Chapter 2 Data Analysis

Units of Measurement Metric System The system of measurement used by Scientists Base unit modified by factor of 10 English System Used in United States – what we are familiar with

Data Analysis (continued) SI Base Units vs. English Units Time

Data Analysis (continued) SI Base Units vs. English Units Time – Second - Second

Data Analysis (continued) SI Base Units vs. English Units Length

Data Analysis (continued) SI Base Units vs. English Units Length – Meter – Inch, Foot, Yard

Data Analysis (continued) SI Base Units vs. English Units Mass

Data Analysis (continued) SI Base Units vs. English Units Mass – Gram – Ounce, Pound, Ton

Data Analysis (continued) SI Derived Units vs. English Units Derived unit is a unit combination of base units (two or more even if the same) Volume

Data Analysis (continued) SI Derived Units vs. English Units Volume – Liter – Ounce, Cup, Pint, Quart, Gallon

Data Analysis (continued) SI Base Units vs. English Units Temperature

Data Analysis (continued) SI Base Units vs. English Units Temperature – Celsius or Kelvin - Fahrenheit Add 273 degrees to go from Celsius to Kelvin

Data Analysis (continued) Prefixes – add to back of your periodic table PrefixSymbolFactorScientific Notation Kilok Decid1/ Centic1/ Millim1/

Density What is it? How much mass packed into an area Sink or float Formula Density = ____Mass_____ Volume

Scientific Notation Number from 1 to 10 and ten raised to a power If exponent is negative the number is less than 1 move to the left If exponent is positive the number is greater than 1 move to the right Addition and subtraction Get the same exponents first Add or subtract the base numbers – keep exponent the same Change exponent as required to base number less than 10

Scientific Notation (cont.) Multiplication (2 Steps) Multiply the bases Add the exponents Change exponent as required to base number less than 10 Division (2 Steps) Divide the bases (as problem dictates) Subtract the exponents (as the problem dictates) Change exponent as required to base number less than 10

Dimensional Analysis Problem solving focusing on the units What do I know (Units given) What do I want to know (Units I want) Conversion Factors Problems How many seconds in 24 minutes? How much is gas in pesos/Liter, assume $2.50/gal and 10 pesos = $1

Dimensional Analysis Problem: How many seconds in 24 minutes? Given x __#___units want = # units want 1 # units given 24 minutes x 60 seconds = 1440 seconds 1 1 minute Note: The minutes start on top so you put them on bottom in step 2. Also the 24 does not carry to step and 1 are the numbers used because there are 60 seconds in 1 minute.

Dimensional Analysis Problem: How much is gas in pesos/Liter, assume $2.50/gal and 10 pesos = $1 Given x __#___units want = # units want 1 # units given 2.50 dollars x 10 pesos x 1 gallon = 6.61 pesos/L gallon 1 dollar 3.78 liters Note: The dollars start on top so you put them on bottom in step 2. The gallons start on bottom so you put them on top is step 3. The math is 2.5 times 10 divided by 3.78

Accuracy and Precision Accuracy How close a measured value is to accepted value “How close are you to the bullseye” Precision How close a SERIES (more than 1) of measurements are to one another “How close are your arrows to each other”

Percent Error Used to evaluate the accuracy of experimental data Formula Percent error = ____error____ X 100 accepted value Use the absolute value of error (+ and – left off) Example on page 37 of textbook

Significant Figures Why do we use them? To reflect the accuracy of the instruments we are measuring with – we can only be as accurate as our least accurate instrument.

Significant Figures (cont) 4 Rules to follow (page 39 textbook) 1. Non-zero numbers are always significant 2. Zeros between non-zero numbers (or sig figs) are significant 3. All final zeros to the right of the decimal are significant 4. Placeholders zeros are not significant (convert to scientific notation to verify) 5. Counting numbers and constants have an infinite number of significant figures

Rounding Use Significant Figures If we are given multiple measurements to do a calculation ex) objects has a volume of 5 L and a mass of 4.56 g we can only calculate density to 1 significant figure. Therefore we round our answer to 1 significant figure.

Rounding (continued) Rules for Rounding (page 40 textbook) Look at the digit 1 to the right of the Significant figure you are rounding too. Round as you always have unless there is a five. Greater than 5 round up (1.46 = 1.5) Less than 5 leave the number (1.43 = 1.4) If 5, look at the next digit Non zero round up (1.451 = 1.5) Zero look at significant figure digit  Even round up (1.450 = 1.5)  Odd leave it (1.350 = 1.3)

Rounding (continued) Addition and subtraction Answer has same number of digits to the right of the decimal as your least measurement (round later) Ex) = Least number of places was 4.5 thus 13.6 Multiplication and division Answer has same number of significant figures as the measurement with fewest significant figures Ex) 4.5 * 4.56 * = Least significant figures was 4.5 thus 94

Graphing Circle Graph Looks like a pie with parts adding up to 100% (or close depending on rounding) Bar Graph “Bars” used to represent data. Height of bar indicates quantity of item. Line Graph Independent Variable on x-axis (the variable you changed) Dependent Variable on y-axis Plot a line as close to as many points as possible Look for correlation of data (linear, positive, negative)