1. Chapter 2: Measurements and Calculations
Section 2.1 The Scientific Method, Objectives:
Describe the purpose of the scientific method.
Distinguish between qualitative and quantitative observations.
Describe the differences between hypotheses, theories, and models.

2. The Scientific Method:
a logical approach to solving problems by observing and collecting data, formulating hypotheses, testing hypotheses, and formulating theories that are supported by data.

3. The Steps:
1) Observations -the use of the senses
to obtain information (collect ________) and
define a problem.
data may be
Qualitative (_____________)
Quantitative (____________)

4. 2) Scientists make generalizations as to a
probable solution based on this initial data and use these generalizations to formulate a hypothesis, or testable statement; as to the solution to the defined problem.

5. Use the chart below to formulate a hypothesis about fertilizer and plant growth.

6. Experimentation -provides data to
support or refute a hypothesis or theory.
Constants are the experimental conditions that remain unchanged by the scientist.
Example from plant growth:
Variables are any experimental conditions that change.

7. Types of variables:
Independent variables are controlled by the experimenter.
Example from plant growth:
Dependent variables are dependent on the variables controlled by the experimenter.

8. 4) The Conclusion:
Unifying remarks (a summary) that communicate the results of your experimentation.
Example from plant growth:

9. The evolution of a hypothesis:
A theory is a broad generalization that explains a body of facts or phenomena.
A Scientific Law is a concise verbal statement or mathematical equation that summarizes a wide range of observations or experiences.

10. Section 2.2 Units of Measure, Objectives:
Distinguish between a quantity, a unit, and a measurement standard.
Name and use SI units for length, mass, time, volume, and density.
Distinguish between mass and weight.
Perform density calculations.

11. Units of Measurement and Quantities
Measurements represent quantities.
A quantity is something that has magnitude, size, or amount.
measurement  quantity
Examples:
(grams, mass) is a unit of measurement.
(grams, mass) is a quantity.

12. The choice of unit depends on the quantity being measured.
SI Measurement
Scientists all over the world have agreed on a single measurement system called Le Système International d’Unités, abbreviated _____.
The five common base units (see next slide).
Most other units are derived from these five.

13. Quantity Base Unit Abbreviation
SI Base Units:
Quantity Base Unit Abbreviation
Length
Mass
Time
Temperature
Amount of Substance

14. (prefixes based on powers of _____) Base Units and the Metric Scale:
The Metric System
(prefixes based on powers of _____)
Base Units and the Metric Scale:

15. Converting Between Prefixes:   ·    Because the prefixes are based on powers of ten, a move on the metric scale between prefixes is a move of the decimal point in the same direction.

16. Ex: Convert 350 cm to km.
Ex: Convert Ml to ml.

17. Volume is the amount of space occupied by an object in 3 dimensions.
More SI Units:
Combinations of SI base units form
derived units.
Volume is the amount of space occupied by an object in 3 dimensions.
The derived SI unit is cubic meters, m3
The cubic centimeter, cm3, is often used.
1 L = 1,000 cm3
1 mL = 1 cm3

18. Derived SI Units, continued
Density is the ratio of mass to volume, or mass ____ by volume.
The derived SI units:
Density is a characteristic physical property of a substance.

19. Density can be used as one property to help identify a substance.

20. Sample Problem: A sample of aluminum metal has a mass of 8. 4 g
Sample Problem: A sample of aluminum metal has a mass of 8.4 g. The volume of the sample is 3.1 cm3. (a) Calculate the density of aluminum. (b) What would be the mass of a 50 cm3 piece of aluminum?

21. Section 2.3 Using Scientific Measurements, Objectives:
Distinguish between accuracy and precision.
Determine the number of significant figures in measurements.
Perform mathematical operations involving significant figures.
Convert measurements into scientific notation.
Distinguish between inversely and directly proportional relationships.

22. Lesson Starter
Discuss using a beaker to measure volume versus using a graduated cylinder. Which is more precise?

23. Accuracy and Precision
Accuracy refers to the closeness of measurements to the correct or accepted value of the quantity measured.
Precision refers to the closeness of a set of measurements of the same quantity made in the same way.

24. Accuracy and Precision, continued
Percent Difference is calculated by subtracting the accepted value from the experimental value and dividing this difference by the accepted value, and then multiplying by 100.
* A measurement of ____________________.

25. Sample Problem:
A student measures the mass and volume of a substance and calculates its density as 1.40 g/mL. The correct, or accepted, value of the density is 1.30 g/mL. What is the percentage error of the student’s measurement?

26. Significant Figures in a measurement consist of all the digits known with certainty plus ONE estimated digit.
The term significant does not mean certain.
What is the reading from the diagram below?

27. Significant Figures, continued
Determining the Number of Significant Figures
Significant figures are critical when reporting scientific data because they give the reader an idea of how well you could actually measure/report your data. Before looking at a few examples, let's summarize the rules for significant figures.
1) ALL non-zero numbers (1,2,3,4,5,6,7,8,9) are ALWAYS significant.
2) ALL zeroes between non-zero numbers are ALWAYS significant.
3) ALL zeroes which are SIMULTANEOUSLY to the right of the decimal point AND at the end of the number are ALWAYS significant.
A helpful way to check rule 3 is to write the number in scientific notation. If you can/must get rid of the zeroes, then they are NOT significant.

28. Sample Problem:
How many significant figures are in each of the following measurements?
a) 28.6 g
b) 3,440 cm
c) 910 m
d) L
e) kg

29. Significant Figures, continued
Rounding

30. Significant Figures, continued
Addition or Subtraction with Significant Figures
When adding or subtracting decimals, the answer must have the same number of digits to the right of the decimal point as there are in the measurement having the fewest digits to the right of the decimal point.
Multiplication or Division with Significant Figures
For multiplication or division, the answer can have no more significant figures than are in the measurement with the least number of significant figures.

31. Sample Problem:
Carry out the following calculations. Express each answer to the correct number of significant figures.
a m m
b g/mL  mL =

32. In scientific notation, numbers are written in the form M × 10n, where the factor M is a number greater than or equal to 1 but less than 10 and n is a whole number.
example: mm becomes:

33. Scientific Notation, continued
1. Determine M by moving the decimal point in the original number to the left or the right so that only one nonzero digit remains to the left of the decimal point.
2. Determine n by counting the number of places that you moved the decimal point. If you moved it to the left, n is positive. If you moved it to the right, n is negative.

34. Scientific Notation, continued
Mathematical Operations Using Scientific Notation
Multiplication and division with scientific notation.
example: (5.23 × 106 µm)(7.1 × 10−2 µm)