measurements and calculations chapter 2. 2.1 scientific method a scientific method is a way to...

MEASUREMENTS AND CALCULATIONS

Chapter 2

2.1 Scientific Method

A scientific method is a way to logically approach a problem by making observations, testing a hypothesis, gathering and analyzing data, and forming conclusions.

There are many scientific methods

observations

Using your senses to gather information

Qualitative: descriptive Quantitative: numerical

Most science experiments utilize quantitative observations

hypothesis

A hypothesis is a testable statement

Often written as “if-then” statements (Ex: if marigold flowers are watered with miracle grow, then their plant growth will be enhanced)

Tested through experiments to determine if accepted or rejected

data analysis

This crucial step is used to determine if the hypothesis is accepted or rejected through statistical analysis (t-test, ANOVA, Mann-Whitney, etc)

Both outcomes can be an important contribution to science since they can be used as a stepping stone for future experiments

Graphs and charts that depict the results are often incorporated into a lab report

conclusions

Based on the results of the experiment, conclusions can be made

Results can then be published and shared with colleagues

models

A visual, verbal, conceptual, or mathematical explanation for something abstract or difficult to explain

Ex: model of an atom

theory

DON’T USE THE WORD THEORY INCORRECTLY!!!!

A theory is a broad generalization that explains a body of facts or phenomenon and is supported by experimental evidence

Theories can change as new advancements in science take place

Ex: the Big Bang Theory

law

A generalized rule that is used to explain a body of observations in the form of a verbal or mathematical statement.

Imply a cause and effect between the observed elements and must always apply under the same conditions

Ex: Law of Gravity

Science is……

Testable- Predictions are tested through experiments and the results either support or do not support the hypothesis or theory. NOTHING IS PROVEN IN SCIENCE!

Tentative- Science CHANGES! All scientific explanations are the best we can do now. Through investigation and technological advancements, we understand more all the time

2.2 Units of Measurement

Scientific Notation: a method to make writing and handling very large or very small numbers easy

34000000 = 3.4 x 107

.000000076 = 7.6 x 10-7

Operations with Scientific Notation Exponents must match with addition and

subtraction

Exponents are added for multiplication

Exponents are subtracted for division

measurements

Chemistry is qualitative and quantitative

Measurements are used to represents quantities

A quantity has magnitude, size or amount

Ex: a liter is a unit of measurement while volume is a quantity

SI Measurements

SI units are used in science (7 base units)

Mass-kilogram (kg) Length- meter (m) Temperature-Kelvin (K) Amount of a substance- mole (mol) All SI units can be modified by using

prefixes Ex: kilo = 1000 = 1 x 103

1 kilometer = 1000 meters = 1 x 103 meters

SI Prefixes

Mega M 106

Kilo K 103

Base units (m, L, g) Centi c 10-2 Milli m 10-3 Micro µ 10-6 Nano n 10-9

Pico p 10-12

Derived units

Formed by combinations of SI units Ex: meters/second

Density = mass/volume Density is important for identifying

substances Given in kg/m3

Density of water = 1 kg/m3

Conversions

Conversion factors express an equality between two different units

Quantity given x conversion factor = quantity sought

Remember: X = 1 1

Factor Label Method

Based on the number of equalities and multiplication and division in series

Ex: convert 250,000 mg to kg

2.5 x 105mg 1 x 10-3 g 1kg = 2.5 x 105-3 x 1 1 1 mg 1x103g 1x1x1x103

2.5 x 102 kg = 2.5 x 10-1kg 1 x 103

2.3 Using Scientific Measurements Accuracy vs Precision

Accuracy is the closeness of measurements to the true value or correct answer

Precision refers to the closeness of a set of measurements to one another. (precision is more related to the way in which the measurements are made)

Accuracy vs Precision

Calculating Percent Error

Percent error = valueaccepted – valueexperimental X 100

valueaccepted

percent error will have a positive value if the accepted value is greater than the experimental value

Will be negative if the accepted value is less than the experimental value

Example #1

What is the percent error if the length of a wire is 4.25 cm if the correct value should be 4.08 cm?

% error = va – ve X 100

va

% error = 4.08 – 4.25 X 100 = - 4.2 %

4.08

Example #2

The actual density of a material is 7.44 g/cm3. A student measures density to be 7.30 g/cm3. What is the percent error?

% error = 7.44 g/cm3 – 7.30 g/cm3 x 100 7.44 g/cm3

= 1.88 %

Significant Figures

Sig figs consist of all the digits known with certainty plus one final digit which is somewhat uncertain or estimated

If the number has no zeroes, all digits are significant

Follow the rules in the table!

Rules for Determining Sig Figs 1.  Always count nonzero digits Example:  21 has two significant figures, while 8.926 has four 2.  Never count leading zeros Example:  021 and 0.021 both have two significant figures 3.  Always count zeros which fall somewhere between two nonzero

digits Example:  20.8 has three significant figures, while 0.00104009 has

six 4.  Count trailing zeros if and only if the number contains a decimal

point Example:  210 and 210000 both have two significant figures, while

210. has three and 210.00 has five 5.  For numbers expressed in scientific notation, ignore the

exponent and apply Rules 1-4 to the number Example:  -4.2010 x 1028 has five significant figures

Direct Proportions

Two quantities are directly proportional to each other if dividing one by the other gives a constant value

Example: doubling the mass of a sample doubles the volume

Inverse Proportions

Two quantities are inversely proportional if their product is constant

Example: doubling the speed cuts the required time in half