 # Chapter 2: Analyzing Data

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Chapter 2: Analyzing Data

SI Units Only US and Liberia use English system
World wide, science uses SI units Benefits of SI Universal Uses multiples of 10 No conversions = less error No fractions (move decimal) Prefixes used for all bases

SI Units

SI Units: Length and Mass
1 inch = ~2.54 cm 1 meter = ~ yard Mass 1 kg = ~ 2.2 lbs Measured on analytic scales in lab Doesn’t factor gravity (therefore in space 1 kg = 0 lbs)

SI Units : Temperature US Fahrenheit freezing = 32 degrees
boiling = 212 degrees) Majority World Celsius Freezing = 0 degrees Boiling = 100 degrees SI Units Kelvin At 0 Kelvin is where particles have lowest energy.

SI Units: mole Amount of a substance
1 mole of any pure element has 6.02 x 1023 atoms. Each element has its own unique molar mass Mass of substance Given on periodic table

\$620,000,000,000,000,000,000,000

Derived SI Units: Volume
Amount of space an object takes up Cubes and Rectangles Length X Width X Height Irregular Shapes Water displacement 1 Liter = ~ 1 quart (larger units) 1 ml = 1 cm3 (most often in lab) 29.6 ml = ~ 1 oz (12 oz can of pop has 355 ml) Water Displacement

Derived SI Units: Density
Amount of mass per unit of volume Can be used to identify substances page 971 Objects greater density sink Object lower density float Mass in grams Volume in ml or cm3

Scientific Notation Science often involves numbers that are very big or very small. Scientific notation makes the numbers easier to write

How wide is our universe?
210,000,000,000,000,000,000,000 miles (22 zeros) This number is written in decimal notation. When numbers get this large, it is easier to write them in scientific notation.

Scientific Notation A number is expressed in scientific notation when it is in the form a x 10n a is between 1 and 10 n is an integer. Example: 6.02 x 1023

Write the width of the universe in scientific notation.
210,000,000,000,000,000,000,000 miles Where is the decimal point now? After the last zero. Where would you put the decimal to make this number be between 1 and 10? Between the 2 and the 1

2.10,000,000,000,000,000,000,000. How many decimal places did you move the decimal? 23 When the original number is more than 1, the exponent is positive. The answer in scientific notation is 2.1 x 1023

1) Express 0.0000000902 in scientific notation.
Where would the decimal go to make the number be between 1 and 10? 9.02 The decimal was moved how many places? 8 When the original number is less than 1, the exponent is negative. 9.02 x 10-8

Write 28750.9 in scientific notation.
x 10-5 x 10-4 x 104 x 105

Practice Problems 2) Express 1.8 x 10-4 in decimal notation. 0.00018
4,580,000

Using a Calculator On the calculator Use or button. Example
4.58 x 106 is typed

4) Use a calculator to evaluate: 4.5 x 10-5 1.6 x 10-2
Type You must include parentheses if you don’t use buttons!! (4.5 x ) (1.6 x ) Write in scientific notation. x 10-3

5) Use a calculator to evaluate:. 7. 2 x 10-9. 1
5) Use a calculator to evaluate: x x 102 On the calculator, the answer is: 6.E -11 The answer in scientific notation is 6 x The answer in decimal notation is

6) Use a calculator to evaluate (0. 0042)(330,000)
6) Use a calculator to evaluate (0.0042)(330,000). On the calculator, the answer is 1386. The answer in decimal notation is 1386 The answer in scientific notation is 1.386 x 103

7) Use a calculator to evaluate (3,600,000,000)(23)
7) Use a calculator to evaluate (3,600,000,000)(23). On the calculator, the answer is: 8.28 E +10 The answer in scientific notation is 8.28 x 10 10 The answer in decimal notation is 82,800,000,000

Write (2.8 x 103)(5.1 x 10-7) in scientific notation.

Write 531.42 x 105 in scientific notation.

Exponents of numbers added MUST be the SAME If not adjust a number to make them the same Give the answer in proper scientific notation

Multiplying and Dividing
Coefficients DO NOT have to be the same 2 step process Multiplication Multiply coefficients Add Exponents Division Divide coefficients Subtract exponent

Example Multiplication

Example Division

Dimensional Analysis 2.75 dozen X 12 eggs 1 dozen = 33 eggs
Used to convert from one unit to another Allows for equivalents Used to convert from US to SI Units Used everyday 1 dozen eggs = how many eggs? How many eggs in 2.75 dozen eggs? 2.75 dozen X 12 eggs 1 dozen = 33 eggs

Dimensional Analysis 1 day X 24 hour 1 day X 60 min 1 hour X 60 sec
Problem How many seconds are in a day? Conversion Factors 60 sec = 1min 60 min = hour 24 hours = 1day Solve 1 day X 24 hour 1 day X 60 min 1 hour X 60 sec 1 min = 86,400 sec

Dimensional Analysis Practice problem: 2.4 page 6 1) Analyze: Reread and determine specific info and data given : Determine what you need to find 2) Plan: Develop method to solve (What conversion factors do you need and how should you arrange them?) 3) Compute: Follow your plan and find answer 4) Evaluate: Make sure your answer makes sense and no errors

Dimensional Analysis Practice: A car is traveling 65.0 miles per hour. How many km per hour is the car traveling? 1 mile = 5280 feet 1 inch = 2.54 cm 65.0 miles x 5280 feet x 12 inches x 2.54 cm x 1 m x 1 km = hour 1 mile 1 foot 1 inch 100 cm 1000 m = km/hr Sig figs = 105 km/hr

Uncertainty in Data Error always present in measurements
SI Units help prevent conversion errors only Data results should be both… Precise Data repeatedly the same Accurate Data results measure close to actual value Average correct

Uncertainty in Data and Significant Digits
Used to estimate numbers Used in lab when collecting quantitative data Helps provide degree of certainty

Rules for Significant Digits
Nonzero numbers ALWAYS significant ex: 45,234 (5 sig figs) Zeros between none zero numbers ALWAYS significant ex: (5 sig figs) Trailing zeros ONLY significant AFTER a decimal point 32,000 Not significant (2 sig figs) Significant (4 sig figs) Leading zeros AFTER decimal point NEVER significant ex: (1 sig fig)

Significant Figures EXAMPLES 12.34 12.01 0.0032 0.3210 893,000
(4 sig figs) 12.01 0.0032 (2 sig figs) 0.3210 (3 sig figs) 893,000

Significant figures ON YOUR OWN 602,000 2.0156 0.00412 516.90 78,091.0
(3 sig figs) 2.0156 (5 sig figs) 516.90 78,091.0 (6 sig figs)

Significant Digits Rounding in Significant digits
If a 5 or greater follows round up If the number following is 4 or less the number remains Example: 1) Round to 3 significant digits Answer 3.58 2) Round to 2 significant digits Answer

Significant Digits On own Round 54,312.98 to 4 significant digits
54,310 Round to 3 significant digits 0.0231 Round to 3 significant digits 0.350

Multiplying/Dividing with Significant Digits
Find the number of significant digits in each number Use the smaller number of significant digits in your final answer. Example: x .201 = 67.2

Multiplying/Dividing with Significant Digits
On own x 3.1 = 2,100 9.340/3 = 3 32,000/.0342 = 940,000

Must line up decimal points in numbers Significant digits not based on total number of significant digits Significant digits based on number of digits after decimal point Example 1) = 48.5

On own = 84.69 902 – 8.02 = 894 0.654 – = 0.561

Representing Data Graphs Used to determine/show patterns 3 main types
Circle/Pie charts Bar Graphs Line Graphs

Representing Data – Circle Graph
Used to show parts of a fixed whole Bar Graph Shows varying qualitative data Quality measured on y-axis Independent variable on x-axis Line Graph Most often used in chemistry Represents data of independent and dependent variable Dependent variable on y-axis

Representing Data- Line Graphs
Independent Variable on x-axis Dependent variable on y-axis Best fit lines Not all data points exactly through all points Line drawn to attempt to make… equal the number of points both above and below line If line straight… Variables are directly related Slope can be used to determine relationship Slope = rise/run = ∆y/∆x + slope: both variables increase or both decrease - slope: one variable increases, other variable decreases

What is the… Independent Variable Dependent Variable What does data represent

Drawing a line graph Pages textbook