1. Chemistry September 9, 2014 Dimensional Analysis

2. Science Starter (2) Duration: 2 minutes 1. What is the difference between accuracy and precision? 2. What is the difference between a hypothesis, theory and law?

3. OBJECTIVES (1) SWBAT – Convert units – Apply SI units – Apply Scientific Notation – Apply Significant Digits

4. AGENDA (1) Do Science Starter (2) Activities – Dimensional Analysis – SI units – Scientific Notation – Significant Figures

5. ACTIVITY

6. MEASUREMENTS (0.5) Measurements is a collection of quantitative data Quantitative has amount while qualitative does not

7. PART 1 (2) Using a ruler, measure the blueprint of the apartment below Measure using the feet and inches side. Write the measurement directly onto the blueprint You have 2 minutes Work with your partner

8. DIMENSIONAL ANALYSIS Convert from foot into meter 1 foot = 0.3048 meter

9. SETUP

10. PART 2 (8) Model the Living Room Guided Practice the Bedroom 1 Independently do the Bedroom 2, Kitchen and Bathroom (you have 5 minutes)

11. DIMENSIONAL ANALYSIS(CONT) Definition: Math system using conversion factors to move from one unit of measurement to a different unit of measurement. Why we use it: Make doing calculations easier when comparing measurements given in different units.

12. PART 3 Making the apartment design bigger for Mr. Giant Multiply your answer in Part 2 by 100,000 Change into scientific notation to make it easier to read

13. SCIENTIFIC NOTATION Use to write very large number and very small number (more manageable) Parts: – Before the decimal point = 1 number – After the decimal points = more than 1 numbers (can be optional) – Exponential number = the number of places the decimal is moved

14. EXAMPLE (3) STEP 1: – Multiply the number by 100,000 STEP 2: – Change into scientific notation

15. SI UNITS International System of Units (SI) 7 SI base units – ampere (A) – measures electric current – kilogram (kg) – measure mass – meter (m) – measure length – second (s) – measure time – kelvin (K) – measure thermodynamic temperature – mole (mol) – measure amount of substance – candela (cd) – measure luminous intensity

16. SI PREFIXES PrefixAbbreviationMeaning Exponential Notation Number teraT1 trillion10 12 1,000,000,000,000 gigaG1 billion10 9 1,000,000,000 megaM1 million10 6 1,000,000 kilok1 thousand10 3 1,000 hectoh1 hundred10 2 100 dekada1 ten10 decid1 tenth10 -1 0.1 centic1 hundredth10 -2 0.01 millim1 thousandth10 -3 0.001 microµ1 millionth10 -6 0.000001 nanon1 billionth10 -9 0.000000001 picop1 trillionth10 -12 0.000000000001 femtof1 quadrillionth10 -15 0.000000000000001

17. EXAMPLES (3) 1 m = 100 cm 1 m = 10 dm 1 m = 0.01 hm 1 m = 0.001 km

18. EXAMPLES (1) 1 g = 100 cg 1 g = 10 dg 1 g = 0.01 hg 1 g = 0.001 kg

19. PART 4 Convert the living room measurements from cm to hm Use dimensional analysis Remember: conversion factor is – 1 meter = 0.01 hm or 1 hm = 100 m – 1 meter = 100 cm

20. PART 4 Take 5 minutes to do the rest

21. AREA PART 5 – Find the area (A=wl) of Mr. Giant’s apartment

22. PERIMETER PART 6 – Find the perimeter (P = 2(w+l)) of the apartment of Mr. Giant

23. SIGNIFICANT FIGURES definition: a prescribed decimal place that determines the amount of rounding off to be done based on the precision of the measurement consist of all digits known with certainty and one uncertain digit.

24. RULES FOR SIGNIFICANT FIGURES

25. RULE 1 nonzero digits are always significant – example: 46.3 m has 3 significant figures – example: 6.295 g has 4 significant figures

26. RULE 2 Zeros between nonzero digits are significant – example: 40.7 m has 3 significant figures – example: 87,009 m has 5 significant figures

27. RULE 3 Zeroes in front of nonzero digit are not significant – example: 0.009587 m has 4 significant figures – example: 0.0009 g has 1 significant figure

28. RULE 4 Zeroes both at the end of a number and to the right of a decimal point are significant – example: 85.00 g has 4 significant figures – example: 9.0700 has 5 significant figures

29. PRACTICE Do problems 1a – 1d on the Measurement Calculation Page

30. MULTIPLICATION/DIVISION RULES Rules for using significant figures in multiplication and division – The number of significant figure for the answer can not have more significant figures than the measurement with the smallest significant figures

31. EXAMPLE Example: 12.257 x 1.162 = 14.2426234 – 12.257 = 5 significant figures – 1.162 = 4 significant figures – Answer = 14.24 (4 significant figures)

32. ADDITION/SUBTRACTION The number of significant figure for the answer can not have more significant number to the right of the decimal point

33. EXAMPLE Example: 3.95 + 2.879 + 213.6 = 220.429 – 3.95 = has 2 significant figures after the decimal points – 2.879 has 3 significant figures after the decimal points – 213.6 has 1 significant figures after the decimal points – Answer = 220.4 (1 significant figure)

34. ROUNDING – Below 5 – round down – 5 or above - roundup

35. EXACT VALUES has no uncertainty – example: Count value – number of items counted. There is no uncertainty – example: conversion value – relationship is defined. There is no uncertainty do not consider exact values when determining significant values in a calculated result

36. WARNING CALCULATOR does not account for significant figures!!!!

37. SCIENTIFIC NOTATION RULES FOR CALCULATION

38. RULE 1 Exponents are count values

39. RULE 2 For addition and subtraction, all values must have the same exponents before calculations

40. EXAMPLE Problem: 6.2 x 10 4 + 7.2 x 10 3 Step 1: 62 x 10 3 + 7.2 x 10 3 Step 2: 69.2 x 10 3 Step 3: 6.92 x 10 4 Step 4: 6.9 x 10 4 (Significant rule: can only have as many as the least significant figure to the right of the decimal)

41. RULE 3 For multiplication, the first factors of the numbers are multiplied and the exponents of 10 are added

42. EXAMPLE Problem: (3.1 x 10 3 )(5.01 x 10 4 ) Step 1: (3.1 x 5.01) x 10 4+3 Step 2: 16 x 10 7 Step 3: 1.6 x 10 8 (Significant rule: can only have as many as the least significant figure)

43. RULE 4 For division, the first factors of the numbers are divided and the exponent of 10 in the denominator is subtracted from the exponent of 10 in the numerator

44. EXAMPLE Problem: (7.63 x 10 3 ) / (8.6203 x 10 4 ) Step 1: (7.63 / 8.6203) x 10 3-4 Step 2: 0.885 x 10 -1 Step 3: 8.85 x 10 -2 (Significant rule: can only have as many as the least significant figure)

45. PRACTICE Do problems 2a – 2d Do problems 3a – 3d

46. SCIENCE EXIT (2) Which measurement contains three significant figures? A. 0.08 cm B. 0.080 cm C. 800 cm D. 8.08 cm

47. SCIENCE EXIT 2 Given: (52.6 cm) (1.214 cm) = 63. 8564 cm What is the product expressed to the correct number of significant figures? 64 cm 2 63.9 cm 2 63.86 cm 2 63.8564 cm 2