Scientific Notation & Round Calculations 8/23/12

Agenda  Bellwork  Metric Video  Measurement Activity Post Lab  Scientific Notation  Rounding Calculations

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)

Domino Metric Conversions (step #4 - review) For metric dominoes: The “multiplier” goes with the BASE unit, And “1” goes with the PREFIX unit

Metric Prefixes (review) PrefixPrefix SymbolMultiplier mega-M (unit) =10 6 (base units) kilo-k (unit) =10 3 (base units) BASE UNIT-10 0 (1) centi-c (unit) =10 -2 (base units) milli-m (unit) =10 -3 (base units) micro-μ (unit) =10 -6 (base units)

Measurement Activity  Part 1: Was similar to historic measurement systems  Standard measurement systems date back to the early 1800’s

Measurement Activity  Part 2: Estimation does have its use when you can’t directly measure something

Measurement Activity  Lab Bench Height  1 m  dm  106 cm  cm or 1063 mm  Hallway  3 m  3.0 m  3.00 m  m

Historic English Units U.S. Length Units: –Point –Pica –Inch –Foot –Yard –Mile

UnitDivisionsSI Equivalent International 1 point (p) µm 1 pica (P ̸ ) 12 p mm 1 inch (in) 6 P ̸ 25.4 mm 1 foot (ft)12 in m 1 yard (yd)3 ft m 1 mile (mi)5280 ft or 1760 yd km US Survey 1 link (li) 33 ⁄ 50 ft or 7.92 in m 1 (survey) foot (ft) 1200 ⁄ 3937 m m 1 rod (rd)25 li or 16.5 ft m 1 chain (ch)4 rd m 1 furlong (fur)10 ch m 1 survey (or statute) mile (mi)8 fur km 1 league (lea)3 mi km

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

Scientific Notation  The components of scientific notation: x  “8.238” is the coefficient  “x 10” is the base  “-31” is the exponent  Where the coefficient has to be a number: 1 ≤ coefficient < 10

Scientific Notation  The Andromeda Galaxy contains at about 200,000,000,000 stars.  Mass of a dust particle is kg.

Scientific Notation  200,000,000,000 stars.  In scientific notation is: 2 x stars

Scientific Notation  kg  In scientific notation is: 7.53 x

Decimal Notation  Given: 3 x 10 6 Is:  Given: 2.84 x Is:

Rounding Calculations

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

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

Estimation vs. Measurement  Estimation:  Length: 17 m  Width: 7 m  Height: 3 m  Volume = 357 m 3  Volume = 400 m 3  Measurement:  Length: m  Width: 9.56 m  Height: 2.68 m  Volume = m 3  Volume = 372 m 3 What is the volume of the room?

Scientific Notation (calculators)  USE THE EXPONENT FUNCTION  (4.8 x ) / (5.134 x ) =  x  Displays will differ  9.3 x (2 sig. figs.)

Scientific Notation  When writing numbers in scientific notation  Express numbers as 4.71 x  ≠ 4.71 x  = 8.83 x  4.71E-61 = 4.71 x

Example #1  3.0 x 4.31 =  3.0 (2 sig. figs.)  4.31 (3 sig. figs.)  Round to 2 sig. figs.  Final answer is 13

Example #2  7000 / =  7000 (1 sig. figs.)  (4 sig. figs.)  Round to 1 sig. figs.  Final answer is 500

Rest of Class  Work on HW: #71-82 due tomorrow  and # due Friday