scientific inquiry and analysis unit 1 units of measure, conversions and graphing 1scientific...

1

SCIENTIFIC INQUIRY AND ANALYSIS

UNIT 1

Units of Measure, Conversions and Graphing


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.


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.


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.


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


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>.

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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 4. 25 July 2014 <http://undsci.berkeley.edu/article/0_0_0/whatisscience_04>.

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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.


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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.


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.


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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.


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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)


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)


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.


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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) (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?


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?


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


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)


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.


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UNITS

• Example: (convert 55 miles to km)


21

UNITS

• Example: (convert 750 mL to pints)


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.


23

UNITS

• Example: Convert 100 km per hr to inches per second


24

UNITS

• Example: Convert 3 to liters per day


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.


26

UNITS

• Example: Convert 210 meters squared (m2) to feet squared (ft2)


210 m2

1 in = 2.54 cm

27

UNITS

• Example: Convert 6.72 grams per cubic meter to slugs per cubic feet


6.72 g

1 in = 2.54 cm, 1 slug = 14.593 kg

m3

Andrew Pantaleo

28

MEASUREMENT

• Always use the smallest division on the scale and estimate the interval between the markings.


10 20

25.5 cm

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MEASUREMENT

• Example: (For the left picture read the blue arrow; for the right read the upper scale and then the lower scale)


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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.


31

MEASUREMENT

• Accuracy, precision & outlier


●1●2

●3●4

●1

●2

●3●4 ●1

●2

●3

●4

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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.


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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.


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)


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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.


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)


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.


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?


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


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


41

GRAPHING

• Parts of a x-y graph:– Axis with scale

marks– Axis titles & units– Axis numbers– Data points– Graph title– Trendline


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.


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)


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


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

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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)


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)


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