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
• 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