PHYSICS. Chapter 1 Review. Rounding Scientific Notation Factor Label Conversions

Transcription

1 PHYSICS Chapter 1 Review Rounding Scientific Notation Factor Label Conversions

2 The Tools Of PHYSICS

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4 Metric Prefixes Prefix Symbol Meaning Kilo K 1000 Deci d tenth Centi c hundreth Milli m thousandth

5 Prefix Prefixes Used with SI Units Prefix Symbol Number Word Exponential Notation tera T 1,000,000,000,000 trillion giga G 1,000,000,000 billion 10 9 mega M 1,000,000 million 10 6 kilo k 1,000 thousand 10 3 hecto h 100 hundred 10 2 deka da 10 ten one 10 0 deci d 0.1 tenth 10-1 centi c 0.01 hundredth 10-2 milli m thousandth 10-3 micro µ millionth 10-6 nano n billionth 10-9 pico p trillionth femto f quadrillionth 10-15

6 Rounding.64 Rounds down to.6.4 or less rounds down.

7 .66 Rounds up to.7.6 or more rounds up.

8 .65 Rounds down to.6 Even number followed by a 5 keep it even.

9 .55 Rounds up to.6 Odd number followed by a 5 round up to even.

10 Why this rounding method? Half the time the number in front of the 5 will be even and rounded down. Half the time the number following the 5 will be odd and rounded up. The error caused by rounding should be balanced out.

11 Scientific Notation Used for very large and very small numbers. Regular numbers are expressed as a number greater than 1 but less than 10, multiplied by a power of 10.

12 M x 10 n where 1 M < 10 and n = any integer n indicates which direction and how many spots to move the decimal point.

13 +n indicates that the original number is greater than one. -n indicates that the original number is less than one.

14 Scientific Notation Examples: x x 10 Original number > 1 Positive exponent Original number < 1 Negative exponent

15 6.02 x exponent Original number is > 1 Therefore: 602

16 6.02 x exponent Original number is < 1 Therefore: Zeros can be added to fill decimal spots Practice Numbers in SN.

17 Scientific Notation on the Calculator Discuss the scientific notation options on personal calculators and do sample calculator problems. Practice SN problems.

18 Precision and Accuracy When making measurements in the laboratory you need to know how good is the measurement. Precision indicates degree of reproducibility of a measured number.

19 Accuracy indicates how close your measurements are to the true value.

20 Precision and Accuracy in the Lab Precise and Accurate Precise but not Accurate

21 Not accurate but precise Accurate but low precision

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23 Accuracy and Precision

24 P a r a l l a x

25 Measurements and Uncertainty It is not possible to know the exact measurement of anything. There is always going to be some guess work involved when measuring.

26 Beaker 47 ml Uncertain Digit

27 Significant Digits These are a PAIN!!! The greater the number of significant digits in a measurement, the greater the certainty.

28 1 cm 2 cm 1.6 cm

29 1.35 cm 1 cm 2 cm

30 1.72 cm 1 cm 2 cm

31 1.60 cm 1 cm 2 cm

32 2.00 cm 1 cm 2 cm

33 1. All nonzero digits are significant. 2. For numbers larger than 1 (one) that contain zeros. A. Zeros to the left of an UNDERSTOOD decimal point are NOT significant contains 2 sig. figs.

34 B. Zeros to the left of an EXPRESSED decimal point ARE significant Contains 4 sig. figs. 3. Zeros between nonzero digits are significant all have four sig.figs.

35 4. For numbers smaller than 1 (one) that contain zeros: A. Zeros to the right of a decimal but to the left of a nonzero digit are NOT significant has two sig. figs.

36 B. Zeros to the right of a decimal and to the right of a nonzero digit ARE significant has four significant digits. Exactness zeros

37 5. Exact numbers or definitions- numbers with no uncertainty. These have as many significant digits as the calculation requires. 60 min = 1 hr 1000 mg = 1 g Typically factor label conversions.

38 Math Operations and Sig. Figs. 1. Multiplication and Division The number with the least certainty limits the certainty of the result.

39 The answer can only have as many sig. figs as contained in the number with the least number of sig. figs. EX: X 1267 = 29,141,000 = 29,000,000

40 9.2 cm x 6.8 cm x cm = cm 3 or 23 cm 3

41 2. Addition and Subtraction The answer should be as accurate as the number with the lesser accuracy.

42 Adding two numbers: (+/- 100) (+/- 10) = /- 100 Subtracting two volumes: ml ml ml = ml +/- 0.1 ml

43 Measurements and Uncertainty It is not possible to know the exact measurement of anything. There is always going to be some guess work involved when measuring.

44 When Measuring Anything: Determine what the markings on the equipment mean. These are the certain digits.

45 Doubtful Digits in Measurements With any analog scientific tool the measurement can only be estimated to one spot past the certain digit. This estimated digit is also called the doubtful digit and is significant!!!

46 Factor Label Method of Conversions Utilizes comparisons of units to solve a problem.

47 Simple Examples of Factor Label 10 students attend a concert and pay $5 for a ticket. What is the total cost? 10 tickets x $ 5.00 = $50.00 ticket

48 If you baby sit for 3 hours and earn $4 per hour, how much do you earn? 3 hours x $ 4.00 = $12.00 hour

49 If you baby sit for 225 minutes and earn $4 per hour, how much do you earn? 225 min X 1 hour x 60 min $ 4.00 hour = $15.00

50 More Factor Label Convert 175 inches to feet. 175 in x 1 foot = 14.6 feet 12 in

51 Convert 25.0 cm to feet. Cm ---> inches ---> feet 25.0 cm x 1 inch x 2.54 cm 1 foot = 12 inches 0.82_ feet

52 Convert 25.0 gal to milliliters. Gallons ---> liters ---> ml 25.0 gal x 3.8 liters x 1 gal 1000 ml = 1 liter ml 9.50 x 10 4 ml

53 Convert 48 oz to kilograms. oz ---> lbs ---> grams ---> kg 48 oz x 1 lb x 16 oz 454 g x 1 lb 1 kg = 1.36 kg 1.4 kg 1000 g

54 How many seconds have you been alive? years ---> days ---> hours ---> sec 17 yrs x 365 days x 1 yr 24 hrs x 1 day 3600 sec = 5.36 x 10 8 sec 1 hr 5.4 x 10 8 sec

55 Area and Volume Factor Label Area conversions: How many cans of paint for a room? How much fabric? How many gallons of driveway sealer?

56 Convert 125 ft 2 to in ft x ( 12 in ) 2 = in 2 ( ) x 10 4 in 2 1 ft The squares goes with the number and the unit.

57 Convert 1250 cm 3 to ft cm x ( 1 in ) 3 x ( 2.54 cm ) 3 ( 1 ft ) 3 = ( 12 in) ft 3 The cubes goes with the number and the unit ft 3

58 Graphing Data ch1_3_movanim.swf

59 Scatter plots of data may take many different shapes, suggesting different relationships.

60 H e i g h t o f P l a n t Age of Plant

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63 Linear Relationships When the line of best fit is a straight line, the dependent variable varies linearly with the independent variable. This relationship between the two variables is called a linear relationship.

64 The relationship can be written as an equation. Y = mx +b

65 The slope is the ratio of the vertical change to the horizontal change. X 2,Y 2 X 1,Y 1

66 What is the slope of the graph? A.0.25 m/s 2 B.0.4 m/s 2 C.2.5 m/s 2 D.4.0 m/s 2

67 Nonlinear Relationships When the graph is not a straight line, it means that the relationship between the dependent variable and the independent variable is not linear. There are many types of nonlinear relationships in science. Two of the most common are the quadratic and inverse relationships.

68 The graph shown in the figure is a quadratic relationship. A quadratic relationship exists when one variable depends on the square of another.

69 A quadratic relationship can be represented by the following equation: y = ax2 + bx + c

70 The graph in the figure shows how the current in an electric circuit varies as the resistance is increased. This is an example of an inverse relationship.

71 P V Boyle s Law

72 In an inverse relationship, a hyperbola results. An inverse relationship can be represented by the following equation: y = a x

73 What is line of best fit? A.The line joining the first and last data points in a graph. B. The line joining the two center-most data points in a graph. C.The line drawn close to all data points as possible. D.The line joining the maximum data points in a graph.

74 Answer: C Reason: The line drawn closer to all data points as possible, is called a line of best fit. The line of best fit is a better model for predictions than any one or two points that help to determine the line.

75 Which relationship can be written as y = mx? A.Linear relationship B.Quadratic relationship C.Parabolic relationship D.Inverse relationship

76 Answer: A Reason: Linear relationship is written as y = mx + b, where b is the y intercept. If y-intercept is zero, the above equation can be rewritten as y = mx.

77 Which type of relationship is shown following graph? A. Linear B. Inverse C. Parabolic D. Quadratic

78 Answer: B Reason: In an inverse relationship a hyperbola results when one variable depends on the inverse of the other.

79 The End