Measurement and the Standard International Units

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Measurement and the Standard International Units

• Scientific Method
• Metric System
• Measurement
• Density
• Scientific Notation
• Conversions Dimensional Analysis
• Graphing

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Scientific Method

• This involves several basic intertwined steps
  which include the following making predictions,
  planning, describing non-numeric events, testing,
  recording observations, evaluating trends,
  reporting conclusions, and seeking feedback and
  criticism from peers.

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Step One

• Identify and state the problem.

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Step Two

• Collect data pertaining to the problem by making
  observations and by carrying out experiments.

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Step Three

• Analyze the data and propose one or more possible
  solutions to the problem (or give an explanation
  for the observations).

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Step Four

• Carry out the proposed plan or experiment.

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Step Five

• Form conclusions based on observations and data
  collected during the experiment.

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Fact

• A close agreement by competent observers. There
  is no scientific experimentation done.
• Example The Earth revolves around the Sun.

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Law

• Rule of nature that sums ups related observations
  and experimental results to describe a pattern in
  nature. They predict what will happen in a given
  situation but do not explain why. Scientific
  laws or principles may be apparent before
  theories develop to explain these laws.
• Example the law of gravity was noticed well
  before scientists experimented with and developed
  theories (logical explanations) about gravity.

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Theory

• An explanation based on many observations
  supported by experimental results. As new
  information is collected a theory may need to be
  revised or discarded and replaced with another
  theory.
• Example Atomic Theory
• (structure of an atom)

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Science is Falsifiable

• Since a theory is only a logical explanation you
  can never prove a theory, not even through
  experimentation.
• A theory can only be disproved. Just one
  controlled, unbiased, valid experiment can
  provide reason for a scientist to question the
  oldest theory.

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Science vs. Technology

• Science involves discovery working with the
  unknown to build our knowledge.
• Technology is the application of known scientific
  knowledge.
• Technology involves using our current knowledge
  to solve problems and help society.
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Metric System
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Standards of Measurement

• A standard is an exact quantity that people agree
  to use for comparison or measurement.
• The first such system of measurement called the
  Metric System was devised by a group of
  scientists in the late 1700s.
• In 1960 an improved version of the Metric System
  was devised and is now called the International
  System of Units. (SI)

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The Seven Fundamental Units of Measurement

• Measurement SI Unit
• Length meter (m)
• Mass gram (g)
• Time second (s)
• Temperature Kelvin (K)
• Amount of Substance mole (mol)
• Intensity of Light Candela (cd)
• Electric Current Ampere (A)

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Commonly Used Prefixes
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Measurement

• Precision the agreement of several measurements
  that have been made in the same way. The more
  decimal places a number has, the more precise it
  is. (9.2763 is more precise than 9.27)
• Ex Measurements of 1.23, 1.25, 1.21 and 1.24 are
  precise.

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Measurement

• Accuracy the closeness of a measurement to the
  accepted value for a quantity.
• Ex Gravity is measured at 9.81 m/s2

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Measurement

• (1) Measurements can be accurate but not precise.
  (2) They can be precise but not accurate. (3)
  They can be both accurate and precise or (4)they
  can be neither accurate nor precise. (See
  pictures below)

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Measurement

• Any time you are making a measurement you will
  experience some type of measuring error.
• These errors may occur as
• Instrumental error- caused by faulty, inaccurate
  apparatus
• Personal error- caused by you or your lab partner
• External error- caused by external conditions
  (wind, temperature, humidity)

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Measuring Length

• When measuring length, we will be using a metric
  ruler or meterstick. The numbered divisions are
  1 cm divisions. The smallest divisions marked
  are 1 mm divisions. Estimating to the next digit
  will give 1/10th of a millimeter.

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Measuring Mass

• When using an electronic balance, write down all
  numbers printed on the screen. When using a
  triple beam balance, the mass can be measured
  accurately to 0.01 grams.

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Measuring Volume

• The amount of space occupied by an object is
  called its volume. There is no specific way to
  measure the objects volume.

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Measuring the Volume of a Solid

• When measuring the volume of a solid object,
  multiply its length x width x height. Typically
  the volume of a solid is measured in either cubic
  centimeters (cm3) or cubic meters (m3).

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Measuring the Volume of a Liquid

• When measuring a liquid volume, one must choose
  the appropriate device based upon the amount of
  liquid to be measured. For smaller amounts of
  liquid, a graduated cylinder is used. For larger
  amounts of liquids, a beaker would be used. The
  most common units used for these types of volumes
  are liters (L) and milliliters (mL).

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Measuring Time

• Many times, we will be using a digital stopwatch
  which are accurate to 1/100th of a second. If a
  stopwatch with a second hand is being used, it
  will measure to nearest second. In this case, an
  estimated measurement to the nearest 1/2 second
  is possible.

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Density

• Density is an important characteristic property
  of matter. When one speaks of lead as being
  heavy or aluminum as light, one is actually
  referring to the density of these metals.
• Density is defined as mass per unit volume.

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Calculating Density

• An object with a mass of 10 grams and a volume of
  5 cm3 has a density of 2 g/cm3.

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A quick way to remember

• The next page is a quick way to remember how to
  find density (D), mass (m), or volume (v).
• 1. Place your thumb (or finger) over the variable
  youre solving for.
• 2. The two variables left tell you what to plug
  into the equation and what operation to do
  (multiplication or division). Multiply number
  beside one another and divide numbers on top of
  one another.

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Density
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Scientific Notation

• Scientific notation is a way of writing very
  large and very small numbers more conveniently.
  A number written in scientific notation has two
  distinct parts
• 1. A number with a decimal point that falls
  between 1 and 10
• 2. The power of ten (either positive or
  negative) that shows which way and how many
  places to move the decimal point to take the
  number out of scientific notation.

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Writing a number in Scientific Notation

• Rewriting 47,000 kg
• Your answer should always have one number to the
  left of the decimal point. Answer 4.
• 2. Write any remaining numbers to the right of
  the decimal. Answer 4.7
• Add x 10 to your answer Answer 4.7 X
  10
• 4. Count the number of places you had to move
  your decimal point and notice which direction you
  moved. Answer 4 places to the left
• If you moved it to the left your number will be
  positive. If you moved it to the right, your
  number will be negative. This number follows you
  x 10 and is written as an exponent. X
  10number (Dont forget your units!)
• Final Answer 4.7 x 104 kg

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Examples

• 1,577,000 mm
• Answer 1.577 x 106 mm
• 0.00012 g
• Answer 1.2 x 10-4 g
• 3. 10054 ml
• Answer 1.0054 x 104 mL

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Working Backwards

• Not always will your calculator be able to enter
  scientific notation. When this happens we have
  to put numbers that are in scientific notation
  back into whole numbers.
• When the number has a positive exponent, move the
  decimal place to the right the same number of
  times as the exponent. Fill in zeroes from the
  right of the numbers to the new decimal point.
• Ex 1.7 x 104 mm 17,000 mm
• 2. When the number has a negative exponent, move
  the decimal to the left the same number of times
  as the exponent. Fill in zeroes from the left of
  the numbers to the new decimal point.
• Ex 5.33 x 10-7 mg 0.000000533 mg

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Examples

• 5.7 x 10-6 kg
• 0.0000057 kg
• 2. 1.04 x 103 mg
• 1040 mm
• 3. 7.6 x 10-1 hl
• 0.76 hl

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Adding and Subtracting in Scientific Notation

• Change each number so that the powers of 10
  match.
• Ex 2.51 x 104 m 1.61 x 103m is changed to 2.51
  x 104 m 0.161 x 104m
• Add or subtract the numbers
• Ex 2.51 0.161 2.671
• 3. Attach the power of ten to your answer along
  with the units
• Ex 2.671 x 104 m
• 4. If your addition or subtraction gives you a
  number larger than 10 or smaller than one, adjust
  your power of 10 accordingly.
• Ex 26.71 would change to 2.671 x 101 and the
  final answer would be 2.671 x 105 m

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Practice

• 7.88 x 104 cm 1.55 x 103 cm
• Answer 7.73 x 104 cm (1.55 x 103 changes to
  0.155 x 104)
• 2. 6.23 x 10-3 dg 1.14 x 10-4 dg
• Answer 6.34 x 10-3 dg (1.14 x 10-4 changes to
  0.114 x 10-3 )

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Multiplying and Dividing

• Multiply or divide the numbers as told.
• When multiplying, add the powers of 10. When
  dividing subtract the powers of 10.
• Adjust the power of 10 to be in proper scientific
  form.
• Ex (2.3 x 103 m)(5.7 x 104 m)
• 2.3 5.7 13.11
• 103 x 104 107
• 13.11 x 107 1.31 x 108 m

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Practice

• 5.2 x 104 mm
• 1.5 x 102 mm
• Answer 3.47 x 102 mm
• 2. (5.55 x 106 cg)(1.47 x 104 cg)
• Answer 8.16 x 1010 cg

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Conversions and Dimensional Analysis or Factor
Label Method

• Not all objects that are measured are in the
  units that are needed. The factor label method
  is a mathematical way to convert from the units
  you have to the units you need. In order to
  eliminate the unwanted units, you design a
  ladder-type set up of equalities that cancel out
  the units you no longer want.
• Example How many liters are there in 3650 mL?

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Steps of Factor Label

• 1. Write down the number (with units) given in
  the problem on the left side of the paper.
• 2. Write the units you are solving for after an
  equals sign on the right side of the paper.
• 3650 mL L

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Steps of Factor Label

• 3. Find an equality relating to the original
  units and write it down in the ladder set up.
  Make sure to put the units that you DO NOT want
  in the denominator. Cross out the units that
  match.
• 3650 mL 1 L L
• 1000 mL

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Steps of Factor Label

• 4. Ask yourself if you want the units in the
  numerator. If you dont, repeat steps 3 and 4
  until you get the correct units in the numerator.
• 5. Solve the problem by multiplying the numbers
  in the numerator, then dividing by the numbers in
  the denominator.
• 3650 mL 1 L 3.65 L
• 1000 mL

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Graphing

• A graph is a visual display of information or
  data. The three main types of graphs are pie
  graphs, bar graphs, and line graphs. The type of
  graph used depends on how the information was
  collected and how it is to be presented.

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Pie Graphs

• A pie graph is used to show how some fixed
  quantity is broken down into parts. The circular
  pie represents the total, and the slices
  represent the parts. The slices are usually
  represented as percentages of the total.

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Example of a Pie Graph

• The pie chart below shows the ingredients used to
  make a sausage and mushroom pizza. The fraction
  of each ingredient by weight shown in the pie
  chart below is now given as a percent. Again, we
  see that half of the pizza's weight, 50, comes
  from the crust. Note that the sum of the percent
  sizes of each slice is equal to 100.
  Graphically, the same information is given, but
  the data labels are different. Always be aware of
  how any chart or graph is labeled.

Click here to make your own pie graph
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Bar Graphs

• A bar graph is useful for showing information
  collected by counting. In a bar graph, the bars
  are not connected, and each bar represents a
  different item that is counted.

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Example of a Bar Graph

• The bar chart below shows the weight in kilograms
  of some fruit sold one day by a local market. We
  can see that 52 kg of apples were sold, 40 kg of
  oranges were sold, and 8 kg of star fruit were
  sold.

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Line Graphs

• Line graphs are used to show trends or continuous
  changes in a relationship between different
  objects.

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