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1
SCIENTIFIC INQUIRY AND ANALYSIS
UNIT 1
Units of Measure, Conversions and Graphing
SCIENTIFIC INQUIRY AND ANALYSIS
2
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.
SCIENTIFIC INQUIRY AND ANALYSIS
3
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
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
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
SCIENTIFIC INQUIRY AND ANALYSIS
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 2014. <http%3A%2F%2Fwww.nytimes.com%2F2008%2F06%2F01%2Fopinion%2F01greene.html%3F_r%3D1>.
6
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
SCIENTIFIC INQUIRY AND ANALYSIS
2. Understanding Science. University of California Museum of Paleontology. Page 4. 25 July 2014 <http://undsci.berkeley.edu/article/0_0_0/whatisscience_04>.
7
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
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. 284.73 rounded to 3 numbers is 285, rounded to 4 numbers is 284.7),
– Example: round 564.478 to 3 numbers. To 4 numbers.
SCIENTIFIC INQUIRY AND ANALYSIS
9
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 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 0.0000076035 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 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)
SCIENTIFIC INQUIRY AND ANALYSIS
12
SYSTEMS OF UNITS
• SI Units– LENGTH: Meter (m)– MASS: Kilogram (kg)– TIME: Seconds (s)
• CGS Units– LENGTH: Centimeter (cm)– MASS: Gram (g)– TIME: Seconds (s)
• BE (British Engineering) Units– LENGTH: Foot (ft)– MASS: Slug (sl)– TIME: Seconds (s)
SCIENTIFIC INQUIRY AND ANALYSIS
13
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
METRIC PREFIXES
SCIENTIFIC INQUIRY AND ANALYSIS
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) (none) One
10n Prefix Symbol Name
10−1 deci d Tenth
10−2 centi c Hundredth
10−3 milli m Thousandth
10−6 micro µ 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
15
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?
SCIENTIFIC INQUIRY AND ANALYSIS
16
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?
SCIENTIFIC INQUIRY AND ANALYSIS
17
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 , likewise the numerator and denominator could be flipped and it would still be equal to one
SCIENTIFIC INQUIRY AND ANALYSIS
18
UNITSCONVERSION 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)
SCIENTIFIC INQUIRY AND ANALYSIS
19
UNITS
• Converting Units• Railroad Method
1. Make a “RR”
2. Put the magnitude of the unit and the units in the upper left RR track.
3. 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.
4. Multiply all the numbers across the top for the numerator and multiply all the numbers across the bottom for the denominator.
5. Divide the numerator by the denominator. Verify the units cancelled out properly.
SCIENTIFIC INQUIRY AND ANALYSIS
20
UNITS
• Example: (convert 55 miles to km)
SCIENTIFIC INQUIRY AND ANALYSIS
21
UNITS
• Example: (convert 750 mL to pints)
SCIENTIFIC INQUIRY AND ANALYSIS
750 mL
1 US gallon = 3.7854 liters
22
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
UNITS
• Example: Convert 100 km per hr to inches per second
SCIENTIFIC INQUIRY AND ANALYSIS
24
UNITS
• Example: Convert 3 to liters per day
SCIENTIFIC INQUIRY AND ANALYSIS
25
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
UNITS
• Example: Convert 210 meters squared (m2) to feet squared (ft2)
SCIENTIFIC INQUIRY AND ANALYSIS
210 m2
1 in = 2.54 cm
27
UNITS
• Example: Convert 6.72 grams per cubic meter to slugs per cubic feet
SCIENTIFIC INQUIRY AND ANALYSIS
6.72 g
1 in = 2.54 cm, 1 slug = 14.593 kg
m3
28
MEASUREMENT
• Always use the smallest division on the scale and estimate the interval between the markings.
SCIENTIFIC INQUIRY AND ANALYSIS
10 20
25.5 cm
29
MEASUREMENT
• Example: (For the left picture read the blue arrow; for the right read the upper scale and then the lower scale)
SCIENTIFIC INQUIRY AND ANALYSIS
30
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.
SCIENTIFIC INQUIRY AND ANALYSIS
31
MEASUREMENT
• Accuracy, precision & outlier
SCIENTIFIC INQUIRY AND ANALYSIS
●1●2
●3●4
●1
●2
●3●4 ●1
●2
●3
●4
32
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.
SCIENTIFIC INQUIRY AND ANALYSIS
33
SIGNIFICANT FIGURES
• Rules of Significant Figures:1. All non-zero numbers are ALWAYS significant
2. All zeroes that fall between two non-zero numbers are significant. (example 1: 13,000 vs. 13002 vs. 13020) (example 2: 1.012 vs. 0.012 vs. 0.0102)
3. For numbers with decimals, final zeroes after the decimal are significant.(example 0.032 vs. 0.320 vs. 1.0320)
– Show the proper number of significant figures by converting the examples into scientific notion.
SCIENTIFIC INQUIRY AND ANALYSIS
34
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 00700 = 258.3m3
(258m3, 258.30m3, 260m3, 300m3)
SCIENTIFIC INQUIRY AND ANALYSIS
35
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
SIGNIFICANT FIGURES
• Distance travelled is 5.02m, 0020.0000m, 56.340m. What is the total distance travelled? What is it if the second distance is 0020m?
5.020020.0000 56.3400081.3600
(81.360m, 81.36m, 81.4m, 81m, 81.3600m)
SCIENTIFIC INQUIRY AND ANALYSIS
37
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
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
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
GRAPHING
Time(seconds)
Position(meters)
0.7 3.8
1.8 3.2
2.6 2.8
3.4 2.2
3.8 1.8
4.1 1.4
4.9 0.8
6.0 0.2
6.5 0
SCIENTIFIC INQUIRY AND ANALYSIS
41
GRAPHING
• Parts of a x-y graph:– Axis with scale
marks– Axis titles & units– Axis numbers– Data points– Graph title– Trendline
SCIENTIFIC INQUIRY AND ANALYSIS
0 1 2 3 4 5 6 70
0.5
1
1.5
2
2.5
3
3.5
4
Graph 1: Movement of a Car
Time (seconds)
Posi
tion
(met
ers)
42
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
GRAPHING
• The equation for the line of best fit is the slope of the line, which is in the format:
Where m is the slope 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
GRAPHING EXAMPLEAge(yrs)
Reaction Time(sec)
50 14.09
80 26.48
70 26.67
50 18.42
30 11.62
30 18.59
60 20.27
60 23.56
30 12.15
20 20.27
SCIENTIFIC INQUIRY AND ANALYSIS
Age(yrs)
Reaction Time(sec)
30 6.16
40 11.18
80 25.80
20 14.20
70 25.09
30 10.63
40 13.24
60 26.51
70 23.98
40 14.18
Age(yrs)
Reaction Time(sec)
20 6.00
30 12.15
70 26.30
90 26.88
70 20.55
40 18.45
50 19.42
90 26.14
45
GRAPHING EXAMPLE
10 20 30 40 50 60 70 80 90 1000.00
5.00
10.00
15.00
20.00
25.00
30.00
f(x) = 0.255214525139665 x + 5.59197765363128
Reaction Time
Age (yrs)
Reac
tion
Tim
e (s
ec)
SCIENTIFIC INQUIRY AND ANALYSIS
46
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