Scientific Notation

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Scientific Notation Round Calculations

• 8/23/12

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Agenda

• Bellwork
• Metric Video
• Measurement Activity Post Lab
• Scientific Notation
• Rounding Calculations

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Bellwork

• Identify which of the following are prefix units
• (a) N (b) cJ (c) µs (d) g (e) km (f) L
• Answer (b) (c) and (e)

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Domino Metric Conversions (step 4 - review)

• For metric dominoes
• The multiplier goes with the BASE unit,
• And 1 goes with the PREFIX unit

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Metric Prefixes (review)
Prefix Prefix Symbol Multiplier
mega- M (unit) 106 (base units)
kilo- k (unit) 103 (base units)
BASE UNIT - 100 (1)
centi- c (unit) 10-2 (base units)
milli- m (unit) 10-3 (base units)
micro- µ (unit) 10-6 (base units)
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Measurement Activity

• Part 1 Was similar to historic measurement
  systems
• Standard measurement systems date back to the
  early 1800s

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Measurement Activity

• Part 2 Estimation does have its use when you
  cant directly measure something

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Measurement Activity

• Lab Bench Height
• 1 m
• 10-11 dm
• 106 cm
• 106.3 cm
• or 1063 mm

• Hallway
• 3 m
• 3.0 m
• 3.00 m
• 2.997 m

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Historic English Units

• U.S. Length Units
• Point
• Pica
• Inch
• Foot
• Yard
• Mile

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Unit Divisions SI Equivalent
International
1 point (p) 352.777778 µm
1 pica (P?) 12 p 4.233333 mm
1 inch (in) 6 P? 25.4 mm
1 foot (ft) 12 in 0.3048 m
1 yard (yd) 3 ft 0.9144 m
1 mile (mi) 5280 ft or 1760 yd 1.609344 km
US Survey US Survey US Survey
1 link (li) 33/50 ft or 7.92 in 0.2012 m
1 (survey) foot (ft) 1200/3937 m 0.30480061 m
1 rod (rd) 25 li or 16.5 ft 5.02921 m
1 chain (ch) 4 rd 20.11684 m
1 furlong (fur) 10 ch 201.1684 m
1 survey (or statute) mile (mi) 8 fur 1.609347 km
1 league (lea) 3 mi 4.828042 km
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Scientific Notation
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Scientific Notation

• Scientific Notation A way to write very large or
  very small numbers in a compact way
• Use scientific notation for numbers larger then
  10,000 and smaller then 0.001

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Scientific Notation

• The components of scientific notation
• 8.238 x 10-31
• 8.238 is the coefficient
• x 10 is the base
• -31 is the exponent
• Where the coefficient has to be a number
• 1 coefficient lt 10

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Scientific Notation

• The Andromeda Galaxy contains at about
  200,000,000,000 stars.
• Mass of a dust particle is 0.000000000753 kg .

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Scientific Notation

• 200,000,000,000 stars.
• In scientific notation is
• 2 x 1011 stars

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Scientific Notation

• 0.000000000753 kg
• In scientific notation is
• 7.53 x 10-10

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Decimal Notation

• Given 3 x 106
• Is 3000000
• Given 2.84 x 10-7
• Is 0.000000284

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Rounding Calculations
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Rounding to Sig. Figs.

• Multiplication and division of numbers
• After the calculation, round the answer to the
  number that has the least amount of sig. figs.
• Note Addition and subtraction have different
  rules

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Sig. Figs. Exceptions in Calculations

• Conversion factors (metric conversion)
• Scaling factors
• Counting number (EX number of trials or number
  of students)
• Round to sig. figs. At the END of a calculation

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Estimation vs. Measurement
What is the volume of the room?

• Estimation
• Length 17 m
• Width 7 m
• Height 3 m
• Volume 357 m3
• Volume 400 m3

• Measurement
• Length 14.53 m
• Width 9.56 m
• Height 2.68 m
• Volume 372.270224 m3
• Volume 372 m3

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Scientific Notation (calculators)

• USE THE EXPONENT FUNCTION
• (4.8 x 10-6) / (5.134 x 10-19)
• 9.349435138 x 1012
• Displays will differ
• 9.3 x 1012 (2 sig. figs.)

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Scientific Notation

• When writing numbers in scientific notation
• Express numbers as 4.71 x 10-61
• 4.71-61 ? 4.71 x 10-61
• 4.71-61 8.83 x 10-42
• 4.71E-61 4.71 x 10-61

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Example 1

• 3.0 x 4.31 12.93
• 3.0 (2 sig. figs.)
• 4.31 (3 sig. figs.)
• Round to 2 sig. figs.
• Final answer is 13

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Example 2

• 7000 / 13.37 523.5602094
• 7000 (1 sig. figs.)
• 13.87 (4 sig. figs.)
• Round to 1 sig. figs.
• Final answer is 500

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Rest of Class

• Work on HW 71-82 due tomorrow
• and 107-132 due Friday