Unit 1 Into to Measurement

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Unit 1 Into to Measurement
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Uncertainty in Data

• Precision A reliable measurement will give about
  the same results time and time again under the
  same conditions. Precision refers to the
  reproducibility of a measurement.
• Accuracy A measurement that is accurate is the
  correct answer or the accepted value for the
  measurement. High accuracy close to accepted
  value.

http//www.youtube.com/watch?vHmY4YiLCCaU
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• Examples
• More Examples
• True Value 34.0 mLMeasurements 34.2 mL, 34.1
  mL, 34.2 mLAccurate and/or Precise?
• True Value 29.3 cmMeasurements 32.3 cm, 32.5
  cm, 32.4 cmAccurate and/or Precise?
• True Value 27.3 sMeasurements 27.9s, 30.2s,
  26.9sAccurate and/or Precise?

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Significant Figures

• You are often asked to combine measurements
  mathematically. When measurements are combined
  mathematically, the uncertainty of the separate
  measurements must be correctly be reflected in
  the final answer.
• A set of rules exists to keep track of the
  significant figures in each measurement.
• The significant figures (SIG FIGS) in a
  measurement include the certain digits and the
  estimated digit of a measurement.

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SIG FIG RULES !!

• Nonzero numbers are always significant.
• 14
• 523
• Zeros between nonzero numbers are always
  significant. Sandwich Zeros
• 101
• 2005
• Zeros after significant figures are significant
  only if they are followed by a decimal point.
  (All final zeros to the right of the decimal are
  significant).
• 100.0
• 2030.0
• Place holder zeros are NOT significant. To
  remove placeholder zeros, rewrite the number in
  scientific notation.
• 0.001
• 0.0000034

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How many sig figs in these measurements?

• 3.4567 _____
• 3.00047 _____
• 0.00003409 _____
• 2.05 X 105 _____
• 0.100 _____
• 3000 _____

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Sig Figs in Calculations

• For multiplication and division The least number
  of sig figs in the measurements determines how
  many sig figs in the final answer.
• Ex 6.15 m x 4.026 m 24.7599 m2 What is the
  fewest of sig figs? (3) so the answer is
  rounded to 24.8 m2
• If a calculation involves several steps, ONLY
  ROUND FINAL ANSWER, carry extra sig figs in
  intermediate steps. If the digit to be rounded is
  less than 5, round down if 5 or more, round up.

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• Ex. 24 cm X 32.8 cm 763.2 cm2
•  
• Round 763.2 cm2 to ____________
•  
• Ex. 8.40 g 4.2 g/mL 2 g/mL
•  
• 2 g/mL must be rounded to ____________

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• For addition and subtraction The sum or
  difference has the same number of decimal places
  as the measurement with the least number of
  decimal places.
• EX 951.0g 1407 g 23.911 g 158.18 g
  2540.091 g But the measurement with the fewest
  places past decimal is 1407 g ( It has no digits
  past decimal) SO the final answer must be rounded
  to 2540. g

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• Ex. 49.1 g 8.001 g 57.101 g
•  
• Round the answer to ___________
•  
• Ex. 81.350 m 7.35 m 74 m
•  
• Round the answer to ____________

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Percent Error

• Percent error compares a measurement with its
  accepted value. A percent error can be either
  positive or negative.
• ERROR measured - accepted x 100
  accepted
• ERROR what you got what is correct x
  100
  what is correct

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Scientific Notation

• Some measurements that you will encounter in
  physics can be very large or small. Using these
  numbers in calculations is cumbersome. You can
  work with these numbers more easily by writing
  them in scientific notation. A number written in
  scientific notation is written in the form 
• M X 10n
• Where M is a number between 1 and 10 (known as
  the coefficient) and 10 is raised to the power of
  n (known as the exponent). Circle the numbers
  that are in correct scientific notation
•  
• 1 X 104 12 X 1012 0.9 X 103
• 2.54 X 10-3 9.99 X 102

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• Step 1 Determine M by moving the decimal point
  in the original number to the left or right so
  that only one nonzero digit is to the left of the
  decimal.do it!!!
• 27508.
•  
• Step 2 Determine n , the exponent of 10, by
  counting the number of decimal places the decimal
  point has moved. If moved to the left, n is
  positive. If moved to the right, n is negative.
• 2.7508
• 4 places to the left, n 4
• Answer 2.7508 X 104

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• Write the following quantities in scientific
  notationdo it!!!
• 0.0050
• 235.4
• 18,903
• 0.0000101
• Write the following quantities in arithmetic
  notationdo it!!!
• 1.45 X 104
• 2.34 X 10-3
• 6.02 X 1023

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Units and Measurements

• The International System of measurement or
  metric system is the preferred system.
• Make sure you are familiar with the basic units
  that we will be using many times throughout the
  year.

Quantity Unit Abbreviations
Time Second s
Length Meter m
Mass Gram g
Temperature Kelvin K
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• Make sure to be familiar with the common prefixes
  that make the base unit larger (kilo- for
  example) and prefixes that make the unit smaller
  ( examples milli - and centi-)
• You should know how to quickly change between the
  units, for example, from liter to milliliter or
  kilograms to grams.

Prefix Symbol
Kilo k.
Hecta h.
Deca da
Base Unit
Deci d
Centi c
Milli m
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Factor Label/ Dimensional Analysis

• Dimensional Analysis A technique of converting
  between units.
• Dimensional analysis use conversion factors. A
  conversion factor is always equal to 1. For
  example 1000m or 60 minute 1 km 1
  hour
• Conversion factors can be flipped to allow for
  cancellation of units.
• Choosing the correct conversion factors requires
  looking carefully at the problem.

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• Step 1 Show what you are given on the left, and
  what units you want on the right.
•  
• Step 2 Insert the required conversion factor(s)
  to change between units. In this case we need
  only one conversion factor, and we show it as a
  fraction, 1 hr/60 min. We put units of minutes
  on the bottom so they will cancel out with the
  minutes on the top of the given.
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• Step 3 Cancel units where you can, and solve
  the math.

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• For example lets look at the following question
• Example 1 Given that there are 5280feet in a
  mile, How many feet are in 2.78 miles?
• Example 2 Convert 89 km into inches

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• Example 3 How many gallons are in 146 Liters? 1
  Gal 4 quarts 1 L 1.057 quarts 1
  L1000ml
• Example 4 How many seconds in 5.00 days?