Chapter 1: Measurement

Many properties of matter are quantitative The Metric System Many properties of matter are quantitative This means that matter can be measured Measured quantities of matter must always be specified in units The units used for scientific measurement are those of the metric system

Units of the Metric System These units are called SI units The metric system is a base-ten decimal system: Each unit is ten times larger than the next smaller unit In 1960, an international system of metric units was agreed upon for use in scientific measurement These units are called SI units

Prefixes used in the metric system Symbol Unit Scientific mega- M 1,000,000.0 10^6 kilo- k 1,000.0 10^3 hecto- h 100.0 10^2 deka- da 10.0 10^1 meter (base) m 1.0 10^0 deci- d 0.1 10^-1 centi- c 0.01 10^-2 milli- 0.001 10^-3 micro- μ 0.000001 10^-6 Nano N 0.000000001 10^-9

Metric Conversions using Dimensional Analysis The key to using dimensional analysis is the correct use of conversion factors What is a conversion factor? A conversion factor is a fraction whose numerator and denominator are the same quantity expressed in different units

Example of a conversion factor: Inches to centimeters Both the numerator and the denominator are expressing the same quantity of length using different units

Unit When using conversion factors, we want the given units to cancel Then we end up with the desired units Unit Example: Using conversion factors, convert 6.25 inches to centimeters

? Step 1: Use our inches-to-centimeters conversion factor Question: Which one do we use? or ?

Step 2: Set up the calculation like this Answer: We want the desired unit in the numerator of the conversion factor Step 2: Set up the calculation like this The inch units cancel, and we are left with centimeters, our desired unit

Let’s use conversion factors to express 2.6 meters as millimeters: Here are the conversion factors we need:

Always set up your calculations so that given units cancel, and you get the desired units at the end

Scientific Method

Science and Induction Scientific investigation can lead to important conclusions based on a type of logic called inductive reasoning An inductive conclusion is a generalization that summarizes many concurrent observations Observation General Principle

Example: All the swans at Lake Mead are white in color All the swans at Lake Powell are white in color All the swans at Lake Michigan are white in color All the swans at Lake Okeechobee are white in color Argument: Therefore, all swans are white

There is a big problem with this argument: This is inductive reasoning: The argument that all swans are white is a generalization made from many specific observations Observation General Principle There is a big problem with this argument: What is it?

If someone finds a black swan at another lake somewhere, our argument, or theory, is no longer valid

Deductive logic differs from inductive logic When using deductive logic, we go from general premises to specific conclusions Who is this guy?

This is Socrates, and we’ll use him in an example of deductive logic

Therefore, Socrates is mortal All men are mortal Socrates is a man Therefore, Socrates is mortal Or… All organisms are composed of tiny cells Socrates is an organism Therefore, Socrates is composed of tiny cells

General Premises Specific Conclusion In the process of science, the deduction usually takes the form of predictions about what the outcomes of our experiments or observations should be We then test the hypothesis by performing an experiment to see whether or not the results are as predicted

As a formal process of inquiry, the scientific method consists of a series of steps. Most science is far less structured than presented here. The key element here is the use of hypothetico-deductive reasoning.

Hypothetico-Deductive Reasoning My flashlight doesn’t work Hypothetico-Deductive Reasoning What’s wrong with my flashlight? The batteries are dead If I my hypothesis is correct… …and I replace the batteries

My flashlight should work! Then: My flashlight should work! But what if my flashlight still doesn’t work?

Alternative hypotheses: The bulb is burned out… We can always generate alternative hypotheses and test them in the same manner… Alternative hypotheses: The bulb is burned out… The contacts are corroded… The on-off switch is broken…

One black swan can disprove our theory that all swans are white The point here is that any one of these hypotheses can be tested according to the scientific method It is also important to note that all these hypotheses are falsifiable under the scientific method Remember our theory about the swans: according to the scientific method we look for evidence that disproves our theory One black swan can disprove our theory that all swans are white

Experimental Design

In order to test a hypothesis we must design a suitable experiment Experiments In order to test a hypothesis we must design a suitable experiment When performing our experiment, we must look for results relating to our hypothesis These results will either support or not support our hypothesis

I will use plants grown hydroponically (in water rather than soil) I want to conduct an experiment to identify essential nutrients required in plants I will use plants grown hydroponically (in water rather than soil) One group of plants will grow in an aqueous solution of complete nutrients Another group of plants will grow in a solution lacking one nutrient

Hydroponic Farming

The control group allows us to compare with the experimental group Our plants growing in a complete nutrient solution is called the control group Our plants growing in a solution missing one nutrient is called the experimental group The control group allows us to compare with the experimental group If the missing nutrient has an effect on the experimental plants, their appearance should be different than the control group plants

What about the variables? For our experiment to succeed, we must identify all of the variables One variable is the growth response of the plants in the incomplete nutrient solution Another variable is the difference in the experimental nutrient solution

We call this variable the independent variable The incomplete nutrient solution is the variable that we, as investigators, are manipulating We call this variable the independent variable We will measure the effect of the independent variable on the growth of the plants The response of the plants to the altered nutrient solution is called the dependent variable

We call the response of the plants the dependent variable because the magnitude of the response “depends” on how we manipulate the independent variable

Homework 1. Create your own experiment using the scientific method. 2. Set it up like the flashlight experiment showing all steps of the scientific method 3. It can be simple like the flashlight or more complicated like the growth of the plant 4. You should list all the steps of the scientific method and show how your experiment follows these steps