1. Practice Quiz Put the following in order from smallest to largest.
1.8x10-5
8.7x1024
0.7x10-3
1.4x1040

2. Answers
Smallest Largest
1.8x x x x1040

3. Scientists (and those studying science) frequently must deal with numbers that are very large or very small.

4. Instead of wasting time by writing many zeros before and after numbers, a method of writing very large and very small numbers was invented. It is called scientific notation.

5. Rules The first figure is a number from 1 to 9.
The first figure is followed by a decimal point and then the rest of the figures.
Then multiply by the appropriate power of 10.

6. Examples
425=4.25x102 (102 is the same as 100, so you are really multiplying 4.25 by 100)
=9.8x10-4 (10-4 is the same as 1/1000, so you are really multiplying 9.8 by 1/1000)

7. Practice
Write the following in scientific notation:
36000
0.0135

8. Try These Try to guess the answer without using your calculator.
4.2x104kg + 7.9x103kg=
5.23x106mm x 7.1x10-2mm=
5.44x107g/8.1x104mol=

9. 4.99x104kg
3.7x105mm2
6.72x102g/mol

10. Metric System

11. Metric System Every measurement has two parts Number Scale (unit)
SI system (le Systeme International) based on the metric system
Prefix + base unit
Prefix tells you the power of 10 to multiply by - decimal system -easy conversions

12. The Fundamental SI Units
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13. Prefixes giga- G 1,000,000,000 109 mega - M 1,000,000 106
kilo - k 1,
deci- d
centi- c
milli- m
micro- m
nano- n

14. The Prefixes Used in the SI System
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15. Some Examples of Commonly Used Units
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16. Deriving the Liter gram is the mass of 1 cm3
Liter is defined as the volume of 1 dm3
gram is the mass of 1 cm3

17. Measurement of Volume
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18. Soda is Sold in 2-Liter Bottles- an Example of SI Units in Everyday Life
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19. Figure 1.7 Common Types of Laboratory Equipment Used to Measure Liquid Volume
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20. Measurement of Volume Using a Buret
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21. Mass and Weight Mass is measure of resistance to change in motion
Weight is force of gravity.
Sometimes used interchangeably
Mass can’t change, weight can

22. Figure 1.8 An Electronic Analytic Balance
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23. Significant Figures

24. Uncertainty Basis for significant figures
All measurements are uncertain to some degree
Precision- how repeatable
Accuracy- how correct - closeness to true value.
Random error - equal chance of being high or low- addressed by averaging measurements - expected

25. Figure 1.10 The Results of Several Dart Throws Show the Difference Between Precise and Accurate
Neither accurate nor precise Precise but not accurate Both precise and accurate
(large random error) (small random error, (small random error,
large systematic error) no systematic error)
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26. Uncertainty Systematic error- same direction each time
Want to avoid this
Better precision implies better accuracy
you can have precision without accuracy
You can’t have accuracy without precision

27. Significant figures Meaningful digits in a MEASUREMENT
Exact numbers are counted, have unlimited significant figures
If it is measured or estimated, it has sig figs.
If not it is exact.
All numbers except zero are significant.
Some zeros are, some aren’t

28. Rules All non zero digits are significant Ex: 127
Zeros between significant digits are always significant
Ex: 106
Leading zeros are never significant
Ex: 0.005
Trailing zeros are significant only if there is a decimal
Ex: 25.30

29. Copy the examples below and write the number of significant figures
7084
421.00
0.538
5000
5x103
5.0 x103
5000.
5120

30. Copy the examples below and write the number of significant figures
7084 4 5x
5.0 x

31. Which zeroes count? In between other sig figs does
Before the first number doesn’t
After the last number counts iff
it is after the decimal point
the decimal point is written in
sig figs
sig figs

32. Multiplication and Division
The final answer should have the same number of sig figs as the measurement having the smallest number of sig figs
Ex: g x g=
Ex: g/5.2mL=

33. Addition and Subtraction
Line the numbers up in column form
Ex: =
Ex: =
Ex: =

34. Doing the math
Multiplication and division, same number of sig figs in answer as the least in the problem
Addition and subtraction, same number of decimal places in answer as least in problem.

35. Rounding Numbers
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36. Significant Figures Song
To the tune of Three Blind Mice

37. Verse 1 Addition and Subtraction line numbers up in columns (Repeat)
Make sure the decimals are aligned right,
Take off the numbers that are on the right
To get the sig figs (Repeat)

38. Verse 2 Multiplication and division count the numbers (Repeat)
Find the one that is the least
That’s the number, the rest will cease
To get the sig figs (Repeat)

39. Temperature

40. Temperature A measure of the average kinetic energy
Different temperature scales, all are talking about the same height of mercury.
Derive a equation for converting ºF toºC

41. 0ºC = 32ºF
32ºF
0ºC

42. (0,32)= (C1,F1) ºF ºC

43. 100ºC = 212ºF
0ºC = 32ºF
0ºC
100ºC
212ºF
32ºF

44. (0,32) = (C1,F1)
(120,212) = (C2,F2) ºF ºC

45. 100ºC = 212ºF
0ºC = 32ºF
100ºC = 180ºF
0ºC
100ºC
212ºF
32ºF

46. 100ºC = 212ºF
0ºC = 32ºF
100ºC = 180ºF
1ºC = (180/100)ºF
1ºC = 9/5ºF
0ºC
100ºC
212ºF
32ºF

47. Figure 1.11 The Three Major Temperature Scales
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48. Figure 1.12 Normal Body Temperature
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49. Equations
F=1.80(C)+32 C=(F-32)/1.80

50. Using the units to solve problems
Dimensional Analysis
Using the units to solve problems

51. Dimensional Analysis Use conversion factors to change the units
1 foot = 12 inches (equivalence statement)
12 in = = 1 ft ft in
2 conversion factors
multiply by the one that will give you the correct units in your answer.

52. Examples #1,2 11 yards = 2 rod 40 rods = 1 furlong 8 furlongs = 1 mile
The Kentucky Derby race is 1.25 miles. How long is the race in rods, furlongs, meters, and kilometers?
A marathon race is 26 miles, 385 yards. What is this distance in rods, furlongs, meters, and kilometers?

53. Example #3
Science fiction often uses nautical analogies to describe space travel. If the starship U.S.S. Enterprise is traveling at warp factor 1.71, what is its speed in knots?
Warp 1.71 = 5.00 times the speed of light
speed of light = 3.00 x 108 m/s
1 knot = 2000 yd/h exactly

54. Example #4
Apothecaries (druggists) use the following set of measures in the English system:
20 grains ap = 1 scruple (exact)
3 scruples = 1 dram ap (exact)
8 dram ap = 1 oz. ap (exact)
1 dram ap = g
1 oz. ap = ? oz. troy
What is the mass of 1 scruple in grams?

55. Example #5
The speed of light is 3.00 x 108 m/s. How far will a beam of light travel in 1.00 ns?

56. Group Practice

57. Group Practice-no flashcards
1) Convert 0.049kg of sulfur to grams. 2) Convert 3µL of saline solution to liters. 3) Convert 150mg of aspirin to grams. 4) Convert 1.18dm3 to mL. 5) Convert nL of water to grams. 6) Convert 4.19L to cubic centimeters 7) Convert cm3 of concrete to cubic meters

58. Complex Conversion Problems

59. #1
A heater gives off heat at a rate of 330kJ/min. What is the rate of heat output in kilocalories per hour? (1 cal=4.184J)

60. #1 Answer
4.7x103 kcal/h

61. #3
At the equator, Earth rotates with a velocity of about 465 m/s. What is the velocity in kilometers per hour? What is the velocity in kilometers per day?

62. #3 Answer
1670km/hr
4.02x104 km/d

63. #2
A water tank leaks water at the rate of 3.9mL/h. If the tank is not repaired, what volume of water in liters will it leak in a year?

64. #2 Answer
34L/yr

65. Density

66. Density Ratio of mass to volume D = m/V
Useful for identifying a compound
Useful for predicting weight
An intrinsic property- does not depend on what the material is

67. Formula Density=Mass/Volume D=m/V
If you know the density triangle, you can get the formulas for m and V.
The units of density are always going to have a division sign in them. Ex: g/mL

68. Densities of Various Common Substances* at 20° C
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69. Example #1
An empty container weighs g. Filled with carbon tetrachloride (density 1.53 g/cm3 ) the container weighs g. What is the volume of the container?

70. Example #2
A 55.0 gal drum weighs 75.0 lbs. when empty. What will the total mass be when filled with ethanol? density g/cm gal = 3.78 L lb = 454 g

71. Examples #3, 4, and 5 (on your own)
3) Mercury has a density of 13.6g/mL. What volume of mercury must be taken to obtain 225g of the metal? 4) Isopropyl alcohol has a density of 0.785g/mL. What volume should be measured to obtain 20.0g of the liquid? 5) A beaker contains 725mL of water. The density of water is 1.00g/mL. Calculate the volume and mass of the water.

72. Answers
3) 16.5mL 4) 31.8mL 5) 0.725L, 0.725g