SCIENTIFIC MEASUREMENT C H A P T E R 3

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1 SCIENTIFIC MEASUREMENT C H A P T E R 3

2 WHAT IS MEASUREMENT? Comparing one object to a standard In science, we use SI Units meters, o C, grams NOT o F, pounds, ounces etc.

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4 TWO TYPES OF MEASUREMENTS 1. Qualitative = descriptive and non-numerical EX: color, odor, texture, etc 2. Quantitative = definite form, numbers and units EX: temperature, mass, length, volume, density

5 SCIENTIFIC NOTATION Used to write very big and very small numbers 6.02 X instead of Number is written as the product of 2 numbers: a coefficient and 10 raised to a power N X 10 x N is a coefficient; a number that is between 1 and ten X is an integer

6 SCIENTIFIC NOTATION RULES Only one digit to the left of the decimal Exponents if the # is greater than one, the exponent is positive if the # is less than one, the exponent is negative In your calculator, use EE or EXP for the x 10 ^ EX: 6.02 x in calculator = 6.02 EE 23

7 CONVERTING A NUMBER INTO SCIENTIFIC NOTATION Step #1: Insert an understood decimal point Step #2: Decide where the decimal must end up so that one number is to its left Step #3: Count how many places you bounce the decimal point Step #4: Re-write in the form M x 10 n X The exponent is the number of places we moved the decimal.

8 CONVERTING A NUMBER INTO SCIENTIFIC NOTATION X 10 9 The exponent is positive because the number we started with was greater than 1.

9 CONVERTING A NUMBER INTO SCIENTIFIC NOTATION Step #1 Locate the decimal Step #2 Decide where the decimal must end up so that one number is to its left Step #3 count how many places you bounce the decimal point Step #4 Re-write in the form N x 10 x

10 CONVERTING A NUMBER INTO SCIENTIFIC NOTATION The exponent is negative because the number we started with was less than 1.

11 CHEM-LOG CONVERT THE FOLLOWING written as 510 written as written as 4.5 x 10-4 written as 3.2 x 10-2 written as 2.89 x 10-3 written as 4.5 x x x If you moved the decimal point to the left, your exponent is positive If you moved to the right, your exponent is negative

12 YOUR TURN P RACTICE USING SCIENTIFIC N OTATION PAG E

13 PERFORMING CALCULATIONS WITH SCIENTIFIC NOTATION Addition and Subtraction If the exponents are the same, add the coefficients Keep the exponent the same in the answer

14 PERFORMING CALCULATIONS WITH SCIENTIFIC NOTATION Addition and Subtraction If the exponents are NOT the same, we must first move a decimal to make them the same Keep the exponent the same in the answer

15 PERFORMING CALCULATIONS WITH SCIENTIFIC NOTATION GET USED TO USING YOUR CALCULATOR 2.5 x 10 4 x 3.2 x x x 10 8

16 PERFORMING CALCULATIONS WITH SCIENTIFIC NOTATION GET USED TO USING YOUR CALCULATOR 2.5 x 10-7 x 3.2 x x x 10-1

17 UNCERTAINTY IN MEASUREMENT Accuracy = a measure of how close a measurement comes to the actual or true value of whatever is measured Precision = a measure of how close a series of measurements are to one another Precise, not accurate

18 UNCERTAINTY IN MEASUREMENT Accurate, not precise

19 UNCERTAINTY IN MEASUREMENT Not precise, not accurate

20 UNCERTAINTY IN MEASUREMENT Precise AND accurate

21 ERROR IN MEASUREMENT Accepted/actual value = the correct value based on reliable references Experimental value = the value measure in the lab Error = accepted experimental % error = I accepted experimental I x 100 accepted

22 CALCULATING ERROR If you only make 33 cookies and the recipe says you should make 36, what is your percent error? Percent Error = I accepted experimental I x 100 accepted accepted = 36 experimental = 33 Percent Error = I I x = 8.3 % error

23 SIGNIFICANT FIGURES Numbers that include ALL digits that can be known plus a last digit that is estimated Digits that have meaning

24 SIGNIFICANT FIGURES Rules regarding zeros Every non-zero digit is significant (567) Zeros between non-zeros are sig (305) Zeros in front of nonzeros are placeholders NOT SIG ( ) Zeros following a nonzero only sig if The come after a decimal point (3.4210) Or a decimal follows (3420.) 3420

25 SIGNIFICANT FIGURES HOW MANY SIG FIGS?????? 4.21 (3) (4) (3) (4) (3) (4) (6)

26 SIGNIFICANT FIGURES IN CALCULATIONS How many significant figures do you need to give in your answer? Answers cannot be more precise than the least precise measurement FOR EXAMPLE, divide 21.4 by 9.8 what s your answer? Answer in calculator says

27 SIGNIFICANT FIGURES IN CALCULATIONS Adding and subtracting The last digit in your answer is set by the first doubtful digit For Example: Answer should only have one significant digit to the right of the decimal point Therefore, the answer should be 4.8

28 SIGNIFICANT FIGURES IN CALCULATIONS Multiplying and dividing Answer contains no more sig figs that the least accurate measurement For example: 3.2 x = Answer should only have two sig figs Therefore, the answer should be 25

29 SIGNIFICANT FIGURES IN CALCULATIONS Rounding If the digit immediately following the last sig fig is less than 5, drop all digits after the last sig fig If the digit is 5 or greater, the value of the digit in the last sig place is increased (rounded) by Answer should only have one significant digit to the left of the decimal point The number that follows the 8 is greater than 5 so drop it answer is 4.9

30 YOUR TURN P RACTICE SIG FIGS I N P ACKET PAGES 1 2 /13 FINISH FOR HOMEWORK!!!

31 INTERNATIONAL SYSTEM OF UNITS (SI) Revised version of the metric system Seven base units length, mass, temp, time, amount, light intensity, electric current Derived units can be calculated using base units density, volume, pressure

32 SI UNITS Length: meter (m) Mass: kilogram (kg) Temperature: kelvin (K) Time: second (s) Quantity: mole (mol) Luminosity: candela (cd) Current: ampere (A)

33 DERIVED UNITS - VOLUME Volume = the space occupied by any sample of matter Derived from length measurements V = l x w x h Can also be measured by volume displacement Units cubic meter (m 3 ) or cubic cm (cm 3 ) 1cm 3 = 1ml

34 DERIVED UNITS - DENSITY Defined: ratio of an object s mass to its volume Equation: D = m/v Units: g/cm 3

35 DENSITY PROBLEM #1 A copper penny has a mass of 3.1 g and a volume of 0.35 cm 3. What is the density of copper? Equation: D = m/v Units: g/cm 3

36 DENSITY PROBLEM #2 A student finds a shiny piece of metal that she thinks is aluminum. In the lab, she determines that the metal has a volume of 245 cm 3 and a mass of 612 g. Calculate the density. Is it aluminum? Density Al = 2.70 g/cm 3 Equation: D = m/v Units: g/cm 3

37 TEMPERATURE Defined: direction of heat transfer When two objects are in contact, heat moves from the object at the higher temperature to the object at the lower temperature

38 TEMPERATURE SCALES Celsius Uses two determined temperatures as reference temp Boiling point of water = 100 o C Freezing point of water = 0 o C Kelvin scale Boiling point of water = 373 K Freezing point of water = 273 K Notice no degree sign 0 K = absolute zero or the point at which all motion stops

39 CONVERTING BETWEEN CELSIUS AND KELVIN K = o C o C = K Ex: convert 25 o C to K Ex: convert 0K to o C K = 25 o C K = 298K o C = 0K o C = -273 o C

40 HOMEWORK FOR TONIGHT CH3 EOC Questions # 36, 39, 40-42, 44, 49, 52, 61, 70, 81

41 DIMENSIONAL ANALYSIS C H A P T E R 4

42 METRIC SYSTEM Americans measure in feet, inches, yards, etc. Based on the king Yard = length of the king s arm Foot = length of the king s foot Pound = amount of marble the king could pick up with one hand New king = new standards The rest of the world measure using the metric system Based on powers of 10

43 Prefix METRIC PREFIXES Symbol Scientific Notation Meaning Mega- M 10 6 Million times kilo- k 10 3 thousand times hecto- h 10 2 Hundred times deca- da 10 1 Ten times BASE ~ ~ Base Unit deci- d / tenth centi- c / hundredth milli- m / thousandth

44 METRIC PREFIXES Prefix Symbol Scientific Notation Pnemonic Device Mega- M 10 6 Most kilo- k 10 3 Kittens hecto- h 10 2 Hate deca- da 10 1 Dogs BASE ~ ~ Because deci- d 10-1 Dogs centi- c 10-2 Can t milli- m 10-3 Meow!

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46

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48 DIMENSIONAL ANALYSIS a way to analyze and solve problems using the units or dimensions of the measurements

49 CONVERSION FACTOR Relationships between two measurements that allow you to convert from one unit to another Ex: 1 yr = 365 days, 1 day = 24 hours

50 3 STEPS TO SOLVING PROBLEMS ACE Method 1. Analyze Identify what is given, unknown, make a plan 2. Calculate Substitute values and use algebra to solve 3. Evaluate Does the answer make sense?

51 SAMPLE PROBLEM #1 How many days are there in 6 weeks? You are looking for this! This is your given.

52 ANALYZE Figure out what relationships you will have to know in order to convert from 1 unit to another. 1 week = 7 days

53 SET UP Start with given and work toward what you are looking for. 6weeks =? days

54 CONVERSION FACTOR 7 days 6 weeks x 1 week days Conversion Factor : top and bottom must be equal in value

55 CANCELING UNITS 6 weeks x 7 days = 42 days 1 week Cancel units : cancel units to leave correct units for the answer Calculate : multiply across top and bottom and divide to get final answer

56 SAMPLE PROBLEM #2 If you are traveling 65 miles per hour, how far will you go in 4 hours?

57 SET UP THE PROBLEM Given: 4 hours, 65 miles = 1 hour Unknown: how many miles? ANALYZE the DIMENSIONS If you have hours and want miles, your conversion factor should be arranged to CANCEL hours and LEAVE miles

58 SAMPLE PROBLEM #2 1. Write your Given over one 4 hours 1 2. times a line 4 hours x 1 3. To cancel hours, the conversion factor must have hours on the BOTTOM 4 hours x 1 1 hour 4. Conversion factor must have desired unit on TOP 4 hours x 65 miles = 260 miles 1 1 hour

59 SAMPLE PROBLEM #3 If you just turned 17 years old, how many seconds old are you? Given: 17 years old Unknown: seconds old Conversion factors: 1 yr = days 1 day = 24 hrs 1 hr = 60 min 1 min = 60 s

60 SAMPLE PROBLEM #3 Solve: 17 yr x day x 24 hr x 60 min x 60 s = 1 yr 1 day 1 hr 1 min When solving dimensional analysis problems, multiply by everything in the numerator and then divide by everything in the denominator and hit enter only ONCE!! In calculator: 17 x x 24 x 60 x =

61 SAMPLE PROBLEM #3 Answer: 17 yrs = 536,479,200 s Check: Does this answer make sense? Yes! 17 years should be a lot of seconds!

62 SAMPLE PROBLEM #4 If you are traveling 50 miles per hour, how many feet per second are you going? Given: 50 miles per hour Unknown: feet per second Conversion factors: 1 mile = 5280 ft 1 hr = 60 min 1 min = 60 s

63 SAMPLE PROBLEM #4 Solve: 50 miles x 5280 feet x 1 hrx x 1 min= 1 hour 1 mile 60 min 60 sec In calculator: 50 x 5280 x 1 x = 73 feet/sec

64 SAMPLE PROBLEM #5 The average American student is in class 330 minutes/day. How many hours a year is this if you have perfect attendance (181 days)? Given: 330 minutes/day; 181 days Unknown: hours a year Conversion factors: 1 day = 24 hours 1 hr = 60 min

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