# Quantitative vs. Qualitative

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Quantitative vs. Qualitative. Make a quantitative observation about your textbook Make a qualitative observation about your textbook. Quantitative vs. Qualitative. Quantitative observation: Qualitative observation:. Precision vs. Accuracy. Archery Activity. Precision vs. Accuracy. - PowerPoint PPT Presentation

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• Quantitative vs. QualitativeQuantitative observation:

Qualitative observation:

• Precision vs. AccuracyArchery Activity

• Precision vs. AccuracyWhich is more precise for measuring volume, a beaker or a graduated cylinder?

• Precision vs. AccuracyAccuracy: refers to the closeness of measurements to the correct or accepted value of the quantity measured.

Precision: refers to the closeness of a set of measurements of the same quantitiy made in the same way.

• Precision vs. AccuracyMeasured values that are accurate are close to the accepted value

Measured values that are precise are close to one another but not necessarily close to the accepted value

• Darts within small area = High precisionArea covered on bulls-eye = High accuracy

• Darts within small area = High precisionArea far from bulls-eye = Low accuracy

• Area far from bulls-eye = Low accuracyDarts within large area = Low precision

• Darts within large area = Low precisionArea centered around bulls-eye = High accuracy (on average)

• Unit conversionsCopy metric conversion from book

• Unit ConversionsPractice problems:750 km = __________m?283 m = __________km112 Mwatt = __________Kwatt?112 Mwatt = __________Gwatt

• Scientific Notation & Significant Figures

• Unit Estimation

• Scientific NotationUsed to make numbers more usable1,000,000,000 = 1x1090.0000000001=1x10-10

• How do you figure this out?You move the decimal until you have only one digit in front of the decimal.If you move right, then the exponent will be NEGATIVE based on the number of places your decimal moved.If you move left, then the exponent will be POSITIVE based on the number of places your decimal moved.

• PracticeGive the following in scientific notation6,289,030,9870.0045006785.60987568.236540035.983400020.23476

• Practice6,289,030,987 =0.004500678 =5.60987 =568.2365400 =35.98340002 =0.23476 =Give the following inscientific notation

6.289030987x1094.500678x10-35.609875.682365400x1023.59834002x102.3476x10-1

• Going the other way1.3487x105 =4.9800456x104 =2.345x101 =5.6789x10-3 =3.591x10-1 =2.0080x10-2 =134,87049,800.45623.450.00567890.35910.020080

• Try For Yourself7.234x10-5=?8.234x103=?5.000x10-4=?9.99998x10-2=?8.555x106=?

• ANSWERS 7.234x10-5 = 0.000 072 34

8.234x103 = 8,234

5.000x10-4 = 0.000 500 0

9.99998x10-2 = 0.099 999 8

8.555x106 = 8,555,000

• Significant Digits - What is it?When we take measurements in science, we can only be sure of our numbers to a certain pointThe numbers we are sure of are called significant digits or significant figures (sig figs)

• Sig Figs - How do we use them?Two typesMeasuredYou actually measure and record your answer to a certain digitCalculatedYou use already measured numbers to compute an answer

• Measured Sig FigsQuestions you can answer:How long is your book?Measure it with a meterstick and read the length.What is the mass of an orange?Put it on a scale and read the mass.How much milk is in the carton?Pour the milk into a graduated cylinder and read the volume.

• Calculated Sig FigsSometimes, youve collected the data and you need to calculate a final answerExample - you find the length, width and height of your book and you want to find the volume. You need to multiply the three numbers together to get an answer.

• Determining what countsSig Fig Rules!All non-zero numbers are significantExample 1,2,3,,9All zeros between non-zero numbers are significant Example1080.305All zeros before a written decimal are significantExample600.

• More RulesAll zeros following non-zero numbers, after a decimal are significantExample1.00 0.003470030These rules are to determine what counts when you are looking at a number.

• PracticeHow many sig figs are in the following numbers?2.3410.0004580560560.560.0003

• Answers2.341 has 4 sig figs

All the numbers are non-zero digits, so they all count!

• Answers0.0004580 has 4 sig figs

The three non-zero numbers 458 and the zero following this set

The first four zeros are place holders - they get the 4 into ten thousands place

• AnswersAnother way to think about 0.0004580 having four sig figs is to write it in scientific notation

0.0004580=4.580x10-4 When you write in scientific notation, you only write the sig figs before you write the x10whatever

So here you see that you wrote the 4, 5, 8, and 0. Those are the sig figs!

• Answers560 has 2 sig figs

This one is tricky. Notice that there is no decimal, so the zero is just a place holder to get the 6 into the tens spot.

• Answers560. Has 3 sig figs.

This time the zero counts because the decimal means it was actually measured.

• Answers560.0003 has 7 sig figs

All zeros are between non-zero digits, so they are all significant.

• How do you know when to stop?When youre measuring, you know when to stop based on your equipment.If your equipment reads to the tens, then you can guess up to one more place. You can read to the onesLets look at it.

• Multi step calculationsKeep One Extra Digit in Intermediate Answers When doing multi-step calculations, keep at least one more significant digit in intermediate results than needed in your final answer. For instance, if a final answer requires two significant digits, then carry at least three significant digits in calculations. If you round-off all your intermediate answers to only two digits, you are discarding the information contained in the third digit, and as a result the second digit in your final answer might be incorrect. (This phenomenon is known as "round-off error.")

• 2 Greatest Sins in Sig FigsWriting more digits in an answer (intermediate or final) than justified by the number of digits in the data.Rounding-off, say, to two digits in an intermediate answer, and then writing three digits in the final answer.

• Calculations - The rules!!!Addition/SubtractionYour answer should have the same number of decimal places as the number with the least number of decimal placesMultiplication/DivisionYour answer should have the same number of sig figs as the number with the least number of sig figsAlways follow the order of operations!

• Practice2.786 + 3.5 = 0.0004 x 3001 = 65 + 45.32 x 90 =45.6 - 34.23 =900.3/30.2450 =

• Percent error determines how accurate an experimental value is compared quantitatively with the correct or accepted value.

Percent error: calculated by subtracting the experimental value from the accepted value, dividing the difference by the accepted value, and then multiplying by 100Percent Error

• Percent ErrorPercent error = Valueaccepted Valueexperimental x 100 Valueaccepted

Percent error can have a positive or negative value

• Percent ErrorA student measures the mass and volume of a substance and calculates its density as 1.40 g/mL. The correct, or accepted value of the density is 1.36 g/mL. What is the percent error of the students measurement?

= 1.36g/mL 1.40 g/mL x 100 = -2.9% 1.36 g/mL

• Percent ErrorWhat is your percent error from the lab when you found the density of water?

= 1.00g/mL g/mL x 100 = -2.9% 1.00 g/mLYour experimental value

• Percent Error pg. 45Two technicians independently measure the density of a new substance.

Technician A Records: 2.000, 1.999, 2.001 g/mLTechnician B Records: 2.5, 2.9, and 2.7 g/mL

The correct value is found to be: 2.701 g/mL.

Which Technician is more precise? Which is more accurate?AB

• Go Through Answers on Packet

• Directly ProportionalTwo quantities are directly proportional ifDividing one by the other gives a constant valuey/x = k k = constantYou can rearrange above equation by saying : y = kxIf one increasesthe other increases at the same rate (doubling one constant = doubles the othr2y/2x = k (constant)

• Directly ProportionalAll directly proportional relationships produce linear graphs that pass through the origin

• Inverse ProportionsTwo quantities are inversely proportional ifTheir product is constantxy = kk = constantThe greater the speed = less time to travel a given distanceDouble speed (2x) = required timeHalving the speed () = 2 times the time

• Inverse Proportional

• How Sweet It IsChemistry Lab

• How Sweet It Is LabBenedicts Solution Water Bath Test:Results:Beverages should have tested positive if they had a sugar sweetenerBeverages should test negative if they had an artificial sweetener

• How Sweet It Is LabWhat beverages tested positive?What beverages tested negative?

Evaluate against labels on Sodas

• How Sweet It Is LabWhat did you notice about the densities of the solutions?

Which ones had artificial sweeteners? Densities less than one?

Which ones had natural sugar sweeteners? Densities more than one?

• How Sweet It Is LabAnalysis Questions1. Evaluate the results against the labels on the soda? Record actual sweeteners on a table in your lab write-up.