1. Measurements and Calculations
Chapter 2
Measurements and Calculations

2. Scientific Method:
A systematic approach to solving problems.

3. 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.

5. Observing Observing is the use of the senses to obtain information.
Observation usually involves making measurements and collecting data.
The data collected can be qualitative (descriptive) or quantitative (numerical).

6. Systems Experiments must be carried out under controlled conditions.
A system is a specific portion of matter in a given region of space that has been selected for study during an experiment.

7. Hypothesis A hypothesis is a testable statement.
They are often stated as “if-then” statements.
The “then” part is the prediction and what is tested.

8. Testing Hypotheses
During testing, the experimental conditions must remain constant and are called controls.
Any condition that changes is called a variable.

9. Theorizing
A model in science is more than a physical object, it is often an explanation of how phenomena occur and how data or events are related. Ex. Atomic Model
A theory is a broad generalization that explains a body of facts or phenomena.

10. Units of Measurement

11. SI Units Système International d’Unités
Uses a different base unit for each quantity

12. A quantity is something that has magnitude, size, and amount.
There are 7 SI base units and all others can be derived.
For example, mass is measured in Kg while weight (the measure of gravity on an object) is measured in Newtons.
Length is measured in meters.
When using a formula, all data must be in it’s base unit. For example, mass must be measured in Kg before plugging it in.

13. Volume
The most commonly used metric units for volume are the liter (L) and the milliliter (mL).
A liter is a cube 1 dm long on each side.
A milliliter is a cube 1 cm long on each side.

14. Derived Units Combinations of SI base units form derived units.
For example, the formula for Density is
D = M / V
Mass is measured in Kg and V is measured in m3.
So what is the unit for Density?

15. Physical property of a substance
Density:
Physical property of a substance d= m V

16. A chunk of gold has a Density of 32 kg/m3 with a mass of 29 kg
A chunk of gold has a Density of 32 kg/m3 with a mass of 29 kg. What is the volume?

17. If you have equal masses of the following metals, which will occupy the largest volume?
Au, density = 19.3 kg/m3
Pb, density = 11.3 kg/m3
Ag, density = 10.5 kg/m3
Cu, density = 8.92 kg/m3
Al, density = 2.70 kg/m3

18. If you have equal masses of the following metals, which will occupy the largest volume?
Au, density = 19.3 kg/m3
Pb, density = 11.3 kg/m3
Ag, density = 10.5 kg/m3
Cu, density = 8.92 kg/m3
Al, density = 2.70 kg/m3

19. Conversions

20. Metric System
Prefixes convert the base units into units that are appropriate for the item being measured.

21. A microgram (mg) is equal to how many grams?10
1  103 g
1  106 g

22. Correct Answer: 1  106 g 1  103 g 10 1  103 g 1  106 g
Recall that the prefix micro-means 106.

23. 5 meters = ? kilometers

24. 3.24 cm = ? Inches if 2.54 cm = 1 inch (Conversion Factor)

25. 3.24 in = ? cm if 2.54 cm = 1 inch

26. Temperature:
A measure of the average kinetic energy of the particles in a sample.

27. Temperature
In scientific measurements, the Celsius and Kelvin scales are most often used.
The Celsius scale is based on the properties of water.
0C is the freezing point of water.
100C is the boiling point of water.

28. Temperature The Kelvin is the SI unit of temperature.
It is based on the properties of gases.
There are no negative Kelvin temperatures.
K = C

29. Temperature
The Fahrenheit scale is not used in scientific measurements.
F = 9/5(C) + 32
C = 5/9(F − 32)

30. It’s 95 degrees Fahrenheit. How much is that in Celsius?

31. It’s 34 degrees Celsius. How much is that in Fahrenheit?

32. What is the room temperature (~72°F) in °C.

33. What is the room temperature (~72°F) in °C.

34. Uncertainty in Measurement

35. Accuracy versus Precision
Accuracy refers to the proximity of a measurement to the true value of a quantity.
Precision refers to the proximity of several measurements to each other.

36. Uncertainty in Measurements
Different measuring devices have different uses and different degrees of accuracy.

37. Percentage Error
Percentage error is calculated by subtracting the accepted value from the experimental value, dividing the difference by the accepted value, and then multiplying by 100.
% Error = (V exp – V accep)/ V accep

38. A student measures the mass and volume of a substance and calculates it’s density at 1.4 kg/m3. The accepted value is 1.3 kg/m3. What is the percent error?

39. Significant Figures
The term significant figures refers to digits that were measured.
When rounding calculated numbers, we pay attention to significant figures so we do not overstate the accuracy of our answers.

40. Significant Figures All nonzero digits are significant.
Zeroes between two significant figures are themselves significant.
Zeroes at the beginning of a number are never significant.
Zeroes at the end of a number are significant if a decimal point is written in the number.

41. Solving Problems
1. Write down each number in problem and what it is. (Write Knowns).
2. Write down what the problem is looking for. (Write unknowns).
3. Choose the equation that fits.
4. Plug in numbers and calculate the answer.

42. Calculate the volume of a sample of aluminum that has a mass of 3
Calculate the volume of a sample of aluminum that has a mass of kg. The density of aluminum is 2.7 kg/m3.