Significant Figures

Scientific MeasurementObjective: To understand the importance of measurements in ChemistryMeasurementsQuality with both number and a unitHistory4000Bc- Egyptians used knotted cords- kite1700Bc- Babylonians used cubits-elbow to finger tip500Bc- Phoenicians used Zebo-finger width300Bc- Romans used a soldiers Boot as a unit-equal to width of 12 fingers900AD- due to trade a standard unit of measurement was needed-Fathom- finger tip to finger tip (Vikings)1500AD- Tudor rules create a furlong= 220cydQueen Elizabeth I- Roman mile= 5280 ft= 8 furlongs1790AD- Metric system was proposed- base 10 system, meter basic uni1 1875AD- Renamed International System of Units (SI)

Scientific NotationSince we deal w/ numbers very small and large5.75 x 104

CoefficientBase Exponent

1. The coefficient must be greater than or equal to 1 and less than 10.2. The base must be 10.3. The exponent must show the number of decimal places that the decimal needs to be moved to change the number to standard notation. A negative exponent means that the decimal is moved to the left when changing to standard notation. Positive to the right

PracticePut following #s into standard notation:3.45 x 1058.009 x 10-62.00 x 103

Put the following #s into scientific notation: 0.0004506 3400000000 234003

Accuracy/PrecisionAccuracy- a measure of how close a measurement comes to the actual or true value of whatever is measuredPrecision- a measure of how close a series of measurements are to one anotherHow do we test accuracy??How to we test precision??

file://localhost/Users/ericfocht/Desktop/chem Resources/chtr21.pdfErrorAccepted Value-correct value based on reference sourcesExperimental Value- measured in the lab

Error = EV-AV

Percent Error = error x 100% Accepted valueWhat are Significant Figures?All the digits that can be known precisely in a measurement, plus a last estimated digit.Guess Digits

Reading Grad. Cylinder

Why do we use Sig Figs?We need to know how precise (how many decimal places we can record) our measurements are.Our calculations can not be more precise than the instruments we used to measure them

When working in the chemistry lab it is important to understand where your measurement came fromSignificant Figure Rules!1. Every non-zero digit in a reported measurements is assumed to be significant27.3 m = 3 significant figures 0.734m = 3 Sig Figs

2. Zeros appearing between nonzero digits are significant 2703 m = 4 Sig Figs70003 m = 5 Sig Figs

3. Left most zeros appearing infront of nonzero digits are not significant, they act as placeholders0.0056 = 2 Sig Figs0.4202 = 4 Sig Figs

Cont.4. Zeros at the end of the number and to the right of the decimal point are always significant.43.00 = 4 Sig Figs1.0110= 5 Sig Figs

5. Zeros at the rightmost end of a number but to the left of the decimal are not significant, they act as place holders 21,800 = 3 Sig Figs 7,000 = 1 Sig fig

Atlantic/Pacific MethodAnother way of looking at it.

Pacific Side Atlantic Side(Decimal is Present) (Decimal is Absent) NUMBER

If the decimal is Present you come in from the left hand side and count every digit as significant starting with the first nonzero digit1.002 = 4 Sig Figs108.008 = 6 Sig FigsAtlantic/Pacific Cont.If the decimal is Absent, then you come in from the right hand side and count every digit as significant starting with the first nonzero digit1239 = 4 Sig Figs12000 = 2 Sig Figs300 = 1 Sig FigPracticeHow many Sig Figs in following #s6075.66030003.0020.0050.00670.006703.40 x 104Significant Figures when Adding or SubtractingThinkYou are only as strong as your weakest link

Your answer can only have the same number of decimal places as the number with the least amount of decimal places3.0001+ 2.33 Weakest link 5.3301 Since our weakest link only has 2 decimal places our answer can only have 2 decimal places.so round the answer to 5.33

Significant figures when multiplying or dividingAgain..think, Your only as strong as your weakest link

Your answer needs to have the same amount of significant figures as the number with the least amount of sig figs3.444 x 2.04 = 7.02576 Since our weakest link only has 3 sig figs, our answer can only have 3 sig figs 7.03Weakest LinkFinal Sig Fig PracticeCalculate:234.0g + 34.00g =34.555g 18.9g =2.33m x 400m =25.000 / 4.09 =AnswersCalculate:234.0g + 34.00g = 268.0 g34.555g 18.9g = 15.7 g2.33m x 400m = 900 m25.000m / 4.09m = 6.11 m

SI Unitsthe ones we are worried aboutLength- meter (m)Mass- kilogram (kg)Temperature- kelvin (K)Time- second (s)Amount of Substance- mole (mol)Extra Unit/baseVolume= LiterEnergyCapacity to do work or to produce heatJoule and calorie (quantity of heat that raises the temp of 1 g of pure water by 1 C)1 J = 0.2390 cal1 cal = 4.184 JMetric SystemDecimal system based on powers of 10See worksheetConversions:Start with given value; move decimal one spot to left or right for each prefix

Conversions Cont.Use conversion factor a ratio of equivalent measurementsWhen a measurement is multiplied by a conversion factor, the number may change, but the value stays the same

23 km x 106 mm= 2.3 x 107 mm 1 km

conversion factorConversions234 m ____ cm23 km ____ mm0.0023 nm ____ Mm23 hm ____ dm100 g ____ mg 78 ml ____ kl45 ml ____ cl 345 g ____ kg More practice w/ conversion factors24 Tm _____ pm6789.0 nm _____ km0.0038 Gm _____ m230 cm _____ Mm0.000000780 Em _____ fm Dimensional AnalysisWay at analyze and solve problems using the units, or dimensions, of the measurementsConverting between units

How many hours are in 1 century?

1 century x 100 yrs x 365 d x 24 hr = 876000 hours 1 cent. 1 yr 1 d

Known conversion factor

25You try!!!Mr. Focht is throwing a pizza party because all of his students studied and got As on their chapter 3 test. However, Mr. Focht is poor from student loan payments. If a large pizza has 8 slices, how many students can Mr. Focht feed with 10 pizzas. (2 slice per student)

10 pizza. x 8 slice x 1 student = 40 students1 pizza2 slicesLittle more difficultYour car's gas tank holds 18.6 gallons and is one quarter full. Your car gets 16 miles/gal. You see a sign saying, "Next gas 73 miles." Your often-wrong brother, who is driving, is sure you'll make it without running out of gas. Figure out if you can make it to the gas station.

18.6 gallon x 1 tank x 16 miles = 74.4 miles1 tank 4 quarter- tank gallon quarter tankMore PracticeIf you are going 50 miles per hour, how many feet per second are you traveling?

50.0 miles x 5280 ft x 1 hour x 1 min = 73.3 ft hour 1 mile 60 min 60 sec sec

Warm UpMy car gets 33 miles to the gallon. How many miles can I travel if my car is currently holding 5.7 gallons of fuel.

You are driving down the road at 55 mph. How many feet will you travel in the next 3o min?DensityRatio of the mass of an object to its volumeD = m/vHow do we measure mass?How do we measure volume?Intensive propertyAs Temp. increases, density usually decreasesException???Density of WaterObtain a 100 ml graduated cylinderMass the graduated cylinderAdd 10.0 ml of waterMass the cylinderAdd 30.0 ml of waterMass the cylinderAdd 50.0 ml of waterMass the cylinderPlat your data on a graph using the graph paper providedAdd line of best fit