1. Measurements and Calculations
Chapter 2
Measurements and Calculations

2. The Scientific Method A logical approach to solving problems.
1. Observation
2. Question/Problem
3. Hypothesis
4. Experiment
5. Analyze
6. Communicate

3. Observations Use senses to obtain information. State the facts
Observations Use senses to obtain information. State the facts!! No opinions! Qualitative = descriptive “The liquid is clear blue.” Quantitative = numerical “The liquid has a density of 1.21 g/mL.”

4. Question/Problem What questions do you have
Question/Problem What questions do you have? Does a problem need to be solved? Formulate a Hypothesis Testable statement or idea “I think…” “If…, then…”

5. Experiment Test your hypothesis Take measurements Collect data Analyze Results What does the data tell you? Patterns? Was the question answered? Problem solved? Develop models & theories Analysis can lead to more questions, too!!!

6. Communicate Publish results Confirmation from other scientists

7. Measurement All measurements require a number and a unit.
“The experiment requires 10.0 mL of ethanol.”
number = quantity of matter
unit = type of measurement

8. Significant Figures The measurement would be recorded as 1.75 cm.
all certain digits plus the estimated digit
The measurement would be recorded as cm.
This measurement contains 3 significant figures.
(“sig figs”)
certain
estimated

9. The number of sig figs in a measurement is determined by the precision of the measuring device.
1 cm
3 cm
0cm
1.1 cm
2.9 cm
0cm
1.10 cm
2.95 cm
0cm

10. Not all digits are significant!! Zeros are questionable!
a) sandwich zeros = SIG
b) at the end of a number with a decimal point = SIG
c) at the end of a number without a decimal point = NOT SIG
d) at the beginning of a number with a decimal point = NOT SIG

11. How many sig figs are in the following measurements?
145.7 meters 10.4 kilograms liters grams 250 milliliters 250. milliliters light years

12. Handling Measured Numbers and Math: Calculations and Sig Figs
The answer to a math problem cannot be more precise than the measured numbers used to get the answer.
Addition & Subtraction Rules:
Your answer should contain the fewest number of decimal places as indicated by the measured numbers.
Multiplication & Division Rules:
Your answer should contain the fewest number of sig figs as indicated by the measured numbers.

13. Examples: 132 g + 11.12 g - 43.0 mL 36.00 g (4.18 cm)(2 cm) 12.0 mL

14. Units of Measurement: SI Base Units
Type of Measurement
Definition
Unit and abbreviation
Mass
Amount of matter present
gram, g
Volume
Space occupied in 3 dimensions
Liter, L
Distance
Space between objects or points
Meter, m
Time
Passage of events
Second, s
Heat
Thermal energy
Joule, J
Temperature
Molecular motion
Degrees Celsius, °C
Kelvin, K
**Use reference paper for SI prefixes!

15. Unit Conversions: The Factor Label Method
Given Quantity x Conversion Factor(s) = Answer
What is a Conversion Factor?
a fraction that shows how two measurements are numerically equal to each other.

16. ex: 1000 milliliters = 1 Liter Conversion Factors would be…. ex: 365
ex: 1000 milliliters = 1 Liter Conversion Factors would be….. ex: days = 1 year Conversion factors would be:

17. Given Quantity x Conversion factor = Answer Ex: 25. 6 mL =. L Ex: 2
Given Quantity x Conversion factor = Answer Ex: 25.6 mL = ? L Ex: 2.90 years = ? days

18. Ex: 78 inches = ? m Ex: 155 pounds = ? kilograms
(1 inch = 2.54 cm) (100 cm = 1 m)
Ex: 155 pounds = ? kilograms
(1 lb = 454 g) (1000 g = 1 kg)

19. Ex: 10.0 miles per hour = ? meters per second
(1 mile = 5,280 ft) (1 m = 3.28 ft)
(1 hr = 60 min) ( 60 s = 1 min)

20. Derived Measurements
measurements that are calculated from other measurements
Area = length x width
Volume = length x width x height
Density = mass
volume

21. Examples:
1. What is the area of a rectangle that measures cm x 5.85 cm?
2. What is the density of a cube that measures 3.46 cm on each side and has a mass of g?
3. The density of a liquid is 1.15 g/mL. What volume of this liquid would have a mass of 25.0 grams?

22. Scientific Notation writing a number as a multiple of 10x.1,
1.6 x x 10-7
Numbers greater than 1 will have a positive exponent.
Numbers less than 1 will have a negative exponent.
You must keep one non-zero digit to the left of the decimal point.

23. Ex: Write the number in scientific notation
Ex: Write the number in scientific notation. 123,000 km = _______________ g = ________________ Ex: Write the number in standard form. 2.4 x 10-2 L = _______________ 5.02 x 105 m = _______________

24. Sci. Notation and Sig Figs
the 10x is NOT significant.
4.555 x 103 has ____sig figs
1.2 x has ____ sig figs
2.00 x has ____ sig figs

25. Sci. Notation and Your Calculator: Every calculator is slightly different. When possible use the EE or EXP button. 2.4 x 105 TYPE: 2.4E5 or 2.4EXP5 Can also use 10x, but you must put () around entire number! 2.4 x 105 TYPE: (2.4 x 10x5)

26. Examples:
4.23 x x 1011 = 4.55 x 1018 = 3.2 x 103 (5.4 x 10-7)(7.80 x 10-3) =

27. Precision vs. Accuracy in Measurement
how close multiple measurements are to each other.
the reproducibility of a measurement.
Accuracy –
how close a single measurement is to an accepted value

28. Accuracy vs. Precision Accurate ? Precise? Accurate? Precise?

29. Percentage Error Describes the accuracy of a measurement.
% error = (accepted value - experimental value) x 100
accepted value
% error can be a positive or a negative answer!!

30. example:
A student measures and calculates the density of a liquid as 1.35 g/mL. If the density of the liquid is actually g/mL, what is the student’s percent error?

31. Proportions
A proportion represents a relationship between two measurements.
Direct Proportion - as one variable increases, the second variable increases.
Inverse Proportion – as one variable increases, the second variable decreases.

32. Direct Proportion
Inverse Proportion