Mr. Rogers' Honors Physics

Indicators
P-1.1 Apply established rules for significant digits, both in reading scientific instruments and in calculating derived quantities from measurement.
P-1.3 Use scientific instruments to record measurement data in appropriate metric units that reflect the precision and accuracy of each particular instrument.
P-1.4 Design a scientific investigation with appropriate methods of control to test a hypothesis (including independent and dependent variables), and evaluate the designs of sample investigations.
P-1.5 Organize and interpret the data from a controlled scientific investigation by using (including calculations in scientific notation, formulas, and dimensional analysis), graphs, tables, models, diagrams, and/or technology.
P-1.6 Evaluate the results of a controlled scientific investigation in terms of whether they refute or verify the hypothesis.
P-1.7 Evaluate conclusions based on qualitative and quantitative data (including the impact of parallax, instrument malfunction, or human error) on experimental results.

Ongoing

P-1.2 Use appropriate laboratory apparatuses, technology, and techniques safely and accurately when conducting a scientific investigation
P-1.8 Evaluate a technological design or product on the basis of designated criteria (including cost, time, and materials).
P-1.9 Communicate and defend a scientific argument or conclusion.
P-1.10 Use appropriate safety procedures when conducting investigations.

Ways of Representing Uncertainty or Precision

5. Explain the difference between accuracy and precision.

   accuracy = difference between the true and estimated values. Often, the estimated value is the average of several measurements, The true value is generally unknown. Precision = the lack of scatter or variability in measured values. High precision = low scatter Low precision = high scatter.

   Formative assessment: Characterize the above targets as high or low accuracy and precision.

6. State a simplified way to estimate measurement uncertainty and explain its limitations. plus or minus 1/2 (smallest scale division) -- assumes correct calibration

7. Name a common form of error caused by the position of a person's head with respect to the measuring instrument. Parallax error. These occur in analog measuring instruments.

8. Explain how significant digits imply a certain level of uncertainty (possible variation) in a quantity.

   Uncertainty = plus or minus 1/2 (least significant digit)

   The uncertainty of digital measuring instruments is considered to be plus or minus 1/2 (least significant digit)

Ways of Representing Uncertainty or Precision (continued)

9. Explain the primary problem involved in calibrating measuring instruments (such as rulers or thermometers) and how it can affect measurements. Calibration is the process of making a measuring instrument give readings that match a known standard that's considered accurate. For example lab scales are often calibrated using the standard of brass weights.

Standards are imperfect

During calibration a measuring instrument has to measure the standard, which introduces measurement errors.

10. Identify the difference between an analog and digital measuring instrument.

11. State a simplified way to estimate the measurement uncertainty of an instrument and explain its limitations. plus or minus 1/2 (smallest scale division) -- assumes correct calibration.

12. Name a common form of error caused by the position of a person's head with respect to the measuring instrument. Parallax error. These occur in analog measuring instruments.

13. Explain how significant digits imply a certain level of uncertainty (possible variation) in a quantity.

    Uncertainty = plus or minus 1/2 (least significant digit)

    The uncertainty of digital measuring instruments is considered to be plus or minus 1/2 (the place value of the least significant digit)

Metacognition Problem Solving Question: Has everyone in the group made an independent calculation or observation? All the members of a group need to make the calculations or observation. When there is agreement the calculations or observations are usually right. In real life there are no answer books. Determining if a solution is right or wrong is up to you.

14. Apply the rules for determining the number of significant digits or figures.
    1. All non-zero numbers count.
    2. Zeros to the left of the decimal point and the 1st non-zero digit don't count. example: 07.12 has 3 sig figs
    3. All zeros to the right of the decimal count only if there are any significant figures to the left of the zeros, examples:

       number	sig fig
       1.00	3
       0.001	1
       0.00100	3
       1.00100	6

    4. All zeros between 2 significant numbers count. example: 2007 has 4 sig

15. Apply the addition and subtraction rules for significant figures. Perform the operation then round to the

    least significant digit with the largest value.

		2	0	0
			1	3	.	7	9	4
				0	.	0	0	0	1
	+		2	7	.	8
Total		2	4	1	.	5	9	4	1
Rounded for sig figs		2	0	0

 

16. Apply the multiplication and division rules for significant figures. Perform the operation then round to the same number of significant digits as the value with the lowest number of significant digits.

     

    241 x 2	= 482
    Adjusted for sig figs	= 500

     

Relevance: Individuals who take Honors Physics will often have future careers in which they make numerically based presentations in a professional environment. Using an excessive number of significant figures is an unfortunate way of destroying one's credibility.