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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
- Factor Labeling
- Density
- Percent Error

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

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

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

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!

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

- 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

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

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

SI Base Units

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

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

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

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

- 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

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

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

Practice Practice Practice

- A car is traveling 65 miles per hour. How many

feet des it travel in one second?

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

Now they will get harder

- If a man can move 35 lbs of dirt per minute, how

many kg per hour will he move?

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

Percent Error

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

Practice

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

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)

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

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