1. Scientific Measurement (Chapter 3)
Dr. Walker

2. Objectives Use the metric system in measurement and calculations
Perform conversions between metric and non-metric units using dimensional analysis
Differentiate between accuracy and precision in measurement
Use proper scientific notation in measurements
Perform calculations using significant figures
Determine percent error

3. Measurement Contains a number AND a unit 39 years old 70 inches tall
200 pounds
37 oC

4. Metric Units
For this class, we will use the metric system for our measurements
Units to know:
Mass – kilogram
Volume – liter
Temperature – Kelvin (or celsius)
Length – meter
Energy -joule

5. Metric Units Metric prefixes to know Milli – 1/1000 Centi – 1/100
1000 mL = 1 L
Centi – 1/100
100 cg = 1 g
Think 100 cents = 1 dollar
Kilo – 1000
1000 g = 1 kg

6. Conversion Factors Allow you to convert from one unit to another
What you saw on the previous page were all examples
1000 mL = 1 L
100 cg = 1 g
1000 g = 1 kg

7. Conversion Factors
Not all conversion factors involve two metric measurements
The following are examples (don’t memorize them)
2.54 cm = 1 in
2.2 lbs = 1 kg
3.79 L = 1 gal
60 seconds = 1 min

8. An Example Problem
My body mass is 97 kg. If 1 kg = 2.2 lbs, what is my weight in pounds?
How could I go about solving this problem?

9. Dimensional Analysis
Method of using conversion factors to solve problems
T – square method
Gift tag
Looks like a “gift tag”
- who it goes to on top
- who is giving the gift on
the bottom
start to
from
You typically will not have a unit here. I’ll show you
an exception later.

10. Dimensional Analysis Example
My body mass is 97 kg. If 1 kg = 2.2 lbs, what is my weight?
Start with the information given
Body mass = 95 kg
What unit are we coming from?
kilograms
What unit are we going to – what does the problem ask for?
My weight in pounds

11. Dimensional Analysis Example
My body mass is 97 kg. If 1 kg = 2.2 lbs, what is my weight in pounds?
We’re going “to” the pound, the unit
asked for in the problem, which
goes in the top right
The initial information (“start”) given is 97 kg.
This goes in the top left of the t-square
97 kg
2.2 lbs
1 kg
We’re converting “from” kilograms,
so it goes in the bottom right

12. Dimensional Analysis Advantage
You don’t have to remember whether you multiply or divide
Plug in the numbers into the template and cancel units accordingly

13. Dimensional Analysis Example
My body mass is 97 kg. If 1 kg = 2.2 lbs, what is my weight?
After setting up the problem, we treat it like we’re manipulating fractions
Top x top, bottom x bottom, then divide accordingly
97 kg
2.2 lbs
= lbs
1 kg
What happens to the kilograms unit? Kilograms are on both the top and the
bottom, so the unit cancels. The units are just like numbers this way. Pounds are
all that is left.

14. Another Example
I need 15 liters of water for an experiment. If I buy 3 gallons of water at the store, do I have enough? (3.79 L = 1 gallon)

15. Another Example
I need 15 liters of water for an experiment. If I buy 3 gallons of water at the store, do I have enough? (3.79 L = 1 gallon)
3 gallons
3.79 L
= L
1 gallon
I need 15 gallons for the experiment,
so I didn’t buy enough water!!

16. Multistep Example How many seconds are in 1 day? We know…
60 seconds = 1 minute
60 minutes = 1 hour
24 hours = 1 day
How do we solve this????

17. Multistep Example
Some problems require more than one conversion to solve
Options
One
Use a different t-square for each conversion
Use the answer from the 1st t-square to start the 2nd one
Two
Use multiple t-squares together to make one big step

18. Multistep Example How many seconds are in 1 day? 1 day 24 hours 1 day
Notice the answer to the first t-square starts the second one
24 hours
60 minutes
= 1440 minutes
1 hour

19. Multistep Example How many seconds are in 1 day? 1440 minutes
(Answer!!!)
1 minute

20. Another way We can do this all in one step Not required 1 day 24 hours
minutes
seconds
1 day
24 hours
60 minutes
60 seconds
= 86,400 seconds
(Answer!!!)
1 day
1 hour
1 minute

21. Uncertainty Precision (left) – reproducibility of measurement
How many times you get the same value
Accuracy (right) – How close it is to known value

22. Uncertainty With Data Sets
A standard 100 g mass was measured several times, providing measurements of 90.2 g, 90.1 g, and 90.2 g.
Is this accurate?
Is this precise?

23. Uncertainty With Data Sets
A standard 100 g mass was measured several times, providing measurements of 90.2 g, 90.1 g, and 90.2 g.
Is this accurate? NO!! The measurements are NOT close to the 100 g known value
Is this precise? YES!! The measurements are all very close TO EACH OTHER!!

24. Uncertainty With Data Sets
A metal with a known density of 3.25 g/mL The density was measured at 3.24 g/mL, 3.23 g/mL, and 3.24 g/mL.
Is this accurate?
Is this precise?

25. Uncertainty With Data Sets
A metal with a known density of 3.25 g/mL The density was measured at 3.24 g/mL, 3.23 g/mL, and 3.24 g/mL.
Is this accurate? YES!! The numbers are all very close the known value
Is this precise? YES!! The numbers are all very close TO EACH OTHER

26. Scientific Notation Used for really big or really small numbers
Examples
Avogadro’s Number – number of atoms in a mole (you’ll learn this later)
6.022 x 1023
Mass of an electron
9.1 x g

27. Rules One number to the left of the decimal Regular Scientific
Move decimal until the above rule is followed
Exponent equals the number of places moved
Regular # > 1, exponent > 0
Regular # < 1, exponent < 0

28. Examples To scientific notation From scientific notation 9.2 x 108
356000
217
From scientific notation
9.2 x 108
4.28 x 102
5.632 x 10-3

29. Examples To scientific notation From scientific notation
Notice we didn’t put the starting or ending zeros in the number
From scientific notation
9.2 x = 920,000,000
4.28 x 102 = 428
5.632 x 10-3 =

30. Significant Figures
Significant figures show how many numbers you may count in a measurement
Many measurements give you a decimal to several places --- can you really trust it?
Examples
Room measurement = 11’4” x 15’2”
In decimal form = x 15.17
Square footage = ft2
Can we really get a measurement to THAT degree of accuracy?

31. The Rules 1) All nonzeros are SIGNIFICANT! 45 in = 2 sig figs
2369 ft = 4 sig figs
115 m = 3 sig figs

32. The Rules
2) Sandwich zeroes (zeroes between non-zeros) are SIGNIFICANT!
104 m = 3 sig figs
2008 ft = 4 sig figs
302 s = 3 sig figs

33. The Rules
3) Trailing zeros do not count…unless they’re behind a decimal
4500 ft = 2 sig figs
2000 yds = 1 sig fig
3570 L = 3 sig figs

34. The Rules
3) Trailing zeros do not count…unless they’re behind a decimal
25.0 m = 3 sig figs
10.0 m = 3 sig figs
10.50 m = 4 sig figs
2.0 x 103 m = 2 sig figs
Gives the number sig figs instead of one!
2.00 x 103 m = 3 sig figs
Gives the number sig figs instead of one!

35. The Rules 4) Leading zeros do not count! 0.0056 m = 2 sig figs
L = 3 sig figs
Notice the sig figs do not start until you hit a nonzero number!
L = 3 sig figs
Notice the combination of rules 3 and 4
The sig figs don’t start until the 5
The decimal makes the last zero count!

36. Additional Examples 2307 in = ____ sig figs 2.50 L = ____ sig figs
g = ____ sig figs
170 in = ____ sig figs
J = ____ sig figs
4.550 x 106 s = ____ sig figs

37. Additional Examples 2307 in = 4 sig figs 2.50 L = 3 sig figs
g = 2 sig figs
170 in = 2 sig figs
J = 4 sig figs
4.550 x 106 = 4 sig figs
Number is 4,550,000
Scientific notation designates an extra sig fig

38. Rules For Operations Multiplication/Division
Based upon lowest number of significant figures
15 x 25 = 375
Round answer to 2 sig figs – 375 rounds to 380!! 2 2
Answer can only have 2 sig figs !!!
Pay attention to first digit you got rid of – standard rounding rules apply!!

39. Rules For Operations 25.0 + 2.658 27.658 Addition/Subtraction
Based on least significant place value
Since there is no sig fig in the
Hundredths or thousandths place
In the top number, you can’t use them in the answer!!!
You must round your answer to the tenths column
becomes 27.7!!
25.0
27.658

40. More Practice - Operations
24 m x 58 m = _____ m2
56 L L = _____ L
250 ft x 175 ft = ______ ft2
8432 m2 / 12.5 m = ______ m
14.2 g g g = ______ g
22.4 m x 11.3 m x 5.2 m = ______ m3
20.6 oC – oC = _____ oC

41. More Practice - Operations
24 m x 58 m = m2
56 L L = L
250 ft x 175 ft = ft2
8432 m2 / 12.5 m = m
14.2 g g g = g
22.4 m x 11.3 m x 5.2 m = m3
20.6 oC – oC = oC

42. Percent Error The bars in the numerator refer to absolute value
% Error = Accepted – Experimental
x 100
Accepted
The bars in the numerator refer to absolute value
All % error values are POSITIVE

43. Example
A standard 100 g mass was measured at 90.2 g. What is the percent error?

44. Example
A standard 100 g mass was measured at 90.2 g. What is the percent error?
% Error = – 90.2
x 100 = 9.8 %
100

45. Example
I was pulled by a police officer who measured my speed at 68 mph with a calibrated radar gun. My speedometer read 55 mph. What was the % error of my speedometer?

46. Example
I was pulled by a police officer who measured my speed at 68 mph with a calibrated radar gun. My speedometer read 55 mph. What was the % error of my speedometer?
% Error =
x 100 = 19.1 % 68

47. Terms To Know Measurement Accuracy Precision Accepted value
Experimental value
Significant figures
Liter
Kilogram
Joule
Meter

48. Required Skills Converting to and from scientific notation
Determining accuracy and precision
Calculating percent error
Determining significant figures
Making calculations with significant figures
Solve conversion problems using dimensional analysis (t-squares)