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**Scientific measurement**

Chapter 3 Scientific measurement

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**Types of measurement Quantitative- (quantity) use numbers to describe**

Qualitative- (quality) use description without numbers 4 meters extra large Hot 100ºC Quantitative Qualitative Qualitative Quantitative

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**Which do you Think Scientists would prefer**

Quantitative- easy check Easy to agree upon, no personal bias The measuring instrument limits how good the measurement is

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**How good are the measurements?**

Scientists use two word to describe how good the measurements are Accuracy- how close the measurement is to the actual value Precision- how well can the measurement be repeated

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Differences Accuracy can be true of an individual measurement or the average of several Precision requires several measurements before anything can be said about it examples

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**Let’s use a golf anaolgy**

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Accurate? No Precise? Yes

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Accurate? Yes Precise? Yes

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Precise? No Accurate? NO

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Accurate? Yes Precise? We cant say!

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**Reporting Error in Experiment**

A measurement of how accurate an experimental value is (Equation) Experimental Value – Accepted Value Experimental Value is what you get in the lab accepted value is the true or “real” value Answer may be positive or negative

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**| experimental – accepted value | x 100**

Reporting Error in Experiment % Error = | experimental – accepted value | x 100 accepted value OR | error| x 100 Answer is always positive

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Example: A student performs an experiment and recovers 10.50g of NaCl product. The amount they should of collected was 12.22g on NaCl. Calculate Error Error = g g = g Calculate % Error % Error = | -1.72g | x 100 12.22g = % error

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**Convert to Scientific Notation And Vise Versa**

Example: 2.5x10-4 (___) is the coefficient and ( ___) is the power of ten 2.5 -4 Convert to Scientific Notation And Vise Versa = ____________ 3.44 x = ____________ 2.16 x 103 = ____________ = ____________ 5.5 x 106 0.0344 2160 1.75 x 10-3

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**Multiplying and Dividing Exponents using a calculator**

(3.0 x 105) x (3.0 x 10-3) = _________________ (2.75 x 108) x (9.0 x 108) = ________________ (5.50 x 10-2) x (1.89 x 10-23) = ____________ (8.0 x 108) / (4.0 x 10-2) = ________________ 9.00 x 102 2.475 x 1017 1.04 x 10-24 2.0 x 1010

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**Adding and Subtracting Exponents using a calculator**

7.5 x x 109 = __________________ 5.5 x x 10-5 = _________________ 5.498 x 10-2

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**Significant figures (sig figs)**

How many numbers mean anything When we measure something, we can (and do) always estimate between the smallest marks. 4.5 inches 2 1 3 4 5

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**Significant figures (sig figs)**

Scientist always understand that the last number measured is actually an estimate 4.56 inches 1 2 3 4 5

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Sig Figs What is the smallest mark on the ruler that measures cm? 142 cm? 140 cm? Here there’s a problem does the zero count or not? They needed a set of rules to decide which zeroes count. All other numbers do count Tenths place Ones place Yikes!

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Which zeros count? Those at the end of a number before the decimal point don’t count 12400 If the number is smaller than one, zeroes before the first number don’t count 0.045 = 3 sig figs = 2 sig figs

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**Which zeros count? Zeros between other sig figs do. 1002**

zeroes at the end of a number after the decimal point do count If they are holding places, they don’t. If they are measured (or estimated) they do = 4 sig figs = 6 sig figs

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**Sig Figs Only measurements have sig figs. Counted numbers are exact**

A dozen is exactly 12 A a piece of paper is measured 11 inches tall. Being able to locate, and count significant figures is an important skill.

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**Sig figs. How many sig figs in the following measurements? 458 g**

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**Sig Figs. 405.0 g 4050 g 0.450 g 4050.05 g 0.0500060 g = 4 sig figs**

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**Question 50 is only 1 significant figure**

if it really has two, how can I write it? A zero at the end only counts after the decimal place. Scientific notation 5.0 x 101 now the zero counts. 50.0 = 3 sig figs

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**Adding and subtracting with sig figs**

The last sig fig in a measurement is an estimate. Your answer when you add or subtract can not be better than your worst estimate. have to round it to the least place of the measurement in the problem

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For example 27.93 6.4 + First line up the decimal places 27.93 6.4 + 27.93 6.4 Find the estimated numbers in the problem Then do the adding 34.33 This answer must be rounded to the tenths place

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**Rounding rules look at the number behind the one you’re rounding.**

If it is 0 to 4 don’t change it If it is 5 to 9 make it one bigger round to four sig figs to three sig figs to two sig figs to one sig fig = 45.46 = 45.5 = 45 = 50

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Practice = = 11.7 6.0 x x 103 6.0 x x 10-3 = = 615 = = 2.118 = 3198 = 3.2 x 103 = 2.12 = 2.1 = = 6.2 = 374 = = 5.6 x 10-2

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**Multiplication and Division**

Rule is simpler Same number of sig figs in the answer as the least in the question 3.6 x 653 2350.8 3.6 has 2 s.f. 653 has 3 s.f. answer can only have 2 s.f. 2400

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**Multiplication and Division**

practice 4.5 / 6.245 4.5 x 6.245 x .043 3.876 / 1983 16547 / 714 = = 0.72 = = 28 = = 0.42 = = = = 23.2

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**The Metric System Easier to use because it is …… a decimal system**

Every conversion is by some power of …. 10. A metric unit has two parts A prefix and a base unit. prefix tells you how many times to divide or multiply by 10.

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**Base Units Length - meter more than a yard - m**

Mass - grams - a bout a raisin - g Time - second - s Temperature - Kelvin or ºCelsius K or C Energy - Joules- J Volume - Liter - half f a two liter bottle- L Amount of substance - mole - mol

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**Prefixes Kilo K 1000 times Hecto H 100 times Deka D 10 times**

deci d 1/10 centi c 1/100 milli m 1/1000 kilometer - about 0.6 miles centimeter - less than half an inch millimeter - the width of a paper clip wire

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Converting K H D d c m King Henry Drinks (basically) delicious chocolate milk how far you have to move on this chart, tells you how far, and which direction to move the decimal place. The box is the base unit, meters, Liters, grams, etc.

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**k h D d c m Conversions 5 6 Change 5.6 m to millimeters**

starts at the base unit and move three to the right. move the decimal point three to the right 5 6

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**k h D d c m Conversions convert 25 mg to grams convert 0.45 km to mm**

convert 35 mL to liters It works because the math works, we are dividing or multiplying by 10 the correct number of times (homework) = g = 450,000 mm = L

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**Volume calculated by multiplying L x W x H**

Liter the volume of a cube 1 dm (10 cm) on a side so 1 L = 10 cm x 10 cm x 10 cm or 1 L = 1000 cm3 1/1000 L = 1 cm3 Which means 1 mL = 1 cm3

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**Volume 1 L about 1/4 of a gallon - a quart**

1 mL is about 20 drops of water or 1 sugar cube

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**Mass weight is a force, Mass is the amount of matter.**

1gram is defined as the mass of 1 cm3 of water at 4 ºC. 1 ml of water = 1 g 1000 g = 1000 cm3 of water 1 kg = 1 L of water

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**Mass 1 kg = 2.5 lbs 1 g = 1 paper clip**

1 mg = 10 grains of salt or 2 drops of water.

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**Density how heavy something is for its size**

the ratio of mass to volume for a substance D = M / V M D V

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**Density is a Physical Property The density of an object remains**

_________ at _______ ________ Therefore it is possible to identify an unknown by figuring out its density. Story & Demo (king and his gold crown) constant constant temperature

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**What would happen to density if temperature decreased?**

As temperature decreases molecules ______ _____ And come closer together therefore making volume _________ The mass ______ ____ _______ Therefore the density would _______ Exception _____________________ Therefore Density decreases ICE FLOATS slow down decrease STAYS THE SAME INCREASE WATER, because it expands.

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Units for Density 1. Regularly shaped object in which a ruler is used. ______ 2. liquid, granular or powdered solid in which a graduated cylinder is used ______ 3. irregularly shaped object in which the water displacement method must be used _____ g/cm3 g/ml g/ml

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Sample Problem: What is the density of a sample of Copper with a mass of 50.25g and a volume of 6.95cm3? D = M/V D = 50.25g / 6.95 cm3 = = 7.23 cm3

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**Sample Problem 2. A piece of wood has a density of**

0.93 g/ml and a volume of 2.4 ml What is its mass? M M = D x V D V M = 0.93 g/ml x 2.4 ml = = 2.2 g

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**Problem Solving or Dimensional Analysis**

Identify the unknown What is the problem asking for List what is given and the equalities needed to solve the problem. Ex. 1 dozen = 12 Plan a solution Equations and steps to solve (conversion factors) Do the calculations Check your work: Estimate; is the answer reasonable UNITS All measurements need a NUMBER & A UNIT!!

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Dimensional Analysis Use the units (__________) to help analyze (______) the problem. Conversion Factors: Ratios of equal measurements. Numerator measurement = Denominator measurement Using conversion factors does not change the value of the measurement Examples; 1 ft = _____ (_________) 1 ft__ or in (_____________ __________) 12 in ft dimensions solve 12 in equality Conversion factors

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What you are being asked to solve for in the problem will determine which conversion factors need to be used. Common Equalities and their conversion factors: 1 lb = _____oz 1 mi = ______ft 1 yr = ______days 1 day = ____hrs 1 hr = ____min 1 min = ____sec 16 5280 365 24 60 60

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**Sample Problems using Conversion Factors:**

How many inches are in 12 miles? Equalities: 1 mi = 5280 ft 1 ft = 12 in 12miles X X = sig figs = 760,000 inches 760,320 inches 12 in 1 ft 5280 ft 1 mi

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**2. How many seconds old is a 17 year old?**

Equalities: 1 yr = 365 days; 1 day = 24 hrs; hr = 60 min; 1 min = 60 sec 17 yrs X X X X = 536,112,000 sec Sig figs = 540,000,000 sec 365 day 1 yr 24 hrs 1 day 60 min 1 hr 60 sec 1 min

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**3. How many cups of water are in 5.2 lbs of water?**

Equalities: 1 lb = 16 oz; 8 oz = 1 cup 5.2 lbs X X = = 10.4 cups Sig figs = 1.0 x 101 cups 83.2 cup 8 16 oz 1 lb 1 cup 8 oz

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**Equalities: 1 g = 1000 mg; 1 L = 1000 ml X X = 13.6 g 1 ml 1000 mg 1 g **

3. If the density of Mercury (Hg) at 20°C is 13.6 g/ml. What is it’s density in mg/L? Equalities: 1 g = 1000 mg; 1 L = 1000 ml X X = 13.6 g 1 ml 1000 mg 1 g 1000 ml 1 L 13,600,000 mg/L 13.6 x 107 mg/L

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