Math and Scientific Method

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Math and Scientific Method

• Unit 1

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Chemistry Math Topics

• Scientific Notation
• Significant Figures (sigfig)
• Rounding
• Exponential Notation
• SI System
• Metric Conversion
• Factor Labeling
• Density
• Percent Error

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Significant Figures

• When a scientist measures something the precision
  of the investigator and instruments must be
  considered
• ALL digits that are part of the measurement are
  significant (important) but sometimes numbers are
  used as place holders and not significant
• These are usually zeros

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Sigfig Rules

• Zeros between digits are significant
• 700007 has 6 sigfig
• Zeros after digits when no digit is present are
  not significant
• 120000 has only 2 sigfig
• Decimals change the rules

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Decimal Rules

• If a decimal is present
• Zeros to the right of the decimal are significant
• 12.00 has 4 sigfig
• Zeros to the left of the decimal are significant
• 3400. is significant
• Zeros to the left of the digits BUT the right of
  the decimal are NOT significant
• 0.00234 has only 3 sigfig

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Rounding

• Basic rules from math
• 5 and above, give it a shove four and below,
  just let it go. DJ
• Because you must round to sigfig, you may need to
  look at several digits to round
• DO NOT ROUND UNTIL THE FINAL ANSWER!

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Rounding to Sigfig

• For addition and Subtraction- the last digit to
  the right in the answer must be the same as the
  LEAST precise in the problem
• -24.5
• 6.27
• 18.23 BUT the sigfig is 18.2

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• For multiplication and division the answer must
  have the same number of digits as the least
  precise in the problem
• 48.4398
• X1.52
• 73.628496 but in sigfig it is 73.6

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Exponential Notation

• A way to express numbers that are very large or
  very small
• Here are the rules
• Only use sigfig
• Decimal always goes after the 1st digit
• The exponent represents the number of spaces
  moved by the decimal
• Positive number if it moves to the left
• Negative if it moves to the right
• 120 000 000 1.2x108
• 0.000 003 450 3.450 x10-6

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SI units Le System International dUnites

• Measurement represents quantity
• Something that has magnitude, size or amount
• The single measurement system that all scientists
  have agreed to
• They are of constant value
• Standardization in style and format were also
  determined

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SI Base Units

• Length meter
• Mass - kilogram
• Time - Second
• Temperature Kelvin
• Amount of substance - mole
• Electric Current - ampere
• Luminous intensity - Candela

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SI Prefixes

• Prefixes added to the names are used to represent
  quantities that are larger or smaller than the
  base units
• You are expected to know these
• K,h,da,unit,d,c,m
• And recognize the rest
• Know the exponential notation for each

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Metric conversion

• Moving from one SI unit to another is metric
  conversion
• Moving the decimal point is how it works
• Practice is the only way to learn this skill

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Factor Labeling

• Used to help change the UNITS of something, so
  that numbers are still equivalent
• Math Fact Multiplying by one does not change the
  value of a number
• When the numerator and denominator are equivalent
  (equal) then it is like multiplying by one

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• If you have 12 dozen donuts, how many donuts do
  you have? See you can use factor labeling
• (12 dozen) x 12 donuts 144 donuts
• 1 dozen

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Here are the steps

• Identify what you have and what you need
• I have 2.5 miles and I need to know how many feet
• Put a one in front of the unit you have, and how
  many of the other unit is equal to (look it up)
• 1 mile5280 feet

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• Set up the problem
• 2.5 mile x 5280feet
• 1 mile
• Solve
• Put it into sigfig

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Practice Practice Practice

• A car is traveling 65 miles per hour. How many
  feet des it travel in one second?

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• Convert the following
• 7.02 kg to lbs
• 8 L to quarts
• 15 inches to cm
• 98 kg to slugs
• 45 kcal to J

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Now they will get harder

• If a man can move 35 lbs of dirt per minute, how
  many kg per hour will he move?

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More two unit problems

• 78 miles/hour to meters/sec
• .345 mm/sec to inches per minute
• 476 gallons/ hour to pints per minute
• Youll see more

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Percent Error

• How far away from the accepted value are you?
• Theoretical actual
• (Actual value expected value) x100
• actual value
• Percent error

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Practice

• Actual 45.6 Expected 46.0
• 89.4 95.0
• 1238.369 1225.
• You get the drift.

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Accuracy and Precision

• Accuracy how close you answer is to the
  accepted value
• The closer you are to the correct answer, the
  more accurate you are
• Precision
• How similar your range of answers are
• You want to be both right ( accurate) and
  repeatable (precise)

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Scientific Method

• A quick review
• A process used to test a hypethosis
• Hypothesis is a tentative explanation to a
  problem or question that is based on observation
  or past knowledge
• A hypothesis must be tested through valid
  experimentation

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Steps in Scientific Method

• Formulate a hypothesis
• Test the hypothesis
• Using controlled experiments with experimental
  and dependent variables
• Experimental what you change
• Dependent what changes as a result
• Obtain data, document and analyze it
• Draw conclusion
• Publish for peer review