1. Scientific Notation & Round Calculations 8/23/12

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

3. 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)

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

5. 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)

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

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

8. 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

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

10. UnitDivisionsSI Equivalent International 1 point (p)352.777778 µm 1 pica (P ̸ ) 12 p4.233333 mm 1 inch (in) 6 P ̸ 25.4 mm 1 foot (ft)12 in0.3048 m 1 yard (yd)3 ft0.9144 m 1 mile (mi)5280 ft or 1760 yd1.609344 km US Survey 1 link (li) 33 ⁄ 50 ft or 7.92 in0.2012 m 1 (survey) foot (ft) 1200 ⁄ 3937 m0.30480061 m 1 rod (rd)25 li or 16.5 ft5.02921 m 1 chain (ch)4 rd20.11684 m 1 furlong (fur)10 ch201.1684 m 1 survey (or statute) mile (mi)8 fur1.609347 km 1 league (lea)3 mi4.828042 km

11. Scientific Notation

12.  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

13. 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 < 10

14. Scientific Notation  The Andromeda Galaxy contains at about 200,000,000,000 stars.  Mass of a dust particle is 0.000000000753 kg.

15. Scientific Notation  200,000,000,000 stars.  In scientific notation is: 2 x 10 11 stars

16. Scientific Notation  0.000000000753 kg  In scientific notation is: 7.53 x 10 -10

17. Decimal Notation  Given: 3 x 10 6 Is: 3000000  Given: 2.84 x 10 -7 Is: 0.000000284

18. Rounding Calculations

19. 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

20. 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

21. Estimation vs. Measurement  Estimation:  Length: 17 m  Width: 7 m  Height: 3 m  Volume = 357 m 3  Volume = 400 m 3  Measurement:  Length: 14.53 m  Width: 9.56 m  Height: 2.68 m  Volume = 372.270224 m 3  Volume = 372 m 3 What is the volume of the room?

22. Scientific Notation (calculators)  USE THE EXPONENT FUNCTION  (4.8 x 10 -6 ) / (5.134 x 10 -19 ) =  9.349435138 x 10 12  Displays will differ  9.3 x 10 12 (2 sig. figs.)

23. 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

24. 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

25. 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

26. Rest of Class  Work on HW: #71-82 due tomorrow  and #107-132 due Friday