Applying Mathematical Concepts to Chemistry DATA ANALYSIS

 concise format for representing extremely large or small numbers  Requires 2 parts:  Number between 1 and …(coefficient)  Power of ten (exponent)  Examples:  6.02 x = 602,000,000,000,000,000,000,000  2.0 x m = m See Appendix C R63 for instructions on how to properly calculate numbers in scientific notation with a calculator SCIENTIFIC NOTATION

 Additional and Subtraction  In order to add or subtract numbers that are expressed in scientific notation, the exponents must be the same.  If the exponents are different, it always helps to convert the number with the smaller exponent to a number with the larger exponent. Don’t worry about having a proper coefficient – you won’t  Once the exponents are equal, add or subtract the coefficients and attach the larger exponent. SCIENTIFIC NOTATION CALCULATIONS Addition and Subtraction Being able to perform scientific notation calculations without a calculator is a great skill to have. It gives you’re the power to evaluate if you made a computational mistake.

 Multiplication.  Multiply the coefficients and add the exponents  If the calculated coefficient is 10 or greater, move the decimal to the left and increase the exponent. SCIENTIFIC NOTATION CALCULATIONS Multiplication and Division In order to multiply or divide numbers that are expressed in scientific notation, the exponents DO NOT have to be the same.  Division  Divide the coefficients and add the exponents  If the calculated coefficient is less than 10, move the decimal to the right and increase the exponent.

 Accuracy- closeness of measurements to the target value  Error - difference between measured value and accepted value  Precision- closeness of measurements to each other ACCURACY VS PRECISION

PERCENT ERROR Example: In order to calibrate a balance a 5.0g mass standard (accepted) was placed on the balance. The output registered 4.8g

MEASUREMENT PRECISION  Measurements are limited in by the precision of the instrument used to measure

SIGNIFICANT DIGITS IN MEASUREMENT  Read one place past the instrument 52.7  If a measurement is observed on one of the graduated lines, you must add a zero at the end of the number to indicate that degree of precision 50.0 Always read the volume of a liquid in a graduated cylinder from the bottom of the meniscus Significant digits in measurement include all of the digits that are known and plus one measure (the last digit) of uncertainty

 1. Nonzero digits are always significant ( SF)  2. Zeros between non-zeros are significant (1003 4SF)  3. Zeros to the right of a decimal and a nonzero are significant ( SF)  4. Placeholder zeros are not significant 0.01g 1 SF1000.g 4 SF 1000g 1 SF1000.0g 5 SF  5. Counting numbers and constants have infinite significant figures 5 people (infinite SF) Relax There are only two situations where zeros are not significant. Evaluate the zeros in any number first. If they are all significant then every digit in your number is significant. RECOGNIZING SIGNIFICANT DIGITS

 Multiply as usual in calculator  Write answer  Round answer to same number of sig figs as the lowest original operator  EX: 1000 x = =  EX: x = = RULE FOR MULTIPLYING/DIVIDING SIG FIGS A CALCULATED ANSWER CANNOT BE MORE PRECISE THAN THE LEAST PRECISE MEASUREMENT FROM WHICH IT WAS CALCULATED

 x  x 230  1.2x10 8 / 2.4 x  / PRACTICE MULTIPLYING/DIVIDING

 Round answer to least “precise” original operator.  Example RULE FOR ADDING/SUBTRACTING = = 980

   1.0 x x 10 4  – PRACTICE ADDING/SUBTRACTING

UNITS OF MEASURE  SI Units- scientifically accepted units of measure:  Know:  Length  Mass  Temperature  Time

THE METRIC SYSTEM G M K h da (base unit) d c m  n p

 hL =__________ L  nm = ___________cm  kg = ___________mg  Online Powers of 10 Demonstration: sof10/ METRIC PRACTICE G M K h da (base unit) d c m  n p

 Degrees Celsius to Kelvin  T kelvin =T celsius  Kelvin to Degrees Celsius  T celsius =T kelvin TEMPERATURE CONVERSIONS

DERIVED QUANTITIES - VOLUME Volume- amount of space an object takes up (ex: liters)  V = l x w x h  1 cm 3 = 1 mL by definition The volume of an irregularly shaped object can be determined by displacing its volume

DERIVED QUANTITIES- DENSITY  Density- ratio of the mass of an object to its volume  Density = mass/volume  D= g/mL  Density depends on the composition of matter, no the amount of matter

DENSITY BY WATER DISPLACEMENT  Fill graduated cylinder to known initial volume  Add object  Record final volume  Subtract initial volume from final volume  Record volume of object

GRAPHING DATA  General Rules  Fit page  Even scale  Best fit/trendline  Informative Title  Labeled Axes with units The Affect of Temperature on Volume