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## Con 1 units

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**The Scientific Method**• 1. Observe the problem • 2. collect data • 3. search for laws that describe the problem • 4. form a hypothesis • 5. form a theory • 6. test or modify the theory.**Steps for the Scientific Method**Step # 1 – Observation • Observation – the act of gathering information (data) • Qualitative data – information with NO numbers • (hot, blue, rainy, cold) • Quantitative data – information with numbers • (98°F, 80% humidity, 0°C)**Steps for the Scientific Method**Step # 2 – Form a Hypothesis • Hypothesis – tentative explanation for what has been observed • There is no formal evidence at this point • It is just a gut feeling**Steps for the Scientific Method**Step # 3 – ExperimentationExperimentation – a set of controlled observations that test the hypothesis • Independent variable – the thing that you change in the experiment • Dependant variable – the thing that changes because you changes the independent variable • Constant – something that does not change during the experiment • Control – the standard for comparison**For example…**• Let’s say we are going to do an experiment testing what happens when you heat and cool a balloon… We will start with a balloon at room temperature**Now we will change something…**I will add heat to one balloon It will expand What will happen to the balloon’s size?**Now let’s cool things down**I will add cool down the balloon It will get smaller What will happen to the balloon’s size?**So what is what?**• What variable did YOU change? • Temperature • What variable changes BECAUSE you changed the temperature? • Size of the balloon • What is did not change in the experiment? • Amount of air in the balloon, what the balloon is made of… • What balloon did you use to compare the others to? • The room temperature balloon (Independent Variable) (Dependent Variable) (Constant) (Control)**Steps for the Scientific Method**Step # 4 – Conclusion • Conclusion – judgment based on the information obtained**Data Analysis: Basic Concepts**Topic 3 Base Units • There are seven base units in SI. • A base unit is a defined unit in a system of measurement that is based on an object or event in the physical world. • A base unit is independent of other units. • Some familiar quantities that are expressed in base units are time, length, mass, and temperature.**Data Analysis: Basic Concepts**Topic 3 Base Units**Data Analysis: Basic Concepts**Topic 3 Time**Data Analysis: Basic Concepts**Topic 3 Derived Units • Not all quantities can be measured with base units. • For example, the SI unit for speed is meters per second (m/s).**Data Analysis: Basic Concepts**Topic 3 Derived Units • Notice that meters per second includes two SI base units—the meter and the second. A unit that is defined by a combination of base units is called a derived unit. • Two other quantities that are measured in derived units are volume and density.**Data Analysis: Basic Concepts**Topic 3 Volume • Volume is the space occupied by an object. • The derived unit for volume is the cubic meter, which is represented by a cube whose sides are all one meter in length. • For measurements that you are likely to make, the more useful derived unit for volume is the cubic centimeter (cm3).**Data Analysis: Basic Concepts**Topic 3 Temperature Scales • Scientists use two temperature scales. • .**Data Analysis: Basic Concepts**Topic 3 Temperature Scales • THe defined the freezing point of water is 0 and the boiling point as 100.**Data Analysis: Basic Concepts**Topic 3 Temperature Scales • The Kelvin scale was devised by a Scottish physicist and mathematician, William Thomson, who was known as Lord Kelvin. • A kelvin (K) is the SI base unit of temperature. • On the Kelvin scale, water freezes at about 273 K and boils at about373 K.**Significant Figures**• Scientist use significant figures to determine how precise a measurement is • Significant digits in a measurement include all of the known digits plus one estimated digit**For example…**• Look at the ruler below • Each line is 0.1cm • You can read that the arrow is on 13.3 cm • However, using significant figures, you must estimate the next digit • That would give you 13.30 cm**Let’s try this one**• Look at the ruler below • What can you read before you estimate? • 12.8 cm • Now estimate the next digit… • 12.85 cm**The same rules apply with all instruments**• The same rules apply • Read to the last digit that you know • Estimate the final digit**Let’s try graduated cylinders**• Look at the graduated cylinder below • What can you read with confidence? • 56 ml • Now estimate the last digit • 56.0 ml**One more graduated cylinder**• Look at the cylinder below… • What is the measurement? • 53.5 ml**Rules for Significant figuresRule #1**• All non zero digits are ALWAYS significant • How many significant digits are in the following numbers? • 3 Significant Figures • 5 Significant Digits • 4 Significant Figures • 274 • 25.632 • 8.987**Rule #2**• All zeros between significant digits are ALWAYS significant • How many significant digits are in the following numbers? 3 Significant Figures 5 Significant Digits 4 Significant Figures 504 60002 9.077**Rule #3**• All FINAL zeros to the right of the decimal ARE significant • How many significant digits are in the following numbers? 3 Significant Figures 5 Significant Digits 7 Significant Figures 32.0 19.000 105.0020**Rule #4**• All zeros that act as place holders are NOT significant • Another way to say this is: zeros are only significant if they are between significant digits OR are the very final thing at the end of a decimal**Rule #5**• All counting numbers and constants have an infinite number of significant digits • For example: 1 hour = 60 minutes 12 inches = 1 foot 24 hours = 1 day**How many sig. Figs. Are in the following numbers?**• 56784 • 40002 • 600 • 34081000.00 • 123.4005 • 38726.000 • 7162534 • 100 • 200.0004**Data Analysis: Basic Concepts**Topic 3 Scientific Notation • When numbers larger than 1 are expressed in scientific notation, the power of ten is positive. • When numbers smaller than 1 are expressed in scientific notation, the power of ten is negative.**Data Analysis: Basic Concepts**Topic 3 Convert Data into Scientific Notation • Remove the extra zeros at the end or beginning of the factor. • Multiply the result by 10n where n equals the number of places moved. • Remember to add units to the answers.**Significant Digits in Calculations**• Now you know how to determine the number of significant digits in a number • How do you decide what to do when adding, subtracting, multiplying, or dividing?**Rules for Addition and Subtraction**• When you add or subtract measurements, your answer must have the same number of decimal places as the one with the fewest • For example: 20.4 + 1.322 + 83 = 104.722**Addition & Subtraction Continued**• Because you are adding, you need to look at the number of decimal places 20.4 + 1.322 + 83 = 104.722 (1) (3) (0) • Since you are adding, your answer must have the same number of decimal places as the one with the fewest • The fewest number of decimal places is 0 • Therefore, you answer must be rounded to have 0 decimal places • Your answer becomes • 105**Rules for Multiplication & Division**• When you multiply and divide numbers you look at the TOTAL number of significant digits NOT just decimal places • For example: 67.50 x 2.54 = 171.45**Multiplication & Division**• Because you are multiplying, you need to look at the total number of significant digits not just decimal places 67.50 x 2.54 = 171.45 (4) (3) • Since you are multiplying, your answer must have the same number of significant digits as the one with the fewest • The fewest number of significant digits is 3 • Therefore, you answer must be rounded to have 3 significant digits • Your answer becomes • 171**Accuracy vs. precision**• The quality of a measurement depends on the measuring instrument and the person making the measurement. • Accuracy = how close the measurement is to the actual value. • Precision = the agreement among the values for the measurement.**For Example…**• Let’s say we had the following dart board Is the accuracy good or bad? Accuracy - GOOD Precision - GOOD Is the precision good or bad?**Try this one**• Let’s say we had the following dart board Is the accuracy good or bad? Accuracy - BAD Precision - GOOD Is the precision good or bad?**Try this one**• Let’s say we had the following dart board Is the accuracy good or bad? Accuracy - BAD Precision - BAD Is the precision good or bad?**Ways to determine density**• 1. regularly shaped objects – direct volume measurement. • 2. Irregularly shaped objects- use water displacement method to fine volume.**Data Analysis: Basic Concepts**Topic 3 Density • Density is a ratio that compares the mass of an object to its volume. • The units for density are often grams per cubic centimeter (g/cm3). • You can calculate density using this equation:**density**• D=m/v • Density units always is g/cm3 • Mass is always in g • Volume is always in cm3 • If it is not you must convert • Note 1ml = 1cm3 ; 1 L = 1 dm3**Dimensional Analysis**• Dimensional analysis is just a big word for going from one unit to another. • Have you ever converted inches into feet or years into days? • If so, then you have done dimensional analysis**Dimensional Analysis**• Dimensional Analysis – method of problem-solving that focuses on changing units • Conversion Factor – a ratio of equal values used to go from one unit to another • Example: 1 foot = 12 inches • Can be written as 1 foot 12 inches**Rules for Dimensional Analysis**• ALWAYS start with the given!!! • Draw a multiplication sign and a line • Place the unit to be canceled on the bottom • Place a conversion factor on the line you have drawn • Cross out units and see what you have left. • You must have one on top & one on the bottom A x B A / /**% error**• % error – the deviation from the accepted value during an experiment. Usually caused by human error. • % error = your value - literature valuex 100 • literature value • It is always a positive number**Data Analysis: Additional Concepts**Topic 3 Graphing • Using data to create a graph can help to reveal a pattern if one exists. • A graphis a visual display of data.