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Ch 3 Scientific Measurement. Accuracy refers to the closeness of measurements to the correct or...

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Ch 3 Scientific MeasurementAccuracy 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 quantity made in the same way.

Percent Error tells you how far away you are from the accepted value

Percent error = observed accepted x 100 accepted value*note: observed value is also the experimental value

Example: Calculate the percent error of a measurement of .225 cm if the correct value is .229 cm.Ans. -1.75%Ex #2/ A student measures three trials of density of gold: 19.2 g/mL, 18.9 g/mL, and 19.0 g/mL. If golds actual density is 19.3 g/mL, what is the percent error?Ans. -1.55%

Error (or uncertainty) exists in any measurement. The amount of uncertainty is determined by finding half of the smallest increment in the measure.Ex/ for the 10 mL graduated cylinder the uncertainty of each measurement is + or - .05 mL since the smallest increment is .1 mLSignificant Figures in a measurement consists of all the digits known with certainty plus one final digit which is uncertain or estimated.

Rules of Significant Numbers and Zeros1. All non-zero numbers in a measured quantity are significant.Ex: 2.34 m= 3 significant figures2. Zeros appearing between non-zero digits are significant.Ex: 2.04 km = 3 SFs 24.005 m= 5 SFs

3. Zeros appearing in front of non-zero digits are not significant.Ex: 0.002345 m= 4 SFs 4. Zeros at the end of a number and to the right of the decimal are significant.Ex: 23.400 kg = 5 SFs0.0023400 kg = 5 SFs

5. Zeros at the end of a number and to the left of the decimal may or may not be significant. It depends on whether it was measured or if it is a placeholder. NOTE: If there is a decimal after the zeros, then they are significantEx: 1000. m = 4 SFsNOTE: If there is no decimal after the zeros, then they are not significant.Ex: 1000 m = 1 SF

How many significant figures are in each of the following measurements?1) 76.23 gAns. 4 SFs2) 6,330. mAns. 4 SFs3) 6330 mAns. 3 SFs4) .00225 mgAns. 3 SFs5) .020030 mgAns 5 SFsRules for Rounding SFsIf the digit following the last digit to be retained is: *examples rounded to 3 SFs 1. Greater than 5 : increase by 1EX/ 55.49 g = 55.5 g2. Less than 5 : Stay the sameEX/ 18.62 g = 18.6 g3. 5, followed by a nonzero digit: increase by 1EX/ 12.257 g = 12.3 g

Rules rounding continuedIf the digit following the last digit to be retained is:4.) 5, not followed by nonzero digit, and preceded by an odd digit :increase by 1 round upEx/ 4.635 g = 4.64 g ( 3 sig figs)

5.) 5, not followed by nonzero digit, preceded by an EVEN digit: stays the sameEx/ 78.65 mL = 78.6 mL Rules for Calculations with SFsAdding or Subtracting Significant Figures

When adding or subtracting decimals, the answer must have the same number of digits to the right of the decimal point as there are in the measurement having the fewest digits to the right.Ex: 5.44 m 2 decimal places - 2.6103 m 4 decimal places 2.8297 m final answer is 2.83 m Multiplying or Dividing Significant FiguresWhen multiplying or dividing with SFs, the answer can have no more SFs than are in the measurement with the fewest number of SFs.Ex: m = DV 2.4 g/mL x 15.82 mL = 37.968 g Final answer is 38 g with 2 SFs

Scientific Notation are the writing of very large or small numbers in the form M x 10n, where M is a number greater than or equal to one, but less than 10, and n is a whole number.Ex: 5 200 000 000 g = 5.2 x 109 gEx:0.000 023 g = 2.3 x 10-5 g

Practice: copy the question & answer 4.52 x 104g (4.5 x 104cm)(2.7 x 103cm)+2.7 x 103g

4.52 x 104g / 2.7 x 103mLCheck your answers 4.52 x 104g (4.5 x 104cm)(2.7 x 103cm) =+2.7 x 103g 1.2 x 108 cm2 4.8 x 104 g

4.52 x 104g / 2.7 x 103mL = 1.7 x 101 g/mL Units of MeasurementInternational System of UnitsCalled the SI system (or Metric System)established in France 1790 (Systeme Internationale dUnites)1960 revised for International scientific agreement.SI system is simple because it is based on factors of 107 Base UnitsQuantity MeasuredUnit abbreviationlength meter mmass gram gtime second selectric current ampere Atemperature Kelvin Kamount of substance mole molluminous intensity (light) candela cd

SI Prefixesk kilo 1000xs (1 km = 1000 m)h hecto 100xs (1 hm = 100 m)dadeka 10xs (1 dam = 10 m)Base Units (m, g, s, mol, cd, A, K)d deci 1/10 (10 dm = 1 m)c centi 1/100 (100 cm = 1 m)mmilli 1/1000 (1000 mm = 1 m)Converting one unit to anotherTwo ways:1. Use a conversion factor that expresses the relationship between the units.Ex/ 1 m = 100 cm Two conversion factors: __1 m__ or 100 cm__ 100 cm 1 mHow many meters in 550 cm?550 cm x __1 m____ = 5.5 m 100 cm

2. Convert units by shifting the decimal place.King Henrys daughter begins dance class Monday.550 cm = __________m6.77 hg = __________ dg

k h da B d c m

Start with given units and jump to desired units. Move decimal same direction as number of jumps.Metric Conversions practice:Copy this practice and turn in when completed:1)40.0 m= _________cm2) 40.0 m= __________km3) 32.41 m= _________dam4) 32.41 m= __________hm5) .005 m= ___________mm6) .005 km= ___________m7) .005 km= __________dm8) .005 mm= __________dam9) 16 km=___________dam10) 16 km ___________cmMetric Conversions practice: Key40.0 m= __4.00 x 103__cm (4000 cm)40.0 m= ___.0400____km32.41 m= ___3.241__dam32.41 m= ___.3241___hm.005 m= ______5____mm.005 km= _____5_____m.005 km= ___5 x 101__dm (50 dm).005 mm= _5 x 10-7___dam (.0000005)16 km=____1600___dam16 km _1600000 or 1.6 x 106_cmDerived Units:come from base units (multiplying or dividing base units)For example: Volume (mL) is considered a derived unit.Using water to fill a cube that is 1 cm on each side:Volume= l x w x hvol= 1 x 1 x 1= 1cm31 cm3= 1 mL in a graduated cylinder.1 L = 1000 mL = 1000 cm3

*The mass of 1 cm3 of water equals 1 gram as well.1 cm3= 1 mL= 1g


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