(TG) Sept 28: Dimensional Analysis

Want to know what 50km/hour is in miles? Its the speed limit, so it would be pretty useful to know if you were ever in a sticky situation...

• This type of conversion is called Dimensional Analysis
• It is very similar to the process of converting currencies

4 Steps to Know:

1.    Find a unit equality
2.    Find the conversion factors
3.    Apply Conversion Factors 
4.    Cancel Units

EXAMPLES:

50 km/hour to miles/hour

50km/h x 1mile/1.6km

UNITS CANCEL: km's is crossed out in the equation

You now multiply the two fractions and get:

50/1.6 per hour

50/1.6 = 31.25

Final Answer: 50km/hour is = to 31.25mi/hour


A Helpful Picture to Illustrate the Process:

(NR) Sept 23: Scientific Notation & Significant Digits

TO REMEMBER!
* Accuracy and precision is VERY important in science.
* Calculators are NOT smart enough to decide what is precise and what isn't.
* Scientists have established rules for rounding off extra digits; you MUST follow them!


SIGNIFICANT DIGITS

• Non-zero digits are always significant.
• If the zero is a place keeper it is not significant.
  example: 0.0098 (2 s.d.)
                0.00043 (2 s.d)
• Any numbers to the left of a decimal point are significant.
  example: 2.00, 27.06, 38.9000
• Zeros after another number are significant.

examples:

HOW MANY SIGNIFICANT DIGITS ARE IN...

14.78? ............_____s.d.
2.04? .............._____s.d.
9.00? .............._____s.d.
0.0038?..........._____s.d.

(answers: 4 s.d., 3 s.d., 3 s.d., 2 s.d.)

• when you multiply/divide ROUND to the number wit hthe fewest S.D.'s 
  example:
  
  
  • 1.38797 x 38.234 = 53.067644 => 53.068

• when adding/subtracting ROUND to the LEAST precise number
  example:
  
  
  • 10.978 - 5.68 = 5.298 => 5.30
  • 20.3 + 18.348 = 38.648 => 38.6
  
  http://www.youtube.com/watch?v=qrpq4qU6Wgg&feature=related 

SCIENTIFIC NOTATION

• used if we need to write the number 2000 with only 2 s.d.'s
  > 2.0 x 10 ^ 3
• used if we want to write the number thirty three billion four hundred million without taking up an entire line.
• Shows really big or really small numbers easily
• makes use of power of 10 

examples:
10^5 = 100000
10^-5 = 0.00001

-convert each question into scientific notation.

13400000 => ____ x 10^__
0.00000542 => ____ x 10^__
23900000 => ____ x 10^__

(answers: 1.34 x 10^7, 5.42 x 10^-6, 2.39 x 10^7)

REMEMBER:
DO NOT USE "^" ON YOUR CALCULATOR!!!  

(DA) Sept 21: SI System & Percent Error

Prefixes Used with SI Units

• We can put a prefix in front of the unit and change the power of it

         ^{- tera (T) 10^12
         - giga (G) 10^9
         - mega (M) 10^6
         - kilo (K) 10^3
         - hecto (h) 10^2
         - deca (da) 10^1
SI Prefixes}

• The SI System uses many prefixes to represent very large or very small numbers
  - deci (d) 10^-1
  - centi (c) 10^-2
  - milli (m) 10^-3
  - micro (µ) 10^-6
  - nano (n) 10^-9
  - pico (p) 10^-12
  - fempto (fm) 10^-15

^{***Don't use scientific notation and prefixes together! IT BECOMES VERY CONFUSING.
Experimental Accuracy}

• In general, the maximum accuracy of any measurement is half of the smallest division of the measuring device
• A ruler with measurements of millimeters has a meximum accuracy of +/- 0.5mm
• The odometer in a car has a maximum accuracy of +/- 50m.

EXAMPLE:

• A graduated cylinder has units of 1.0 mL. The accuracy of the cylinder is +/-0.5mL
• Liquid in a graduated cylinder will typically form a curved top called a meniscus
• The volume is taken at the bottom of the cylinder

The curved top is called a Meniscus

Expressing Error

• Error is a fundemental part of science
• There are usually 3 reasons of error
  1) Physical errors in the measuring device
  2) 'Sloppy' measuring
  3) Changing ambient conditions
  

Calculating Error

• Two different possibilities
  
  1) Absolute Error
           - Measured value minus accepted value
           - Absolute Error = Measured - Accepted
  
  2) Percentage Error
           - Most common
           - Percent Error = Absolute Error / Accepted Value
      
        |  Measured - Accepted |
  % = |           Accepted           | x100

WHAT IS CHEMISTRY?

CHEMISTRY:
the science of matter;
the branch of the natural sciences dealing with the composition of substances and their properties and reactions