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**Chapter 3 Scientific Measurement**

Hingham High School Mr. Clune Full screen view – click screen in lower right corner (Internet Explorer 4.0 & higher)

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**Measurements Qualitative measurements - words**

Quantitative measurements – involves numbers (quantities) Depends on reliability of instrument Depends on care with which it is read Scientific Notation Coefficient raised to power of 10

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Scientific Notation Multiplication Multiply the coefficients, add the exponents 4 + 7 = 11 (2 X 104) X (3 X 107) 2 X 3 = 6 6 X 1011

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**2 X 104 8 X 109 9 - 5 = 4 4 X 105 8 4 = 2 Scientific Notation Division**

Divide the coefficients, subtract the denominator exponent from numerator exponent 8 X 109 4 X 105 9 - 5 = 4 8 4 = 2 2 X 104

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Scientific Notation Before adding or subtracting in scientific notation, the exponents must be the same Calculators will take care of this

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Scientific Notation Addition Line up decimal; add as usual the coefficients; exponent stays the same (25 X 104) + (3.0 X 106) (25 X 104) + (300. X 104) (325 X 104)

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Scientific Notation Subtraction Line up decimal; subtract coefficients as usual; exponent remains the same (25 X 104) - (150. X 103) (25 X 104) - (15.0 X 104) (10 X 104)

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**Measurements and Their Uncertainty**

Need to make reliable measurements in the lab Accuracy – how close a measurement is to the true value Precision – how close the measurements are to each other (reproducibility)

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Bad Accuracy And Good Precision

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Bad Accuracy And Bad Precision

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Good Accuracy And Bad Precision

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Good Accuracy And Good Precision

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**Measurements and Their Uncertainty**

Accepted value – correct value based on reliable references Experimental value – the value measured in the lab Error – the difference between the accepted and experimental values

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**Measurements and Their Uncertainty**

Error = accepted – experimental Can be positive or negative Percent error = the absolute value of the error divided by the accepted value, times 100% | error | accepted value % error = x 100%

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**% Error = 2% % Error Example Accepted Value = 100g**

Experimental Value = 102g % Error = | Acc – Exp | Acc X 100% % Error = | 100 – 102 | 100 X 100% % Error = 2%

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Significant Figures Significant figures in a measurement include all of the digits that are known, plus a last digit that is estimated. Note Fig. 3.4, page 66 Rules for counting sig. figs.? Zeroes are the problem East Coast / West Coast method

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**2. Zeros between nonzero digits 10003 mL (5) 0.2005 ms (4)**

Significant Figures 1. All nonzero digits 457 cm (3) 0.35 g (2) 2. Zeros between nonzero digits 10003 mL (5) ms (4)

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**3. Zeros to the left of the first nonzero digits in a number are **

Significant Figures 3. Zeros to the left of the first nonzero digits in a number are not significant; they merely indicate the position of the decimal point. 0.02 g (1) cm (2)

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**4. When a number ends in zeros that are to the right of the decimal **

Significant Figures 4. When a number ends in zeros that are to the right of the decimal point, they are significant. g (3) 3.0 cm (2)

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**5. When a number ends in zeros that are not to the right of a decimal **

Significant Figures 5. When a number ends in zeros that are not to the right of a decimal point, the zeros are not necessarily significant. 130 cm (2) 10,300 g (3)

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**Counting Significant Fig.**

Sample 3-1, page 69 Rounding Decide how many sig. figs. Needed Round, counting from the left Less than 5? Drop it. 5 or greater? Increase by 1 Sample 3-2, page 70

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**Sig. fig. calculations Addition and Subtraction**

The answer should be rounded to the same number of decimal places as the least number in the problem Sample 3-3, page 60

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**{ 26.46 + 4.123 30.583 Sig. fig. calculations**

this has the least digits to the right of the decimal point (2) 26.46 30.583 Rounds off to

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**Sig. Fig. calculations Multiplication and Division**

Round the answer to the same number of significant figures as the least number in the measurement Sample 3-4, page 61

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**{ 2.61 x1.2 3.132 Sig. Fig. calculations**

this has the smaller number of significant figures (2) 2.61 x1.2 3.132 Rounds off to 3.1

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**International System of Units**

The number is only part of the answer; it also need UNITS Depends upon units that serve as a reference standard The standards of measurement used in science are those of the Metric System

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**International System of Units**

Metric system is now revised as the International System of Units (SI), as of 1960 Simplicity and based on 10 or multiples of 10 7 base units Table 3.1, page 63

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**International System of Units**

Sometimes, non-SI units are used Liter, Celsius, calorie Some are derived units Made by joining other units Speed (miles/hour) Density (grams/mL)

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**Common prefixes Kilo (k) = 1000 (one thousand)**

Deci (d) = 1/10 (one tenth) Centi (c) = 1/100 (one hundredth) Milli (m) = 1/1000 (one thousandth) Micro () = (one millionth) Nano (n) = (one billionth)

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**Length In SI, the basic unit of length is the meter (m)**

Length is the distance between two objects – measured with ruler We make use of prefixes for units larger or smaller

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**Volume The space occupied by any sample of matter**

Calculated for a solid by multiplying the length x width x height SI unit = cubic meter (m3) Everyday unit = Liter (L), which is non-SI

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**Volume Measuring Instruments**

Graduated cylinders Pipet Buret Volumetric Flask Syringe

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Volume changes? Volume of any solid, liquid, or gas will change with temperature Much more prominent for GASES Therefore, measuring instruments are calibrated for a specific temperature, usually 20 oC, which is about normal room temperature

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Volume – (m3)

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Volume (L) 1dm3=1L

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Volume

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Volume (mL) 1cm3=1mL 1cm

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Volume – Liter (L) 1L=1.05qt

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**Units of Mass Mass is a measure of the quantity of matter**

Weight is a force that measures the pull by gravity- it changes with location Mass is constant, regardless of location

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Mass – KiloGram (kg) 1kg=2.2lbs

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Working with Mass The SI unit of mass is the kilogram (kg), even though a more convenient unit is the gram Measuring instrument is the balance scale

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**Temperature Kelvin (K) Based on Absolute Zero Celsius (°C)**

Water freezes at 0°C (273K) Water boils at 100°C (373K)

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Temperature Water freezes at 0°C (273K) Water boils at 100°C (373K)

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BP of H2O FP of H2O Temperature (°C, K) Absolute Zero

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**°C = K - 273 345K = ? °C °C = 345K – 273 72°C Temperature**

Convert Kelvin to Celsius °C = K - 273 345K = ? °C °C = 345K – 273 72°C

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**K = °C + 273 20 °C = ? K K= 20°C – 273 293K Temperature**

Convert Celsius to Kelvin K = °C + 273 20 °C = ? K K= 20°C – 273 293K

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Time – Seconds (s)

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**The capacity to do work or produce heat**

Energy The capacity to do work or produce heat Joule (J) Calorie (Cal) Energy needed to raise 1g of 1 °C

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Homework Practice Problem 16 Page 78 Section Assessment Questions: 18-27(odd) Page 79 Due: 10/7/04

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Dimensional Analysis Converting Units

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Conversion Problems 50cm = ?m 100cm = 1m 1m 100cm 100cm 1m

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Conversion Problems 1m 100cm 50cm X = 0.50 m

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Conversion Problems 0.045kg =? g 1000g = 1kg 1kg 1000g 1000g 1kg

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Conversion Problems 1000g 1kg 0.045kg X = 45g

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Conversion Problems 2.5hr =? s 60min = 1hr 1hr 60min 60min 1hr

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Conversion Problems 2.5hr =? s 60s = 1min 1min 60s 60s 1min

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Conversion Problems 60s min 60min 1hr 2.5hr X X = 9000s

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Homework Practice Problem 35-37 Pages Due: 10/7/04

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**Density Which is heavier- lead or feathers?**

It depends upon the amount of the material A truckload of feathers is heavier than a small pellet of lead The relationship here is between mass and volume- called Density

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**The formula for density is: mass volume **

Common units are g/mL, or possibly g/cm3, (or g/L for gas) Density is a physical property, and does not depend upon sample size Density =

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**Things related to density**

What happens when corn oil and water are mixed? Why? Will lead float?

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**Density and Temperature**

What happens to density as the temperature increases? Mass remains the same Most substances increase in volume as temperature increases Thus, density generally decreases as the temperature increases

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**Density and water Sample 3-10,11, page 91-92**

Water is an important exception Over certain temperatures, the volume of water increases as the temperature decreases Does ice float in liquid water? Why? Sample 3-10,11, page 91-92

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Specific Gravity A comparison of the density of an object to a reference standard (which is usually water) at the same temperature Water density at 4 oC = 1 g/cm3 1g of H2O = 1mL = 1 g/cm3

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**Formula Note there are no units left, since they cancel each other**

D of substance (g/cm3) D of water (g/cm3) Note there are no units left, since they cancel each other Measured with a hydrometer – p.72 Uses? Tests urine, antifreeze, battery Specific gravity =

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**Temperature Heat moves from warmer object to the cooler object**

Glass of iced tea gets colder? Remember that most substances expand with a temp. increase? Basis for thermometers

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**Temperature scales Celsius scale- named after a Swedish astronomer**

Uses the freezing point(0 oC) and boiling point (100 oC) of water as references Divided into 100 equal intervals, or degrees Celsius

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**Temperature scales Kelvin scale (or absolute scale)**

Named after Lord Kelvin K = oC + 273 A change of one degree Kelvin is the same as a change of one degree Celsius No degree sign is used

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**Temperature scales Water freezes at 273 K Water boils at 373 K**

0 K is called absolute zero, and equals –273 oC Fig. 3.19, page 75 Sample 3-6, page 75

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