Chapter 2: Measurement & Problem Solving pg LO: I can use scientific notation with sig figs in mathematic calculations.

Math in Chemistry? Types of math involved 1.Addition, subtraction, multiplication, division, solving for variables, etc. 2.Scientific Notation 3.Significant figures (Sig. Figs) 4.Conversion factors

Scientific Notation Ex: How can we write a large number like 3,560,000,000 more compactly?  Solution: Use scientific notation!  allows for numbers to be represented as multiplied by powers of 10. ex. 10 x 10 x 10 x 10 = 10,000 or 10 4 How to change a number into scientific notation Move the decimal to after the first real number (left or right).

Rules of scientific notation 1)3,560,000,000  3.56 x 10 9 A positive exponent (3.56 x 10 9 ) Means decimal moved to the left n times. 2)  3.56 x A negative exponent (3.56 x ) Means decimal moved to the right n times. Question: is x but how many total numbers should I write down in the final answer?

Important Rules for Sig Figs Numbers are significant if… 1)A nonzero number ex. Any real number: )Zeros between two numbers ex. 104 or )Trailing zeros after a number with a decimal ex or )Zeros between a decimal and a real number ex or

Important Rules for Sig Figs Numbers are insignificant if… 1)Leading zeros to the left of the first nonzero number ex )Trailing zeros after a number without a decimal ex. 270 (2 sig figs) Special cases and additional understanding 1)Exact numbers have an unlimited number of sig figs (conversion factors, etc.) ex. 1 inch = 2.54cm 2)Last digits of a number are assumed to be uncertain  estimated by +/- 1

Practice How many significant figures are in the numbers below? 1)28 = 2) = 3) = 4) = 5) =

Important Rules for Sig Figs in calculations Multiplication & Division 1)The result carries the same sig figs as the factor with the least amount of sig figs. -may also have to express result in scientific notation! Ex: Multiply 185 x 14 x 2.00 = 5180 = Divide1792/240 = =

Important Rules for Sig Figs in calculations Addition & Subtraction 1)The result carries the same number of decimal places as the factor with the least amount of decimal places. Ex: Add = = Subtract19.68 – – 2.0 = =

Chapter 2: Measurement & Problem Solving pg LO: I can use unit conversions to convert units in math calculations.

Unit Conversions Setting up ratios (comparing one unit to another) in order to convert a given unit into a desired unit through multiplication. GOAL: Cancel units to achieve desired unit

Unit Conversions Example How many feet (ft.) are in 194 centimeters (cm)?1 inch = 2.54 cm Note: Important conversion factors are on the PDF “End Paper” tab.

Question: How many centimeters (cm) are in 72 miles? 1 mile = 5280 ft, 1 inch = 2.54 cm

Units of Measurement Two common systems: English & Metric (International System or SI). Common Base Units Meter (m) = length Kilogram (kg) and (g) = mass Seconds (s) = time Joule (J) = Energy

Metric Prefixes A numerical prefix that changes a number by powers of 10 Examples What is the meaning? Kilometer = Centimeter = Decigram = Pg. 26 of your text!

Metric Prefixes

1. Convert 2.54 km to mm.

Metric Prefixes 2. Convert 35 km to cm.

Temperature (Kelvin vs. Celsius) Kelvin: SI base unit of temperature. Unit = K 0 K = Absolute zero  all particles (atoms) no longer have energy (heat). Changing between Kelvin & Celsius temperature Kelvin  Celsius = Kelvin Temp – 273 = Celsius Temp Celsius  Kelvin = Celsius Temp = Kelvin Temp

Unit Conversions What do I do when a unit conversion is raised to a power? You must also raise the conversion factor(s) to that power.

Unit Conversions Question: How many cubic feet (ft 3 ) are in 4102 cubic centimeters (cm 3 )? 1 inch = 2.54 cm

Density What is Density? A ratio of an objects mass to its volume How is it calculated? Density =_mass_  D = M Volume V Density is… …Thus density can be used as a conversion factor!

Density Ex: The density of aluminum is 2.70 g/mL. What is the volume in liters of 256 g of an aluminum sample?

Unit Conversions Things to Remember Always write every number with its associated unit Identify your starting point (given unit) and devise a solution map towards what you must find (desired unit) Check sig figs last when doing your calculations Determine if your answer makes sense