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Unit Dimensional Analysis

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The most commonly used metric units for volume are the liter (L) and the milliliter (mL) ... A milliliter is a cube 1 cm long on each side. Mega M. Kilo k ... – PowerPoint PPT presentation

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Title: Unit Dimensional Analysis


1
Unit Dimensional Analysis
2
Uncertainty in Measurement
3
Uncertainty in Measurements
  • Different measuring devices have different uses
    and different degrees of accuracy.

4
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

5
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
6
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
7
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

8
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

9
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
10
Units of Measurement
  • Metric System

11
SI Units
  • Système International dUnités
  • Uses a different base unit for each quantity

12
Metric System
  • Prefixes convert the base units into units that
    are appropriate for the item being measured.

13
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.

14
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
15
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

16
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
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