Section 5.1 Scientific Notation and Units Objectives

Transcription

1 Objectives 1. To show how very large or very small numbers can be expressed in scientific notation 2. To learn the English, metric, and SI systems of measurement 3. To use the metric system to measure length, volume and mass

2 Arithmetic is being able to count up to twenty without taking your shoes off Mickey Mouse Mickey also says Do you remember what an exponent is?

3 A. Scientific Notation size large size size slider small Very large or very small numbers can be expressed using scientific notation The number is written as a number between 1 and 10 multiplied by 10 raised to a power. e.g is 7.2 x 10 3 The power of 10 depends on: The number of places the decimal point is moved. The direction the decimal point is moved. Left Positive exponent Right Negative exponent

4 A. Scientific Notation Representing Large Numbers 93,000,000 miles from the Earth to the Sun (sunlight takes 8 minutes to reach us) 93,000,000 = 9.3 x 10,000,000 = 9.3 x 10 x 10 x 10 x 10 x 10 x 10 x 10 = 9.3 x 10 7 (Decimal point moved 7 digits to the left) Number between 1 and 10 Appropriate power of ten

5 A. Scientific Notation Representing Small Numbers To obtain a number between 1 and 10 we must move the decimal point to the right = = 1/10000 (one ten-thousandth)

6 Convert the following numbers between normal and scientific notation: , x x x x x x 10-7

7 Convert the following numbers/sums into correct scientific notation: 35.9 x x x x x x x 10 7

8 Scientific Notation Math - Exponents x x x / / / /10 3 1/10 5 1/10-2 1/10-7

9 Scientific Notation Math Multiplication - multiply the numbers, add the indices 1.2 x 10 4 multiplied by 5 x 10 6 = Division - divide the numbers, subtract the indices 5.5 x 10 8 divided by 1.1 x 10 2 = (For all operations reconvert answers to full scientific notation)

10 Scientific Notation Math Addition or subtraction: Convert to the same base and perform the operation Then reconvert to scientific notation 1.04 x 10 3 plus 6.8 x 10 2 =

11 Combined Operations Give the answer in scientific notation 7.5 x x x 10 6 x 1.5 x x x 10 5 x 4 x x x x 10 3 x 5 x 10-6

12 Measurement A quantitative observation Consists of 2 parts Number Unit tells the scale being used

13 B. Units Units provide a scale on which to represent the results of a measurement. What units can you think of? Time is God s way of making sure everything doesn t happen at once (Unknown)

14 B. Units There are 3 commonly used unit systems. English (used in the United States) Metric (broadly used across the World) SI (most formal version of Metric used in science)

15 Countries not yet officially metric: USA, Liberia, Myanmar

16 Metric/SI Prefixes size slider Prefixes are used to denote different sizes of each unit:

17 (10-12 ) pico p (10-15 ) femto f (10-18 ) atto a (10-21 ) zepto z (10-24 ) yocto y Multiplication factor (scientific notation) Section 5.1 Prefix (10 24 ) yotta Y (10 21) zetta Z (10 Full List of Metric Prefixes ) exa E (10 15 ) peta P (10 12 ) tera T (10 9 ) giga G (10 6 ) mega M 1000 (10 3 ) kilo k 100 (10 2 ) hecto h 10 (10 1 ) deka da 0.1 (10-1 ) deci d 0.01 (10-2 ) centi c (10-3 ) milli m (10-6) micro µ (10-9 ) nano n Symbol

18 Metric Dollars 100 dollars 1 hectodollar 1x dollars 1 dekadollar 1x dollar 1 dollar 1x dime 1 decidollar 1X cent 1 centidollar 1X10-2

19 C. Measurements of Length, Volume and Mass Length Fundamental unit is the meter 1 meter = inches Comparing English and metric systems Who is taller a woman 5 ft 6 inches or a man 1.62 meters tall?

20 C. Measurements of Length, Volume and Mass * *

21 C. Measurements of Length, Volume and Mass Volume Amount of 3-D space occupied by a substance Fundamental unit is meter 3 (m 3 ) 1 liter = 2.11 Pints 250mL of milk is close to ½ Pint, 1 Pint, 1 Quart, 1 Gallon?

22 C. Measurements of Length, Volume and Mass Mass Quantity of matter in an object Fundamental unit is kilogram = 2.2 lbs

23 C. Measurements of Length, Volume and Mass How many quarters in a row to make a meter? What is the weight in kg of a man who weighs 180 lbs? How many liters in a six-pack of soda cans?

24 A man with a watch knows what time it is. A man with two watches is never sure (Unknown)

25 I weigh some sugar on my kitchen scales and some more sugar on my lab balance. The results are shown below. How much sugar should I say I have, in total, without being misleading? Kitchen scales: 2.2 kilograms Lab scale: grams (1kg = 1000g)

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27 Objectives 1. To learn how uncertainty in a measurement arises 2. To learn to indicate a measurement s uncertainty by using significant figures 3. To learn to determine the number of significant figures in a calculated result

28 A. Uncertainty in Measurement A measurement always has some degree of uncertainty.

29 A. Uncertainty in Measurement Different people estimate differently. Record all certain numbers and one estimated number.

30 B. Significant Figures Significant figures are the meaningful figures in our measurements and they allow us to generate meaningful conclusions Numbers recorded in a measurement are significant. All the certain numbers plus first estimated number e.g cm We need to be able to combine data and still produce meaningful information There are rules about combining data that depend on how many significant figures we start with

31 B. Significant Figures Rules for Counting Significant Figures 1. Nonzero integers always count as significant figures has 4 significant figures 23.3 has 3 significant figures

32 B. Significant Figures Rules for Counting Significant Figures 2. Zeros a. Leading zeros - never count significant figures b. Captive zeros - always count significant figures c. Trailing zeros - count only if the number is written with a decimal point significant figure significant figures significant figures

33 B. Significant Figures Rules for Counting Significant Figures 3. Exact numbers - unlimited significant figures Not obtained by measurement Determined by counting: 3 apples Determined by definition: 1 in. = 2.54 cm

34 How Many Significant Figures? , x x x minutes in an hour 500 laps in the race

35 B. Significant Figures - Round off to 1,2,3,4 significant figures

36 B. Significant Figures Rules for Multiplication and Division I measure the sides of a rectangle, using a ruler to the nearest 0.1cm, as 4.5cm and 9.3cm What does a calculator tell me the area is? What is the range of areas that my measurements might indicate (consider the range of lengths that my original measurements might cover)?

37 B. Significant Figures Rules for Multiplication and Division The number of significant figures in the result is the same as in the measurement with the smallest number of significant figures.

38 B. Significant Figures Rules for Addition and Subtraction The number of significant figures in the result is the same as in the measurement with the smallest number of decimal places.

39 Rules for Combined Units Multiplication / Division When you Multiply or Divide measurements you must carry out the same operation with the units as you do with the numbers 50 cm x 150 cm = 7500 cm 2 20 m / 5 s = 4 m/s or 4 ms -1 16m / 4m = 4 Addition / Subtraction When you Add or Subtract measurements they must be in the same units and the units remain the same 50 cm cm = 200 cm 20 m/s 15 m/s = 5 m/s

40 Calculate the following. Give your answer to the correct number of significant figures and use the correct units 11.7 km x km = 12 mm x 34 mm x mm = m / 7 s = 108 kg / 550 m 3 = 23.2 L + 14 L = 55.3 s s = cm 4.2 cm = km km =

41 Objectives 1. To learn how dimensional analysis can be used to solve problems 2. To learn the three temperature scales 3. To learn to convert from one temperature scale to another 4. To practice using problem solving techniques 5. To define density and its units

42 Conversions 45.7 cm is how many meters? 11.3 kg is how many milligrams? What is tricky about this kind of calculation?

43 I am driving in Canada. I have a journey of 120 km and I need to estimate how many liters of gas to buy. I know my car fuel mileage is 24 miles per gallon. (1 mile is 1.6 km, 1 gallon is 3.79 liters)

44 A. Tools for Problem Solving Converting Units of Measurement We can convert from one system of units to another by a method called dimensional analysis using conversion factors Unit 1 conversion factor = Unit 2 Conversion Factor has Unit 2 /Unit 1

45 A. Tools for Problem Solving Converting Units of Measurement Conversion factors are built from an equivalence statement which shows the relationship between the units in different systems. 1 inch = 2.54cm Conversion factors are ratios of the two parts of the equivalence statement that relate the two units. 1 inch or 2.54cm 2.54cm 1 inch

46 A. Tools for Problem Solving Converting Units of Measure 2.85 cm =? in cm conversion factor =? in. Equivalence statement 2.54 cm = 1 in. Possible conversion factors Does this answer make sense? (P166 Q39 c-h,)

47 Multiple Steps 2.85 cm is how many feet? 7.1 years is how many hours? Let s go back and solve the Canadian Driving Problem

48 A. Tools for Problem Solving Tools for Converting from One Unit to Another Step 1 Find an equivalence statement that relates the 2 units. Step 2 Choose the conversion factor by looking at the direction of the required change (cancel the unwanted units). Step 3 Multiply the original quantity by the conversion factor. Step 4 Make sure you have the correct number of significant figures.

49 I am driving in Canada. I have a journey of 120 km and I need to estimate how many liters of gas to buy. I know my car fuel mileage is 24 miles per gallon. (1 mile is 1.6 km, 1 gallon is 3.79 liters) Ask yourself these questions Where are we starting from? Where do we want to go? What information do we know that helps us? How do we get to a solution? Does your answer make sense?

50 I am driving in Canada. I have a journey of 120 km and I need to estimate how many liters of gas to buy. I know my car fuel mileage is 24 miles per gallon. (1 mile is 1.6 km, 1 gallon is 3.79 liters)

51 32 Degrees?

52 ..or 32 Degrees?

53 Degrees?..

54 B. Temperature Conversions There are three commonly used temperature scales, Fahrenheit, Celsius and Kelvin.

55 B. Temperature Conversions Converting Between the Kelvin and Celsius Scales Note that The temperature unit is the same size. The zero points are different. To convert from Celsius to Kelvin we need to adjust for the difference in zero points.

56 B. Temperature Conversions Converting Between the Kelvin and Celsius Scales 70 o C =? K T C = T K = 343 K

57 B. Temperature Conversions Converting Between the Fahrenheit and Celsius Scales Note The different size units The different zero points To convert between Fahrenheit and Celsius we need to make 2 adjustments. T oc =?

58 Convert These Temperatures 200 o C to K -52 o C to K 345K to o C 11K to o C 212 o F to o C 32 o F to o C 525 o F to o C 25 o C to o F -20 o C to o F 200 o F to K

59 At what temperature would a Celsius and a Fahrenheit thermometer read the same? T o F = To C

60 C. Density Density is the amount of matter present in a given volume of substance. Write down all the statements relating the three properties D, M and V

61 How to Remember the Density Relationships Q. Where do you get your permit? A. At the DMV m D v

62 Calculate the Missing Quantity: Mass Volume Density 4530 g 225 cm 3? g/cm g 25.0 ml? g/cm lb 500. cm 3? g/cm g L? g/cm 3? g 45 cm g/cm g? ml 10.5 g/cm 3? g 10. L g/ml 1.45 kg? L 2.67 g/ml Remember the DMV 1 lb = 454 g

63 C. Density H 2 = kg/m3 Is the hydrogen number correct?

64 Density of Water One gram of water has a volume of 1 milliliter The density of water is? D = M/V Density of water = 1 g/ml or 1g/cm3 How much does 150 ml of water weigh? What is the density of water in kg/m3? (Egg density demo)