How Reliable are Measurements?

1
How Reliable are Measurements?

• Objectives
• Define and compare accuracy and precision.
• Use significant figures and rounding to reflect
  the certainty of data.
• Use percent error to describe the accuracy of
  experimental data.

2
Accuracy and Precision

• Accuracy how close is your answer to the
  correct or accepted value?
• Precision how close are a series of repeated
  measurements? (Can you get the same or close
  answer over and over?)

3
Accuracy and Precision, cont.
4
Accuracy and Precision, cont.
Density Data Collected By 3 Different Students
Student A Student B Student C
Trial 1 1.54 g/cm3 1.40 g/cm3 1.70 g/cm3
Trial 2 1.60 g/cm3 1.68 g/cm3 1.69 g/cm3
Trial 3 1.57 g/cm3 1.45 g/cm3 1.71 g/cm3
Average 1.57 g/cm3 1.51 g/cm3 1.70 g/cm3
The actual density was 1.59 g/cm3. 1. Which
student was the most accurate? 2. Which student
was the most precise?
5
Percent Error

• Percent Error
• experimental value- accepted value X 100
• accepted value
• If the experimental value is 1.54 g/cm3, and the
  accepted value is 1.59 g/cm3, what is the percent
  error?
• Refer to Example Problem on p.38 for answer.

6
Rules for Significant Figures

• Non-zero numbers are ALWAYS significant.
• 72.3
• Zeros BETWEEN non-zero numbers are significant.
• 7023
• All FINAL zeros AFTER the decimal point are
  significant.
• 72.3000
• Zeros that act as place-holders are NOT. (If they
  disappear when you convert the number to
  scientific notation, they are not significant.)
• 7200 7.2 x 103 0.0072 7.2 x
  10-3
• Counting numbers and defined constants are ALL
  significant numbers. 60 s 1 min

7
Practice

• How many significant figures in the following
  masses?
• 0.00040230 g
• 405,000 kg
• Ended here on Tuesday!!!

8
Calculations With Significant Figures

• Addition/Subtraction Your final answer can only
  have the same number of numbers to the right of
  the decimal point as your value with the FEWEST
  digits to the right of the decimal point.
• Example 28.0 23.538 25.68 77.218
• Which value has the fewest decimal places?
• Final answer?

9
Put It All Together

• Assignment
• Practice Problems (p.39) 31, 32
• Practice Problems (p.41) 35, 36 (Lets look at
  36c!!!)
• Practice Problems (p.42) 37, 38
• Section Review (p.42) 39-41

10
Calculations With Significant Figures, cont.

• Multiplying/Dividing Your final answer can only
  have the same number of significant figures as
  the measurement with the fewest significant
  figures.
• Example 3.20 x 3.65 x 2.05 23.944
• Which value has the fewest significant figures?
• Final answer?
• What if the first value had been 3.2?