Observations, Measurements And Calculations

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Unit 0 – Observations, Measurements and Calculations
1.3 Thinking Like a Scientist - 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"
A. Observing and Collecting Data
1. Observing
a. The use of the senses to obtain information
(1) quantitative data
(2) qualitative data
2. Experimenting
a. Carrying out a procedure under controlled conditions
3. System
a. A specific portion of matter in a given region of space that has been selected for study during an experiment or observation
B. Formulating Hypotheses
1. Generalizations about data are used to formulate a testable statement, or hypothesis
C. Testing Hypotheses
1. Experimentation yields data that results in the discarding, modification, or adoption of a hypothesis or theory
D. Theorizing
1. A theory is a broad generalization that explains a body of facts or phenomena
a. It must allow for successful prediction of future behaviors within a system
E. Publish Results
1. Experimental results must be repeatable by other scientists
3.1 Measurements and Their Uncertainty
Scientific Notation
A. Scientific Notation
1. A method of representing very large or very small numbers
a. M x 10n
(1) M is a number between 1 and 10
(2) n is an integer
(3) all digits in M are significant
B. Reducing to Sci Notation
1. Move decimal so that M is between 1 and 10
2. Determine n by counting the number of places the decimal point was moved
a. Moved to the left, n is positive
b. Moved to the right, n is negative
A. Mathematical Operations Using Scientific Notation
1. Addition and subtraction
a. Operations can only be performed if the exponent on each number is the same
2. Multiplication
a. M factors are multiplied
b. Exponents are added
3. Division
a. M factors are divided
b. Exponents are subtracted (numerator - denominator)


Accuracy, Precision, and Error
A. Accuracy
1. The nearness of a measurement to its accepted value
B. Precision
1. The agreement between numerical values of two or more measurements that have been made in the same way
a. You can be precise without being accurate
b. Systematic errors can cause results to be precise but not accurate
C. Calculating Percent Error (Relative Error)

 Valueaccepted − Valueexp erimental
Percent Error = 


1. Percent error can

 x100

have negative or positive values

D. Error in Measurement
1. Some error or uncertainty exists in all measurement
a. no measurement is known to an infinite number of decimal places
2. All measurements should include every digit known with certainty plus the first digit that is uncertain - these are the significant figures

Significant Figures
A. Determining the Number of Significant Figures
1. All nonzero digits are significant
2. Rules for zeros
Zeros appearing between nonzero digits are significant
a) 40.7 L has three sig figs
b) 87 009 km has five sig figs
Zeros appearing in front of nonzero digits are not
a) 0.095 987 m has five sig figs significant b) 0.0009 kg has one sig fig
Zeros at the end of a number and to the right of a
a) 85.00 g has four sig figs decimal are significant
b) 9.000 000 000 mm has 10 sig figs
Zeros at the end of a number but to the left of a decimal
a) 2000 m may contain from one to four sig figs, may or may not be significant. If such a zero has been depending on how many zeros are placeholders. measured, or is the first estimated digit, it is significant.
For measurements given in this text, assume that
On the other hand, if the zero has not been measured or
2000 has one sig fig. estimated but is just a placeholder, it is not significant. A b) 2000. m contains four sig figs, indicated by the decimal placed after the zeros indicates that they are presence of the decimal point significant. B. Addition