1. Scientific Measurement

2. Measurements Quantities with both a number and a unit
Used to measure a physical property
.5 grams
Mass
2 liters
Volume
1.6 meters
Length

3. Why does this matter? In chemistry, we make lots of measurements
Examples?
We need to have a common language of measurement so that we can understand each other’s results.

4. Scientific Notation
In chemistry, we deal with numbers that are very big and very small
How many water molecules are in the beaker?
600,000,000,000,000,000,000,000
What is the width of a water molecule?
meters

5. Scientific Notation
How can we express big and small numbers in a simpler way?
Powers of 10
10 = = 100
100 = = 10-1
1000 = = 10-2
10,000 = = 10-3
Exponent = # of places you move the decimal point to get behind the first digit
Left = positive
Right = negative

6. Scientific notation

7. Practice problem Express the following numbers in exponential form:
100,000
100
0.001 .1 1

8. Scientific notation
To put a number in scientific notation, express it as the product of
A number between 1 and 10
A power of 10
Example:
5000 meters = 5 x 1000 meters
= 5 x 103 meters
.025 liters = 2.5 x .01 liters
= 2.5 x 10-2 liters

9. Practice problems
Express the following numbers in scientific notation:
5280 feet
grams
602,000,000,000,000,000,000,000 atoms

10. Accuracy v. Precision
Accuracy = how close your measurements are to the correct value
Ex: I can run a mile in 7 minutes
If you measure my mile time and get 7 minutes, you are highly accurate
If you measure my time and get 8 minutes you are inaccurate

11. Precision Precision = how close your measurements are to each other
If you measure my mile time and get 7 minutes three times, you are very precise
If you measure my mile time and get 8 minutes three times, you are still very precise
But you are not very accurate.

12. Accuracy v. Precision

13. Error
Error is the difference between your measurement and the accepted value
Error = experimental value – accepted value

14. Practice problem Calculate the error: Experimental value = 1 meter
Accepted value = 1.02 meters
Experimental value = 10.7 seconds
Accepted value = 10.5 seconds

15. Percent Error How much error is a lot of error?
If my measurement of the weight of a car is 10 lbs too much, do I care?
If my measurement of the weight of a baby is 10 lbs too much, do I care?

16. Percent error
Percent error is an expression of error as a percentage of the accepted value
𝑃𝑒𝑟𝑐𝑒𝑛𝑡 𝑒𝑟𝑟𝑜𝑟= |error| 𝑎𝑐𝑐𝑒𝑝𝑡𝑒𝑑 𝑣𝑎𝑙𝑢𝑒 x 100%

17. Percent error practice
Mr. Tunney’s new car weighs 2795 lbs. The dealership weighs the car at 2805 lbs.
What is the error? What is the percent error?
When Mr. Tunney was born, he weighed 9.5 lbs. The doctor weighed him at 19.5 lbs.

18. Percent error practice
Felipe sticks a thermometer in a pot of boiling water, and measures its temperature as 99.1°C. The true temperature of boiling water is 100°C.
What is Felipe’s error? What is his percent error?

19. Significant Figures
The accuracy of our measurements is limited by the accuracy of our tools
What’s the smallest increment marked on this scale?

20. Significant Figures
When making measurements, you can record as many digits as your tool measures, and you can estimate one more digit.
All of these digits have useful information, so they are called significant figures

21. Significant figures? Can I measure this length as 11.754325 cm?
Why/why not?
How many significant figures should this measurement have?

22. Significant figure rules
How do I know how many significant figures a given measurement has?
Example: I tell you I am meters tall. How many significant figures are there?
Rules:
All nonzero digits are significant
All zeroes between nonzero digits are significant
Leftmost zeroes are not significant
Rightmost zeroes are significant if they follow a decimal point or are followed by a decimal point

23. Significant Figures Rules
All nonzero digits are significant
How many significant figures:
220
1000
345

24. Significant figure rules
All zeroes between nonzero digits are significant
How many sig. figs?
202
1050
10,002

25. Significant Figures Rules
Leftmost zeroes are not significant
How many sig. figs?
100
0245
0.003
1.01

26. Homework 9/30 13) Error = -1.6°C, Percent error = 1.3%
14) a. unlimited b. 5 c d. 3
15) 6.6 x b. 4.0 x c d x e. 1.9 x 1014

27. Significant Figures Rules
Zeroes at the end of a number to the right of a decimal point are significant
How many sig. figs?
1.00
0.01

28. Zeroes at the end of a number are also significant if they are followed by a decimal point
How many sig figs?
10200
10200.

29. Significant Figures Rules
Countable or standard measurements have infinite sig. figs
How many sig. figs?
4 apples
60 seconds/minute

30. Significant Figures in Calculations
In general, a calculated answer cannot be more precise than the least precise measurement from which it was calculated.

31. Addition and Subtraction
Round your answer to the largest digit that is the least significant digit of one of your measurements
Example: 12.52
349.0
369.76
Answer = 369.7

32. Multiplication and Division
Round your answer to the same number of sig. figs as the term with the least number of sig. figs
175 m x 0.1 m = 17.5 m
Answer = 20 m

33. Practice problems

34. The Metric System
The metric system is an international system of units designed to make measurements simple and easy
The five metric units we’ll use in class are
Meters
Grams
Kelvins
Seconds
Moles

35. Meters and Seconds Meters (m) are the metric unit of distance
1 meter ≈ 3.3 feet
Seconds (s) are the metric unit of time

36. Grams Grams (g) are the metric unit of mass
A paperclip weighs about 1 gram

37. Kelvins A kelvin (K) is the metric degree of temperature
1 degree Kelvin = 1 degree Celsius
BUT the Kelvin scale starts at the lowest temperature possible, -273°C
To convert from Celsius to Kelvin, subtract 273.

38. Moles A mole is the metric unit of quantity 1 mole = 6.02 x 1023
Very large, usually used for talking about how many atoms or molecules are in an object.

39. Metric prefixes
We can use a standard set of prefixes to make the scale of metric units more convenient
Mega = 1 million times the unit
Kilo = 1 thousand times the unit
Hecto = 100 times the unit
Deka = 10 times the unit
Deci = 1/10 of the unit
Centi = 1/100 of the unit
Milli = 1/1000 of the unit
Micro = 10-6 of the unit
Nano = 10-9 of the unit
Pico = of the unit

40. Volume
Volume is the amount of space an object occupies. Volume = length x width x height
The most common units we’ll use are a cubic centimeter (cm3) and a liter (L)
A liter equals 1000 cm3

41. Energy Energy is the capacity to do work or produce heat
The Joule (J) is the metric unit of energy.
The calorie is another (non-metric) unit of energy
1 calorie = 4.18 Joules

42. Homework 10/3
21) a. 1/1000 or b c. 1/10 or d. 1/100 or 10-2
22) m3, L, dL, cL, mL, μL
23) 8.8 x 102 cm3
25) C = K – 273
26) 443 K
41) 1 hour/60 min b) 103mg/1g c) 103mL/1dm3
42) 1.48 x 107 micrograms b) 3.72 g c) 6.63 x 104 cm3

44. Practice problems How many: Meters in a kilometer?
Centigrams in a gram?
Milliliters in a liter?
Microkelvins in a kelvin?
Joules in a Megajoule?
Nanometers in a meter?
Moles in a hectomole?

45. Conversion Problems
A quantity can usually be expressed in several different ways
1 dollar = 4 quarters = 10 dimes = 20 nickels
The same is true of scientific quantities
1 meter = 10 decimeters = 100 centimeters
How do we convert from one unit to another?

46. Conversion problems How do we convert from one unit to another?
Conversion factors
A conversion factor is a ratio of equivalent measurements used to convert one unit to another.
Example: 1 meter (m) = 100 centimeters (cm)
Convert 2 m to cm
2 m x 100 𝑐𝑚 1 𝑚 = 200 cm

47. Conversion problems How do I choose a conversion factor?
Find an equivalency between the unit your measurement is in and the unit you’re changing to
Set up a ratio of equivalent measurements
Place your desired unit on top
Converting 760 grams to kilograms
1000 g = 1 kg
760 g x 1 𝑘𝑔 1000 𝑔 = 760 𝑘𝑔 = 0.76 kg

48. Practice problems Convert using conversion factors:
750 milliliters to liters
15 centimeters to meters
1.5 decimeters to meters
750 kilojoules to Megajoules
5 nanograms to grams
4.5 kilokelvins to centikelvins

49. Dimensional Analysis
Solve the following problems with conversion factors:
How many seconds are in 8 hours?
How many inches are in a mile?
How many Joules are in 200 calories?

50. Density Use your intuition
What is more dense, a bucket of pennies or a bucket of feathers?
What is more dense, a block of wood or a block of iron?
What does density mean?

51. Density What is density?
Density is the ratio of an object’s mass to it’s volume
Density = 𝑚𝑎𝑠𝑠 𝑣𝑜𝑙𝑢𝑚𝑒
Stated another way, density is a measure of how tightly matter is packed in an object

52. Practice problem
You have four blocks of different elements. Use a ruler and a balance to calculate the density of each.

53. Buoyancy
Density determines whether an object will sink or float in a fluid.
More dense  sink
Less dense  float
Is wood more or less dense than water?
Is a rock more or less dense than water?
Is a person more or less dense than water?