1. SCIENTIFIC INQUIRY AND ANALYSIS
UNIT 1
Units of Measure, Conversions and Graphing
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2. SCIENTIFIC INQUIRY AND ANALYSIS
Unit 1 Objectives
Identify the metric and SI units used in science.
Use metric units to estimate length, volume, and mass of various objects.
Perform calculations involving scientific notation and conversion factors with and without calculators.
Convert between common metric prefixes and units of measurement.
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3. SCIENTIFIC INQUIRY AND ANALYSIS
Unit 1 Objectives
Compare and contrast accuracy and precision.
Understand the use of significant figures in measurements.
Demonstrate the rules of significant figures in calculations.
SCIENTIFIC INQUIRY AND ANALYSIS

4. SCIENTIFIC INQUIRY AND ANALYSIS
Unit 1 Objectives
Differentiate between dependent and independent variables.
Construct a linear scatter plot graph with properly scaled axis.
Draw a line of best fit, write its equation and make a prediction based on the equation.
SCIENTIFIC INQUIRY AND ANALYSIS

5. SCIENTIFIC INQUIRY AND ANALYSIS
SCIENCE
Science is a way of life. Science is a perspective. Science is the process that takes us from confusion to understanding in a manner that’s precise, predictive and reliable — a transformation, for those lucky enough to experience it, that is empowering and emotional. To be able to think through and grasp explanations — for everything from why the sky is blue to how life formed on earth — not because they are declared dogma but rather because they reveal patterns confirmed by experiment and observation, is one of the most precious of human experiences.1
1. Greene, Brian. "Put a Little Science in Your Life." NY Times 1 June 2008, Op Ed sec.: n. pag. NY Times. NY Times. Web. 25 July <http%3A%2F%2Fwww.nytimes.com%2F2008%2F06%2F01%2Fopinion%2F01greene.html%3F_r%3D1>.
SCIENTIFIC INQUIRY AND ANALYSIS

6. SCIENTIFIC INQUIRY AND ANALYSIS
GOAL OF SCIENCE
“Science as a collective institution aims to produce more and more accurate natural explanations of how the natural world works, what its components are, and how the world got to be the way it is now. Classically, science's main goal has been building knowledge and understanding, regardless of its potential applications . . .”2
2. Understanding Science. University of California Museum of Paleontology. Page July 2014 <
SCIENTIFIC INQUIRY AND ANALYSIS

7. SCIENTIFIC INQUIRY AND ANALYSIS
NUMBERS IN SCIENCE
As stated before science tries to provide explanations of how the natural world works. Explanations often times are accomplished with numbers and equations.
With this in mind, we will study how numbers are represented in science and how they are used.
SCIENTIFIC INQUIRY AND ANALYSIS

8. SCIENTIFIC INQUIRY AND ANALYSIS
ROUNDING NUMBERS
Rounding numbers
When rounding numbers, evaluate one more digit from the left than asked to round to.
If that number is less than 5 than the rounded numbers do not change. If that number is 5 or greater than the rounded number gets changed by one. (i.e rounded to 3 numbers is 285, rounded to 4 numbers is 284.7),
Example: round to 3 numbers. To 4 numbers.
SCIENTIFIC INQUIRY AND ANALYSIS

9. SCIENTIFIC INQUIRY AND ANALYSIS
SCIENTIFIC NOTATION
Scientific notation is a method of representing very large or very small numbers in a concise format
Base numbers on the power of 10
100 = 1, 101 = 10, 102 = 10 x 10 = 100, etc.
10-1= 1/10 = 0.1, 10-2 = 1/100 = 0.01, etc.
For numbers > 1 move decimal to the left, for numbers < 1 move decimals to the right.
SCIENTIFIC INQUIRY AND ANALYSIS

10. SCIENTIFIC INQUIRY AND ANALYSIS
SCIENTIFIC NOTATION
Proper scientific notation
Put a decimal to the right of the first non-zero number and then multiply by the correct base 10 number
Example 1: Express in scientific notation rounded to 4 digits (do not count the leading zeroes)
Example 2: Express 299,792,458 in scientific notation rounded to 3 digits.
SCIENTIFIC INQUIRY AND ANALYSIS

11. SCIENTIFIC INQUIRY AND ANALYSIS
SCIENTIFIC NOTATION
Scientific notation rules
1/10n = 10-n
(A x10n) x (B x10m) = (A x B) x10n+m
(A x10n) / (B x10m) = (A / B) x10n-m
Example 1: (3.2 x 10-2) x (3.0 x 106)
Example 2: (3.2 x 102) / (1.6 x 10-2)
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12. SCIENTIFIC INQUIRY AND ANALYSIS
SYSTEMS OF UNITS
SI Units
LENGTH: Meter (m)
MASS: Kilogram (kg)
TIME: Seconds (s)
CGS Units
LENGTH: Centimeter (cm)
MASS: Gram (g)
BE (British Engineering) Units
LENGTH: Foot (ft)
MASS: Slug (sl)
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13. SCIENTIFIC INQUIRY AND ANALYSIS
METRIC PREFIXES
SI & CGS Units can be expressed as whole numbers (45000 meters), in scientific notation (4.5 x 104 meters) or with a metric prefix 45 kilometers.
A metric prefix just another way of representing a scientific notation.
SCIENTIFIC INQUIRY AND ANALYSIS

14. SCIENTIFIC INQUIRY AND ANALYSIS
METRIC PREFIXES
10n
Prefix
Symbol
Name
1024
yotta Y
Septillion
1021
zetta Z
Sextillion
1018
exa E
Quintillion
1015
peta P
Quadrillion
1012
tera T
Trillion
109
giga G
Billion
106
mega M
Million
103
kilo k
Thousand
102
hecto h
Hundred
101
deca da
Ten
100
(none)
One
10n
Prefix
Symbol
Name
10−1
deci d
Tenth
10−2
centi c
Hundredth
10−3
milli m
Thousandth
10−6
micro
Millionth
10−9
nano n
Billionth
10−12
pico p
Trillionth
10−15
femto f
Quadrillionth
10−18
atto a
Quintillionth
10−21
zepto z
Sextillionth
10−24
yocto y
Septillionth
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15. SCIENTIFIC INQUIRY AND ANALYSIS
UNITS
Metric prefix indicates the magnitude of the unit.
Example: 220 kilometers (km) is how many meters?
Example: 5 picoFarads (pF) capacitor is how many Farads (F)?
Example: 1 x 106 centimeters (cm) is how many meters (m)?
Example: 22 microseconds (μs) is how many seconds?
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16. SCIENTIFIC INQUIRY AND ANALYSIS
UNITS
Fundamental vs. Derived Units
As discussed earlier, length, mass & time are fundamental units.
The four other fundamental units are electric current, temperature, luminous intensity and amount of substance (mol)
Derived units are compound units made up of two or more fundamental (base) units. What are some examples?
Additional fundamental units are electric current, thermodynamic temperature, luminous intensity and amount of substance (mol).
SCIENTIFIC INQUIRY AND ANALYSIS

17. SCIENTIFIC INQUIRY AND ANALYSIS
UNITS
Converting Units
When doing problems all units must be in the same system. (i.e. SI, CGS or BE) Therefore, some parameters need to be converted from one system to another.
Conversion factors are equal to 1. What does that mean? For example: 1 inch = 2.54 centimeters. A ratio of the two would be 1 𝑖𝑛𝑐ℎ 2.54 𝑐𝑚 =1, likewise the numerator and denominator could be flipped and it would still be equal to one 𝑐𝑚 1 𝑖𝑛𝑐ℎ =1
SCIENTIFIC INQUIRY AND ANALYSIS

18. UNITS CONVERSION FACTORS
Standard Measurements
12 inches = 1 foot
3 feet = 1 yard
5280 feet = 1 mile
8 ounces = 1 cup
2 cups = 1 pint
2 pints = 1 quart
4 quarts = 1 gallon
16 ounces = 1 pound
2000 pounds = 1 ton
Time
60 seconds = 1 minute
60 minutes = 1 hour
24 hours = 1 day
7 days = 1 week
365 days = 52 weeks = 12 months = 1 year
Metric
Conversion between metric prefixes (i.e. centimeter to kilometer)
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19. SCIENTIFIC INQUIRY AND ANALYSIS
UNITS
Converting Units
Railroad Method
Make a “RR”
Put the magnitude of the unit and the units in the upper left RR track.
Use a series of conversion factors to cancel out the unwanted units. You must memorize the conversion factors on the previous slide. All other conversion factors will be given to you.
Multiply all the numbers across the top for the numerator and multiply all the numbers across the bottom for the denominator.
Divide the numerator by the denominator. Verify the units cancelled out properly.
SCIENTIFIC INQUIRY AND ANALYSIS

20. SCIENTIFIC INQUIRY AND ANALYSIS
UNITS
Example: (convert 55 miles to km)
SCIENTIFIC INQUIRY AND ANALYSIS

21. SCIENTIFIC INQUIRY AND ANALYSIS
UNITS
Example: (convert 750 mL to pints)
SCIENTIFIC INQUIRY AND ANALYSIS

22. SCIENTIFIC INQUIRY AND ANALYSIS
UNITS
Special Units
Compound units are parameters made up of more than one unit (i.e. miles per hour, gallons per minute, meters per second)
When converting these units, the magnitude goes in the upper left (numerator) of the RR track along with the first unit.
The second unit goes in the lower left (denominator) of the RR track.
Both units must be converted to have a valid conversion.
SCIENTIFIC INQUIRY AND ANALYSIS

23. SCIENTIFIC INQUIRY AND ANALYSIS
UNITS
Example: Convert 100 km per hr 𝑘𝑚 ℎ𝑟 to inches per second 𝑖𝑛 𝑠𝑒𝑐
SCIENTIFIC INQUIRY AND ANALYSIS

24. SCIENTIFIC INQUIRY AND ANALYSIS
UNITS
Example: Convert 3.7 gpm 𝑔𝑎𝑙 𝑚𝑖𝑛 to liters per day 𝑙 𝑑𝑎𝑦
SCIENTIFIC INQUIRY AND ANALYSIS

25. SCIENTIFIC INQUIRY AND ANALYSIS
UNITS
Special Units
Exponential units are parameters made up of a unit that is raised to a power, typically area and volume (i.e. meters squared (m2), feet cubed (ft3), cubic centimeters (cc))
Put the magnitude of the unit and the unit in the upper left RR track.
Use a series of conversion factors to cancel out the unwanted units. The conversion factor (number and unit) must be squared or cubed to match the unit being converted.
Multiply all the numbers across the top for the numerator and multiply all the numbers across the bottom for the denominator.
Divide the numerator by the denominator. Verify the units cancelled out properly.
SCIENTIFIC INQUIRY AND ANALYSIS

26. SCIENTIFIC INQUIRY AND ANALYSIS
UNITS
Example: Convert 210 meters squared (m2) to feet squared (ft2)
210 𝑚 𝑐𝑚 𝑚 𝑖𝑛 𝑐𝑚 𝑓𝑡 𝑖𝑛 2 = 210× =2260 𝑓𝑡 2
SCIENTIFIC INQUIRY AND ANALYSIS

27. SCIENTIFIC INQUIRY AND ANALYSIS
UNITS
Example: Convert 6.72 grams per cubic meter 𝑔 𝑚 3 to slugs per cubic feet 𝑠𝑙 𝑓𝑡 3
6.72 𝑔 𝑚 𝑘𝑔 𝑔 1 𝑠𝑙𝑢𝑔 𝑘𝑔 𝑚 𝑐𝑚 𝑐𝑚 𝑖𝑛 𝑖𝑛 𝑓𝑡 3 = 190, ,593,000,000 =1.30× 10 −5 𝑠𝑙 𝑓𝑡 3
SCIENTIFIC INQUIRY AND ANALYSIS

28. SCIENTIFIC INQUIRY AND ANALYSIS
MEASUREMENT
Always use the smallest division on the scale and estimate the interval between the markings. 10 20
Make note about significant figures.
25.5 cm
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29. SCIENTIFIC INQUIRY AND ANALYSIS
MEASUREMENT
Example: (For the left picture read the blue arrow; for the right read the upper scale and then the lower scale)
Make note about significant figures.
SCIENTIFIC INQUIRY AND ANALYSIS

30. SCIENTIFIC INQUIRY AND ANALYSIS
MEASUREMENT
Accuracy - the degree of closeness of a measured or calculated quantity to its actual (true) value.
Precision – is how close a set of data is to one another or the degree of exactness of a measurement. (i.e. ±0.1 cm)
Precision of a measuring instrument – ½ of the smallest division of the instrument scale.
Outlier – a data point(s) that appear(s) to deviate markedly from other members of the sample in which it occurs.
Reference: see FOS lab manual in regards to measuring for significant figures
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31. SCIENTIFIC INQUIRY AND ANALYSIS
MEASUREMENT
Accuracy, precision & outlier ●1 ●2 ●3 ●4 ●1 ●2 ●3 ●4 ●1 ●2 ●3 ●4
Reference:
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32. SCIENTIFIC INQUIRY AND ANALYSIS
SIGNIFICANT FIGURES
Significant Figures – is the number of digits in a number whose values are known. The margin of error is understood to be one-half the value of the last significant place.
Reference:
SCIENTIFIC INQUIRY AND ANALYSIS

33. SCIENTIFIC INQUIRY AND ANALYSIS
SIGNIFICANT FIGURES
Rules of Significant Figures:
All non-zero numbers are ALWAYS significant
All zeroes that fall between two non-zero numbers are significant. (example 1: 13,000 vs vs ) (example 2: vs vs )
For numbers with decimals, final zeroes after the decimal are significant.(example vs vs )
Show the proper number of significant figures by converting the examples into scientific notion.
Examples converted into scientific notation(1.3 x 104, x 104, x 104)(3.2 x 10-2,3.20 x 10-1)
SCIENTIFIC INQUIRY AND ANALYSIS

34. SCIENTIFIC INQUIRY AND ANALYSIS
SIGNIFICANT FIGURES
When multiplying or dividing numbers, the number of significant figures in the final answer equals the smallest number of significant figures in any of the original factors.
Example: the dimension of a box are 1.23m x 0.30m x 00700m. What is the volume?
1.23 x 0.30 x = 258.3m3
(258m3, m3, 260m3, 300m3)
SCIENTIFIC INQUIRY AND ANALYSIS

35. SCIENTIFIC INQUIRY AND ANALYSIS
SIGNIFICANT FIGURES
When adding or subtracting numbers, the last significant figure in the answer occurs in the last column (from l. to r.) containing a number that results from a combination of digits that are all significant.
SCIENTIFIC INQUIRY AND ANALYSIS

36. SCIENTIFIC INQUIRY AND ANALYSIS
SIGNIFICANT FIGURES
Distance travelled is 5.02m, m, m. What is the total distance travelled? What is it if the second distance is 0020m?
5.02
56.340
(81.360m, 81.36m, 81.4m, 81m, m)
SCIENTIFIC INQUIRY AND ANALYSIS

37. SCIENTIFIC INQUIRY AND ANALYSIS
GRAPHING
Graphing is a means of visually illustrating data in order to see trends or predict a trend.
The simplest of graphs is the x-y or scatter plot. It plots points on an x-y coordinate system. Do not get this confused with a line graph.
SCIENTIFIC INQUIRY AND ANALYSIS

38. SCIENTIFIC INQUIRY AND ANALYSIS
GRAPHING
When graphing, we start with the data first.
For a simple x-y data we are tracking how a parameter changes for another given parameter.
For example:
How does position of an object change over time?
How many gallons of water flows by over time?
How much mass is occupied in a given volume?
SCIENTIFIC INQUIRY AND ANALYSIS

39. SCIENTIFIC INQUIRY AND ANALYSIS
GRAPHING
The data must be placed in table. One type of data is x and the other is y.
What is the difference?
Independent variable – is the data that can be manipulated or controlled.
Dependent variable – is the data that is effected in an experiment or is the data that responds to the independent variable
SCIENTIFIC INQUIRY AND ANALYSIS

40. SCIENTIFIC INQUIRY AND ANALYSIS
GRAPHING
Time
(seconds)
Position
(meters)
0.7
3.8
1.8
3.2
2.6
2.8
3.4
2.2
4.1
1.4
4.9
0.8
6.0
0.2
6.5
SCIENTIFIC INQUIRY AND ANALYSIS

41. SCIENTIFIC INQUIRY AND ANALYSIS
GRAPHING
Parts of a x-y graph:
Axis with scale marks
Axis titles & units
Axis numbers
Data points
Graph title
Trendline
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42. SCIENTIFIC INQUIRY AND ANALYSIS
GRAPHING
Sometimes the data points represent a trend.
In the case of a linear relationship, we can use the line of best fit.
A line of best fit uses a straight line to approximate the trend of the data points.
A line of best fit may touch the data points, but it does not need to and in most cases does not.
SCIENTIFIC INQUIRY AND ANALYSIS

43. SCIENTIFIC INQUIRY AND ANALYSIS
GRAPHING
The equation for the line of best fit is the slope of the line, which is in the format:
𝑦=𝑚𝑥+𝑏
Where m is the slope 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛 and b is the y-intercept (the value of y when x = 0)
This is very useful because it will allow you to predict what happens to the dependent variable (y) given a value for independent variable (x)
SCIENTIFIC INQUIRY AND ANALYSIS

44. SCIENTIFIC INQUIRY AND ANALYSIS
GRAPHING EXAMPLE
Age
(yrs)
Reaction Time
(sec) 50
14.09 80
26.48 70
26.67
18.42 30
11.62
18.59 60
20.27
23.56
12.15 20
Age
(yrs)
Reaction Time
(sec) 30
6.16 40
11.18 80
25.80 20
14.20 70
25.09
10.63
13.24 60
26.51
23.98
14.18
Age
(yrs)
Reaction Time
(sec) 20
6.00 30
12.15 70
26.30 90
26.88
20.55 40
18.45 50
19.42
26.14
SCIENTIFIC INQUIRY AND ANALYSIS

45. SCIENTIFIC INQUIRY AND ANALYSIS
GRAPHING EXAMPLE
SCIENTIFIC INQUIRY AND ANALYSIS

46. SCIENTIFIC INQUIRY AND ANALYSIS
MEASUREMENT LAB
Length
Mass
Volume
Square or rectangular box (h x w x l)
Right circular cylinder (πr2h)
Sphere (4/3πr3)
Pyramid (1/3Bh, where B is area of the base = ½bh)
Cone (1/3πr2h, πr2 is the area of the base)
SCIENTIFIC INQUIRY AND ANALYSIS