1. DATA ANALYSIS Using the Metric System Scientific Notation
Percent Error
Using Significant Figures
Accuracy and Precision
Graphing Techniques

2. Using the Metric System
A. Why do scientists use the metric system?
The metric system was developed in France in used in all scientific work because it has been recognized as the world wide system of measurement since 1960.
SI system is from the French for Le Systeme International d’Unites.
The metric system is used in all scientific work because it is easy to use. The metric system is based upon multiples of ten. Conversions are made by simply moving the decimal point.

3. Base Units (Fundamental Units)
QUANTITY NAME SYMBOL _______________________________________________ Length meter m Mass kilogram kg Amount of Substance mole mol Time second s

4. Derived Units Base Units – independent of other units
Derived Units – combination of base units
Examples
density  g/L (grams per liter)
volume  m x m x m = meters cubed
Velocity  m/s (meters per second

5. Metric Units Used In This Class
QUANTITY NAME SYMBOL
Length meter m
centimeter cm
millimeter mm
kilometer km
Mass gram g
kilogram kg
centigram cg
milligram mg
Volume liter (liquid) L (l)
milliliter (liquid) mL (ml)
cubic centimeter (solid) cm3

6. Metric Units Used In This Class
Density grams/milliliter (liquid) g/mL
grams/cubic centimeter (solid) g/cm3
grams/liter (gas) g/L
Time second s
minute min
hour h
volume measurement for a liquid and a solid
( 1 mL = 1 cm3) These are equivalents.

7. Equalities You Need To Know
1 km = 1000 m 1 m = 100 cm 1 m = 1000 mm 1L = 1000 mL 1kg = 1000g 1 g = 100cg 1 g = 1000 mg

8. Making Unit Conversions
Make conversions by moving the decimal point to the left or the right using:
“ king henry died unit drinking chocolate milk”
Examples
10.0 cm = __________m
34.5 mL = __________L
28.7 mg = __________kg

9. SCIENTIFIC NOTATION
Scientific Notation: Easy way to express very large or small numbers
A.0 x 10x
A – number with one non-zero digit before decimal
x -exponent- whole number that expresses the number decimal places
if x is (-) then it is a smaller
if x is (+) than it is larger

10. PRACTICE Convert to Normal Convert to SN 2.3 x 1023 m 3,400,000,
3.4 x cm

11. Multiplying Calculating in Scientific notation
Multiple the numbers
Add the exponents
(2.0 x 104) (4.0 x 103) = 8.0 x 107

12. Dividing 9.0 x 107 3.0 x 102 3.0 x 105 divide the numbers
subtract the denominator exponent from the numerator exponent
9.0 x x 102
3.0 x 105

13. Add
Add or subtract
get the exponents of all # to be the same
calculate as stated
make sure the final answer is in correct scientific notation form
7.0 x x =
7. 0 x x = 7.3 x 104
70, ,000 = = 7.3 x104

14. subtract
7.0 x x =
7.0x 104 – .30 x 104 = 6.7 x 104
70, =67,000

15. PRACTICE Add: 2.3 x 103 cm + 3.4 x 105 cm Subtract:
Multiply:
: x 103 cm X x cm
Divide:
: x 103 cm / x cm

16. Calculating Percent Error
% Error =accepted value–experimental value X 100= % accepted or actual value Subtract -Divide then multiply by 100

17. Calculating Percent Error
EXAMPLE – A student determines the density of a piece of wood to be .45g/cm. The actual value is .55g/cm. What is the student’s percent error? X 100% = .10 = .18 x 100% = 18%

18. The following lesson is one lecture in a series of Chemistry Programs
developed by
Professor Larry Byrd
Department of Chemistry
Western Kentucky University

19. Introduction
If someone asks you how many inches there are in 3 feet, you would quickly tell them that there are 36 inches.
Simple calculations, such as these, we are able to do with little effort.
However, if we work with unfamiliar units, such as converting grams into pounds, we might multiply when we should have divided.

20. The fraction ( 4 x 5) / 5 can be simplified by dividing the numerator (top of fraction) and the denominator (bottom of fraction) by 5:
= 4
Likewise, the units in (ft x lb) / ft reduces to pounds (lb) when the same units ( ft )are canceled:
= lb

21. CONVERSION FACTOR
A CONVERSION FACTOR is a given Ratio-Relationship between two values that can also be written as TWO DIFFERENT FRACTIONS.
For example, 454 grams =1.00 pound, states that there are
454 grams in 1.00 pound or that
1.00 pound is equal to 454 grams.

22. Ratio-Relationship
We can write this Ratio-Relationship as two different CONVERSION-FACTOR-FRACTIONS:
These fractions may also be written in words as grams per pound or as
1.00 pound per 454 grams, respectively.
The "per" means to divide by.
or as

23. Example If we want to convert 2.00 pounds into grams, we would:
first write down the given quantity (2.00 lbs)
pick a CONVERSION-FACTOR-FRACTION that when the given quantities and fractions are multiplied, the units of pounds on each will cancel out and leave only the desired units, grams.
We will write the final set-up for the problem as follows:
= grams

24. If we had used the other conversion-factor-fraction in the problem:
We would know that the ABOVE problem was set-up incorrectly since WE COULD NOT CANCEL Out the units of pounds and the answer with pounds / grams makes no sense. =

25. Four-step approach When using the Factor-Label Method
it is helpful to follow a four-step approach
in solving problems:
What is question – How many sec in 56 min
What are the equalities- 1 min = 60 sec
Set up problem (bridges) 56 min 60 sec
1 min
Solve the math problem -multiple everything on top
and bottom then divide 56 x 60 / 1

26. Using Significant Figures (Digits)
value determined by the instrument of measurement plus one estimated digit
reflects the precision of an instrument
example – if an instrument gives a length value to the tenth place – you would estimate the value to the hundredths place

27. 1. all non-zero # are Sig fig- 314g 3sf 12,452 ml 5sf
2. all # between non-zero # are sig fig m sf
6.01mol sf
s s
3. place holders are not sf 0.01kg sf

28. 4. zeros to the right of a decimal are sig fig if 3.0000s 5sf
Preceded by non-zero m sf
m sf
5. Zero to right of non-zero w/o decimal point 600m 1sf
are not sig fig m 3sf
600.0 m sf
m sf

29. RULES FOR USING SIGNIFICANT FIGURES
use the arrow rule to determine the number of significant digits
decimal present all numbers to right of the first non zero are significant (draw the arrow from left to right)
> sig. digits
> sig. digits
> sig. digits
> sig. digits

30. RULES FOR USING SIGNIFICANT FIGURES
use the arrow rule to determine the number of significant digits
decimal not present < all numbers to the left of the first non zero are significant (draw arrow from right to left)
< sig. digits
< sig. digit

31. Use appropriate rules for rounding
If the last digit before rounding is less than
5 it does not change
ex to 3 places  343
1.544 to 2 places  1.54
If the last digit before rounding is greater
than 5 – round up one
ex to 3 places  206
10.75 to 2 places  11

32. use fewest number of decimal places rule for addition and subtraction
1) ) ) )
_________ ______ _______ ______

33. Use least number of significant figures rule for multiplication and division
23.7 x 6.36
2) x 14
3) / 25
4) / .005

34. Reliability of Measurement
ACCURACY – how close a measured value is to the accepted value
PRECISION – how close measurements are to one another - if measurements are precise they show little variation
* Precise measurements may not be accurate

35. Are his results precise?
Precision- refers to how close a series of measurements are to one another; precise measurements show little variation over a series of trials but may not be accurate.
LESS THAN .1 IS PRECISE
Oscar performs an experiment to determine the density of an unknown sample of metal. He performs the experiment three times:
19.30g/ml
19.31g/ml
Certainty is +/- .01
Are his results precise?

36. Are his results accurate? Need to calculate percent error.
Accuracy – refers to how close a measured value is to an (theoretical) accepted value.
The metal sample was gold( which has a density of 19.32g/ml)
Certainty is +/- .01
Are his results accurate? Need to calculate percent error.
5% OR LESS IS ACCURATE
Oscar finds the volume of a box 2.00cm3 (ml)
It is really 3.00ml is it precise? Accurate? Percent error

37. Oscar finds the volume of a box 2.00cm3 (ml)
It is really 3.00ml is it precise?
To know if it is precise you need more trials
Accurate? Percent error
Actual - Experimental X % =
Actual
3-2
X 100 = 33.3%

38. Activity: basket and paper clip
1. Throw 3 paper clips at basket
2. Measure the distance from the basket to determine accuracy and precision
Cm3= ml and dm3= l Liter

39. Graphing
graph – a visual representation of data that reveals a pattern
Bar- comparison of different items that vary by one factor
Circle – depicts parts of a whole
Line graph- depicts the intersection of data for 2 variables
Independent variable- factor you change
Dependent variable – the factor that is changed when independent variable changes

40. Graphing Creating a graph- must have the following points Title graph
Independent variable – on the X axis – horizontal- abscissa
Dependent variable – on Y axis – vertical- ordinate
Must label the axis and use units
Plot points
Scale – use the whole graph
Draw a best fit line- do not necessarily connect the dots and it could be a curved line.

41. Interpreting a graph Run X2 –X1 Slope- rise Y2 –Y1
relationship
direct – a positive slope
inverse- a negative slope
equation for a line – y = mx + b
m-slope
b – y intercept
extrapolate-points outside the measured values- dotted line
interpolate- points not plotted within the measured values-dotted line

42. WORK ON GRAPHING EXERCISES
Graphical analysis – click and go

43. GRAPHING LAB Creating a graph- must have the following points
1.Title graph
2. Independent variable –on the X axis–horizontal- abscissa
3. Dependent variable – on Y axis – vertical- ordinate
4. Must label the axis and use units
5. Plot points
6. Scale – use the whole graph
7. Draw a best fit line- do not necessarily connect the dots and it could be a curved line.

44. GRAPHING Interpreting a graph Run X2 –X1 Slope= rise Y2 –Y1
relationship
direct relationship– a positive slope
Inverse relationship- a negative slope
equation for a line – y = mx + b
m-slope
b – y intercept
extrapolate-points outside the measured values- dotted line
interpolate- points not plotted within the measured values-dotted line

45. Bulldozer Lab