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Math and Scientific Method

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Math and Scientific Method Unit 1 Chemistry Math Topics Scientific Notation Significant Figures (sigfig) Rounding Exponential Notation SI System Metric Conversion ... – PowerPoint PPT presentation

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Title: Math and Scientific Method


1
Math and Scientific Method
  • Unit 1

2
Chemistry Math Topics
  • Scientific Notation
  • Significant Figures (sigfig)
  • Rounding
  • Exponential Notation
  • SI System
  • Metric Conversion
  • Factor Labeling
  • Density
  • Percent Error

3
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

4
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

5
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

6
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!

7
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

8
  • 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

9
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

10
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

11
SI Base Units
  • Length meter
  • Mass - kilogram
  • Time - Second
  • Temperature Kelvin
  • Amount of substance - mole
  • Electric Current - ampere
  • Luminous intensity - Candela

12
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

13
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

14
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

15
  • 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

16
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

17
  • Set up the problem
  • 2.5 mile x 5280feet
  • 1 mile
  • Solve
  • Put it into sigfig

18
Practice Practice Practice
  • A car is traveling 65 miles per hour. How many
    feet des it travel in one second?

19
  • Convert the following
  • 7.02 kg to lbs
  • 8 L to quarts
  • 15 inches to cm
  • 98 kg to slugs
  • 45 kcal to J

20
Now they will get harder
  • If a man can move 35 lbs of dirt per minute, how
    many kg per hour will he move?

21
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

22
Percent Error
  • How far away from the accepted value are you?
  • Theoretical actual
  • (Actual value expected value) x100
  • actual value
  • Percent error

23
Practice
  • Actual 45.6 Expected 46.0
  • 89.4 95.0
  • 1238.369 1225.
  • You get the drift.

24
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)

25
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

26
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
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