Unit Dimensional Analysis

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Unit Dimensional Analysis
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Uncertainty in Measurement
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Uncertainty in Measurements

• Different measuring devices have different uses
  and different degrees of accuracy.

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Significant Figures

• The term significant figures refers to digits
  that were measured.
• When rounding calculated numbers, we pay
  attention to significant figures so we do not
  overstate the accuracy of our answers.
• The AP College Board expects you to report your
  answers within /- 1 sig fig

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Significant Figures

• Nonzero s are always significant.
• Zeroes
• at the beginning of a number are never
  significant (leading zeroes).
• 0.0025
• between two significant figures are always
  significant (captive zeroes).
• at the end of a number are significant if a
  decimal point is written in the number (trailing
  zeroes).

0100
1.008
30043
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How many sig figs?

• 200
• 5.30 x 103
• 500300
• 0.0500300
• 0.05003
• 0.0105
• p

• 7600
• 809.000
• 1000
• 1000.0
• 1000.00
• 3 cars

Exact s have infinite sig figs 4/3 p r3 100 cm
1 m
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Significant Figures

• Multiplication or Division
• After operation is performed, answer is rounded
  to least number of significant figures in any of
  the numbers used in the calculation.
• 4.56 x 1.4
• 6.38
• 6.4

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Significant Figures

• Addition or subtraction
• After operation is performed, answers are
  rounded to the least of decimal places
• 12.11
• 18.0
• 1.013
• 31.123
• 31.1

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Scientific Notation
of decimal places

• General format M x 10x
• Number of sig figs must be consistent!
• 350
• 0.004010

Value between 1.0 gtlt 10.0
3.5 x 102
4.010 x 10-3
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Units of Measurement

• Metric System

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SI Units

• Système International dUnités
• Uses a different base unit for each quantity

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Metric System

• Prefixes convert the base units into units that
  are appropriate for the item being measured.

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Volume

• The most commonly used metric units for volume
  are the liter (L) and the milliliter (mL).
• A liter is a cube 1 dm long on each side.
• A milliliter is a cube 1 cm long on each side.

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Mega M
1 liter dm3 1 mL cm3
-----
-----
Kilo k
Hecto h
Deka da
Base Unit gram. Liter, meter, mole, kelvin
Deci d
Convert 1.71 nm to cm 1.71 nm x ________
Centi c
cm
1
1.71 x 10-7 cm
Milli m
nm
107
-------
------
Micro µ
1.Whichever unit is larger gets the one. 2. Count
how many steps away. 3. Other unit gets a 1 with
that many zeros (steps)
------
------
Nano n
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Unit Dimensional Analysis

• Use the units to do the work!
• Convert 3.20 km into mm
• 3.20 km x ______mm
• km
• 3.20 km x ______mm
• 1 km
• 3.20 km x _ 106_mm
• 1 km
• 3.20 x 106 mm

• Convert 71 cm3 into m3
• Begin with linear relationship
• 100 cm 1 m
• Then cube both fill in conversion factor
• 71 cm3 x ___1_ m3
• 1000000 cm3
• 7.1 x 10 -5 m3

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Convert 5.341 km/hr to m/sec

• Using units, set up without numbers
• 5.341 km x __m x __hr x __min
• hr km min
  sec
• 5.341 km x _1000 m x _1_hr x _1_min
• hr 1 km 60
  min 60 sec
• 1.484 m/s