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Measurements Chapter 1

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Units of Measurement You are making a measurement when you Check you weight Read your watch Take your temperature Weigh a cantaloupe What kinds of measurements did you make today?

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Standards of Measurement When we measure, we use a measuring tool to compare some dimension of an object to a standard.

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Some Tools for Measurement

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Learning Check From the previous slide, state the tool (s) you would use to measure A. temperature ____________________ B. volume ____________________ ____________________ C. time____________________ D. weight ____________________

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Solution From the previous slide, state the tool (s) you would use to measure A. temperaturethermometer B. volume measuring cup, graduated cylinder C. timewatch D. weightscale

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Measurement in Chemistry In chemistry we do experiments measure quantities use numbers to report measurements

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Stating a Measurement In every measurement there is a Number followed by a Unit from measuring device

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Learning Check What is the unit of measurement in each of the following examples? A. The patients temperature is 102°F. B. The sack holds 5 lbs of potatoes. C. It is 8 miles from your house to school. D. The bottle holds 2 L of orange soda.

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Metric System (SI) n Is a decimal system based on 10 n Used in most of the world n Used by scientists and hospitals

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Units in the Metric System length meter m volumeliterL mass gram g temperatureCelsius °C

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Learning Check Identify the measurement in metric units. A. Johns height is 1) 1.5 yards2) 6 feet3) 2 meters B. The volume of saline in the IV bottle is 1) 1 liters2) 1 quart3) 2 pints C. The mass of a lemon is 1) 12 ounces 2) 145 grams3) 0.6 pounds

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Measurements Measured Numbers and Significant Figures

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Measured Numbers When you use a measuring tool to determine a quantity such as your height or weight, the numbers you obtain are called measured numbers.

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Reading a Meterstick. l I.... I 3....I.... I 4.. cm First digit (known)= 2 2.?? cm Second digit (known)= ? cm Third digit (estimated) between Length reported=2.75 cm or2.76 cm or2.77 cm

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Known + Estimated Digits Known digits 2 and 7 are 100% certain The third digit 6 is estimated (uncertain) In the reported length, all three digits (2.76 cm) are significant including the estimated one

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Learning Check. l I.... I 9....I.... I 10.. cm What is the length of the line? 1) 9.2 cm 2) 9.22 cm 3) 9.23 cm How your answer compare with your neighbors answer? Why or why not?

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Learning Check l I.... I 6....I.... I 7.. cm What is the length of the line? 1) 6.0 cm 2) 6.06 cm 3) 6.60 cm

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Zero as a Measured Number. l I.... I I.... I 5.. cm What is the length of the line? First digit 4.?? cm Second digit 4.5? cm Last (estimated) digit is 4.50 cm (not to the left or right of.5)

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Exact Numbers Obtained when you count objects 2 soccer balls 1 watch 4 pizzas Obtained from a defined relationship 1 foot = 12 inches 1 meters = 100 cm Not obtained with measuring tools

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Learning Check A. Exact numbers are obtained by 1. measuring 2. counting 3. definition B. Measured numbers are obtained by 1. measuring 2. counting 3. definition

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Learning Check Classify each of the following as an exact (1) or a measured (2) number. A.___Gold melts at 1064°C B.___1 yard = 3 feet C.___A red blood cell with diameter 6 x cm D.___There were 6 hats on the shelf E.___A can of soda contains 355 mL of soda

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Significant Figures in Measurement The numbers reported in a measurement are limited by the measuring tool Significant figures in a measurement include the known digits plus one estimated digit

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1.8 Any digit that is not zero is significant kg 4 significant figures Zeros between nonzero digits are significant 606 m 3 significant figures Zeros to the left of the first nonzero digit are not significant 0.08 L 1 significant figure If a number is greater than 1, then all zeros to the right of the decimal point are significant 2.0 mg 2 significant figures If a number is less than 1, then only the zeros that are at the end and in the middle of the number are significant g 3 significant figures Significant Figures Summary

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Counting Significant Figures Number of Significant Figures cm4 5.6 ft lb___ m___ Complete: All non-zero digits in a measured number are (significant or not significant).

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Leading Zeros Number of Significant Figures mm oz lb____ mL ____ Complete: Leading zeros in decimal numbers are (significant or not significant).

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Sandwiched Zeros Number of Significant Figures 50.8 mm min lb____ m ____ Complete: Zeros between nonzero numbers are (significant or not significant).

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Trailing Zeros Number of Significant Figures 25,000 in yr1 48,600 gal3 25,005,000 g ____ Complete: Trailing zeros in numbers without decimals are (significant or not significant) if they are serving as place holders.

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Learning Check A. Which answers contain 3 significant figures? 1) ) ) 4760 B. All the zeros are significant in 1) ) ) x 10 3 C. 534,675 rounded to 3 significant figures is 1) 535 2) 535,000 3) 5.35 x 10 5

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Learning Check In which set(s) do both measured numbers contain the same number of significant figures? 1) 22.0 and ) and 40 3) and 150,000

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State the number of significant figures in each of the following measured/calculated numbers: A m B L C g D m E. 2,080,000 bees Learning Check SF3

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Significant Numbers in Calculations A calculated answer cannot be more precise than the measuring tool. A calculated answer must match the least precise measurement. Significant figures are needed for final answers from 1) adding or subtracting 2) multiplying or dividing

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Adding and Subtracting The answer has the same number of decimal places as the measurement with the fewest decimal places one decimal place two decimal places answer 26.5 one decimal place E.g., = 31

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Learning Check In each calculation, round the answer to the correct number of significant figures. A = 1) ) ) 257 B = 1) ) ) 40.7

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Multiplying and Dividing Round (or add zeros) to the calculated answer until you have the same number of significant figures as the measurement with the fewest significant figures.

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Learning Check A X 4.2 = 1) 9 2) 9.2 3) B ÷ 0.07 = 1) ) 62 3) 60 C X = X ) 11.32) 11 3)

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Measurements Prefixes and Equalities

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Metric Prefixes Increase or decrease basic unit by 10 Form new units larger or smaller than the basic units Indicate a numerical value prefix=value 1 kilometer=1000 meters 1 kilogram=1000 grams

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Prefixes that Increase A Unit PrefixSymbolValue giga-G mega-M kilo-k1 000

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Prefixes that Decrease A Unit PrefixSymbolValue deci-d0.1 centi-c0.01 milli-m0.001 micro- (mu) nanon

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Learning Check Match 1) length 2) mass 3) volume ____ A. A bag of tomatoes is 4.6 kg. ____ B. A person is 2.0 m tall. ____ C. A medication contains 0.50 g Aspirin. ____ D. A bottle contains 1.5 L of water.

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Learning Check Select the unit you would use to measure A. Your height 1) millimeters2) meters 3) kilometers B. Your mass 1) milligrams2) grams 3) kilograms C. The distance between two cities 1) millimeters2) meters 3) kilometers D. The width of an artery 1) millimeters2) meters 3) kilometers

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Learning Check Indicate the prefix to use for 1. A mass that is 1000 times greater than 1 gram 1) kilo2) milli3) mega 2. A length that is 1/100 of 1 meter? 1) deci2) centi3) milli 3. A unit of time that is 1/1000 of a second. 1) nanosecond 2) microsecond 3)millisecond

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Equalities State the same measurement in two different units length 10.0 in cm

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Fundamental & Derived SI units and Metric Equalities 1m = 100 cm Length 1 km =1000 m 1m = 100 cm1m = 1000 mm 1 kg = 1000 g Mass 1 kg = 1000 g1 g = Volume 1 kL = 1000 L 1L = 100 cL 1L = 1000 mL Matter is anything that takes up space and has mass Fundamental SI Units (Derived SI units are derived from these base units):

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Volume – SI derived unit for volume is cubic meter (m 3 ) 1 cm 3 = (1 x m) 3 = 1 x m 3 1 dm 3 = (1 x m) 3 = 1 x m 3 1 L = 1000 mL = 1000 cm 3 = 1 dm 3 1 mL = 1 cm 3

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A m = 1 ___1) mm 2) km3) dm B g = 1 ___ 1) mg2) kg3) dg C. 0.1 L = 1 ___1) mL2) cL3) dL D m = 1 ___ 1) mm 2) cm3) dm Learning Check

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Give the value of the following units: A. 1 kg = ____ g 1) 10 g2) 100 g 3) 1000 g B. 1 mm = ____ m 1) m2) 0.01 m 3) 0.1 m Learning Check

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Some American Equalities 1 ft= inches 1 lb=16 oz 1 quart = pints 1 quart=4 cups Why are the quantities in each pair equal?

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Some Metric-American Equalities 1 in.=2.54 cm 1 qt=946 mL 1 L=1.06 qt 1 lb = 454 g 1 kg=2.20 lb Remember these for exams.

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Equalities given in a Problem Example 1 At the store, the price of one pound of red peppers is $2.39. Equality: 1 lb red peppers =$2.39 Example 2 At the gas station, one gallon of gas is $1.34. Equality: 1 gallon of gas=$1.34

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Accuracy – how close a measurement is to the true value Precision – how close a set of measurements are to each other accurate & precise but not accurate & not precise Accuracy vs. Precision

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Conversion Factors Fractions in which the numerator and denominator are quantities expressed in an equality between those units Example: 1 in. = 2.54 cm Factors: 1 in. and 2.54 cm 2.54 cm 1 in.

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Learning Check Write conversion factors that relate each of the following pairs of units: A. Liters and mL B. Hours and minutes D. Meters and kilometers

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Solution A. quarts and mL 1 L = 1000 mL 1 L and 1000 mL 1000 mL 1 L B. hours and minutes1 hr = 60 min 1 hr and 60 min 60 min 1 hr C. meters and kilometers 1 km = 1000 m 1 km and 1000 m 1000 m 1 km

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Measurements Problem Solving Using Conversion Factors

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Initial and Final Units 1. A person has a height of 2.0 meters. What is that height in inches? Initial unit = mFinal unit = _______ 2) Blood has a density of 1.05 g/mL. If a person lost 0.30 pints of blood at 18°C, how many ounces of blood would that be? Initial = pintsFinal unit = _______ inches ounces

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How many minutes are in 2.5 hours ? Initial unit 2.5 hr Conversion Final factor unit 2.5 hr x 60 min = 150 min 1 hr cancel Answer (2 SF)

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Learning Check A rattlesnake is 2.44 m long. How long is the snake in cm? 1) 2440 cm 2)244 cm 3)24.4 cm

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Solution A rattlesnake is 2.44 m long. How long is the snake in cm? 2)244 cm 2.44 m x 100 cm = 244 cm 1 m

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Learning Check How many seconds are in 1.4 days? Unit plan: days hr min seconds 1.4 days x 24 hr x ?? 1 day

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Solution CF2 Unit plan: days hr min seconds 2 SF Exact 1.4 day x 24 hr x 60 min x 60 sec 1 day 1 hr 1 min = 1.2 x 10 5 sec

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Unit Check What is wrong with the following setup? 1.4 day x 1 day x 60 min x 60 sec 24 hr 1 hr 1 min

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Unit Check 1.4 day x 1 day x 60 min x 60 sec 24 hr 1 hr 1 min Units = day 2 -sec/hr 2 Not the final unit needed

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Learning Check An adult human has 4650 mL of blood. How many gallons of blood is that? Unit plan: mL qt gallon Equalities:1 quart = 946 mL 1 gallon = 4 quarts Your Setup:

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Solution Unit plan: mL qt gallon Setup: 4650 mL x 1 qt x 1 gal = 1.23 gal 946 mL 4 qt 3 SF equality exact 3 SF

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Steps to Problem Solving Read problem Identify data Write down a unit plan from the initial unit to the desired unit Select conversion factors Change initial unit to desired unit Cancel units and check Do math on calculator Give an answer using correct significant figures

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Learning Check If the ski pole is 3.0 feet in length, how long is the ski pole in mm?

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Solution 3.0 ft x 12 in x 2.54 cm x 10 mm = 1 ft 1 in. 1 cm

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Learning Check If your pace on a treadmill is 65 meters per minute, how many seconds will it take for you to walk a distance of 8450 feet?

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Initial 8450 ft x 12 in. x 2.54 cm x 1 m 1 ft 1 in. 100 cm x 1 min x 60 sec = 2400 sec 65 m 1 min final (2 SF) Solution

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Measurements Density

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Density compares the mass of an object to its volume D = mass = g or g volume mL cm 3 Note: 1 mL = 1 cm 3

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Learning Check D1 Osmium is a very dense metal. What is its density in g/cm 3 if g of the metal occupies a volume of 2.22cm 3 ? 1) 2.25 g/cm 3 2)22.5 g/cm 3 3)111 g/cm 3

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Solution 2) Placing the mass and volume of the osmium metal into the density setup, we obtain D = mass = g = volume2.22 cm 3 = g/cm 3 = 22.5 g/cm 3

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Volume Displacement A solid displaces a matching volume of water when the solid is placed in water. 33 mL 25 mL

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Learning Check What is the density (g/cm 3 ) of 48 g of a metal if the metal raises the level of water in a graduated cylinder from 25 mL to 33 mL? 1) 0.2 g/ cm 3 2) 6 g/m 3 3) 252 g/cm 3 33 mL 25 mL

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Solution 2) 6 g/cm 3 Volume (mL) of water displaced = 33 mL - 25 mL= 8 mL Volume of metal (cm 3 ) = 8 mL x 1 cm 3 = 8 cm 3 1 mL Density of metal = mass = 48 g = 6 g/cm 3 volume 8 cm 3

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Learning Check3 Which diagram represents the liquid layers in the cylinder? (K) Karo syrup (1.4 g/mL), (V) vegetable oil (0.91 g/mL,) (W) water (1.0 g/mL) 1) 2) 3) K K W W W V V V K

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Density as Conversion Factors A substance has a density of 3.8 g/mL. Density = 3.8 g/mL Equality 3.8 g = 1 mL Conversion factors. 3.8 g and 1 mL 1 mL 3.8 g

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Density Connections MassVolume kg L gmL (cm 3 ) mg

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Learning Check The density of octane, a component of gasoline, is g/mL. What is the mass, in kg, of 875 mL of octane? 1) kg 2) 614 kg 3) 1.25 kg

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Solution 1) kg Unit plan: mL g kg Equalities: 1 mL = g and 1 kg = 1000 g Setup: 875 mL x g x 1 kg = kg 1 mL 1000 g density metric factor

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Learning Check If blood has a density of 1.05 g/mL, how many liters of blood are donated if 575 g of blood are given? 1) L 2) 1.25 L 3) 1.83 L

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Solution 1) Unit Plan: g mL L 575 g x 1 mL x 1 L = L 1.05 g 1000 mL

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Learning Check A group of students collected 125 empty aluminum cans to take to the recycling center. If 21 cans make 1.0 pound of aluminum, how many liters of aluminum (D=2.70 g/cm 3 ) are obtained from the cans? 1) 1.0 L2) 2.0 L3) 4.0 L

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Solution 1) 1.0 L 125 cans x 1.0 lb x 454 g x 1 cm 3 21 cans 1 lb 2.70 g x 1 mL x 1 L = 1.0 L 1 cm mL

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Learning Check You have 3 metal samples. Which one will displace the greatest volume of water? Discuss your choice with another student. 25 g Al 2.70 g/mL 45 g of gold 19.3 g/mL 75 g of Lead 11.3 g/mL

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Solution 1)25 g Al x 1 mL = 9.2 mL 2.70 g 25 g Al 2.70 g/mL

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Chapter 1 Measuring Temperature

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Temperature Particles are always moving. When you heat water, the water molecules move faster. When molecules move faster, the substance gets hotter. When a substance gets hotter, its temperature goes up.

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Learning Check Suppose you place water in a freezer. A. The water particles move 1) faster 2) slower 3) the same B. The water will get 1) hotter 2) colder 3) stay the same C. The temperature of the water will be 1) higher 2) lower 3) the same

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Temperature Measures the hotness or coldness of an object Determined by using a thermometer that contains a liquid that expands with heat and contracts with cooling.

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Temperature Scales

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Units of Temperature between Boiling and Freezing FahrenheitCelsius Kelvin Water boils 212°F 100°C 373 K 180°100°C 100K Water freezes 32°F 0°C 273 K

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Learning Check A. Temperature of freezing water 1) 0°F 2) 0°C 3) 0 K B. Temperature of boiling water 1) 100°F 2) 32°F 3) 373K C. Number of Celsius units between the boiling and freezing points of water 1) 1002) 180 3) 273

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Fahrenheit Formula 180°F = 9°F =1.8°F 100°C 5°C 1°C Zero point: 0°C = 32°F °F = 9/5 (T°C) + 32 or °F = 1.8 (T°C) + 32

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Celsius Formula Rearrange to find T°C °F = 1.8 T°C + 32 °F - 32 = 1.8 T°C ( ) °F - 32 = 1.8 T°C °F - 32 = T°C 1.8

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Temperature Conversions A person with hypothermia has a body temperature of 29.1°C. What is the body temperature in °F? °F = 1.8 (29.1°C) + 32 exact tenth's exact = = 84.4°F tenths

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Learning Check The normal temperature of a chickadee is 105.8°F. What is that temperature in °C? 1) 73.8 °C 2) 58.8 °C 3) 41.0 °C

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Solution 3) 41.0 °C Solution: °C = (°F - 32) 1.8 =( ) 1.8 =73.8°F 1.8°= 41.0°C

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Learning Check Pizza is baked at 455°F. What is that in °C? 1) 437 °C 2) 235°C 3) 221°C

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Learning Check On a cold winter day, the temperature falls to - 15°C. What is that temperature in °F? 1) 19 °F 2) 59°F 3) 5°F

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Kelvin Scale On the Kelvin Scale 1K = 1°C 0 K is the lowest temperature 0 K = - 273°C K °C K = °C + 273

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Learning Check What is normal body temperature of 37°C in kelvins? 1) 236 K 2) 310 K 3)342 K

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Three States of Matter solid liquid gas

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Physical or Chemical? A physical change does not alter the composition or identity of a substance. A chemical change alters the composition or identity of the substance(s) involved. ice melting sugar dissolving in water hydrogen burns in air to form water Phase Change

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An extensive property of a material depends upon how much matter is is being considered. An intensive property of a material does not depend upon how much matter is being considered. mass length volume density temperature color Extensive and Intensive Properties

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Matter - anything that occupies space and has mass. mass – measure of the quantity of matter SI unit of mass is the kilogram (kg) 1 kg = 1000 g = 1 x 10 3 g weight – force that gravity exerts on an object weight = c x mass on earth, c = 1.0 on moon, c ~ 0.1 A 1 kg bar will weigh 1 kg on earth 0.1 kg on moon

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