1. Measurements and Calculations
Chapter 2 Notes
Measurements and Calculations

2. The Scientific Method
The scientific method is a logical approach to solving problems by observing and collecting data, formulating and testing hypotheses, then developing theories that are supported by data.
The scientific method is broken into five steps

3. Five Steps of Scientific Method
Observing and collecting data
Observing uses the senses to obtain information
Qualitative observation: non-numerical information
Quantitative observation: numerical information
Formulating hypotheses
Hypotheses are testable statements
Usually in the form of If - Then statements

4. Testing hypotheses Theorizing
Design and implement an experiment that will test the If – Then statement
Theorizing
Model: explanation of how phenomena occur and how data or events are related
Theory: broad generalization that explains a body of facts

5. Publish results
This is done so that others can duplicate experiment to verify the results

6. SI Units of Measurements
Quantity: something that has magnitude, size, or amount
Weight: measure of the gravitational pull on matter
Kilogram (kg)
Mole: measure of the amount of a substance
Length: measure of distance
Meter (m)
Time: system for measuring intervals
Seconds (s)

7. Derived SI Units
Volume: amount of space occupied by an object. Length X Width X Height
Cm3 or mL
Density: mass per unit of volume
Grams per cm3 or mL

8. Conversion Factors
Conversion factors are a ratio derived from the equality between two different units that can be used to convert from one unit to the other

9. Deriving Conversion Factors
Set up an equality
Write two possible combinations
Pick combination that has the unit needed on top and the unit to cancel on bottom

10. Using Scientific Measurement
Accuracy: closeness of a measurement to the accepted value
Precision: closeness of a set of measurements made in the same way
Percent error
= accepted value – experimental value X 100%
accepted value

11. Significant Figures All known digits plus one estimated digit
Atlantic / Pacific rule
If a decimal is ABSENT, start counting from the ATLANTIC (right) side with the first non-zero number and count all digits to the left
If a decimal is PRESENT, start counting from the PACIFIC (left) side with the first non-zero number and count all digits to the right

12. Scientific Notation
In scientific notation, numbers are written in the form of M X 10n, where the factor M is a number greater than or equal to 1 but less than 10 and n is a whole number
Big numbers have positive exponents
Small numbers have negative exponents

13. Examples of Scientific Notation
65,000 km = 6.5 x 104 km
mm = 1.2 x 10-4 mm
560,000 km
= 5.6 x 105 km
33,400 kg
= 3.34 x 104 kg m
= x 10-4 m

14. Mathematical Operations with Significant Figures
Addition and Subtraction
The answer can have no more places past the decimal than the least of the terms being added or subtracted
Multiplication and Division
The answer can have no more significant figures than the least of the terms being multiplied or divided

15. Direct Proportions
Two quantities are directly proportional to each other if dividing one by the other gives a constant value
y / x = k
k is a proportionality constant
y = k x
Graphing the data gives you a straight line

16. Inverse Proportions
Two quantities are inversely proportional to each other if their product is constant
xy = k
Graphing the data produces a curve called a hyperbola