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3/28/2017 Measurements Chapter 1

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**Units of Measurement You are making a measurement when you**

3/28/2017 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**

3/28/2017 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**

3/28/2017 Some Tools for Measurement

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3/28/2017 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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3/28/2017 Solution From the previous slide, state the tool (s) you would use to measure A. temperature thermometer B. volume measuring cup, graduated cylinder C. time watch D. weight scale

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**Measurement in Chemistry**

3/28/2017 Measurement in Chemistry In chemistry we do experiments measure quantities use numbers to report measurements

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**In every measurement there is a Unit from measuring device**

3/28/2017 Stating a Measurement In every measurement there is a Number followed by a Unit from measuring device

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3/28/2017 Learning Check What is the unit of measurement in each of the following examples? A. The patient’s 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) Is a decimal system based on 10**

3/28/2017 Metric System (SI) Is a decimal system based on 10 Used in most of the world Used by scientists and hospitals

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**Units in the Metric System**

3/28/2017 Units in the Metric System length meter m volume liter L mass gram g temperature Celsius °C

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**Learning Check Identify the measurement in metric units.**

3/28/2017 Learning Check Identify the measurement in metric units. A. John’s height is 1) 1.5 yards 2) 6 feet 3) 2 meters B. The volume of saline in the IV bottle is 1) 1 liters 2) 1 quart 3) 2 pints C. The mass of a lemon is 1) 12 ounces 2) 145 grams 3) 0.6 pounds

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**Measured Numbers and Significant Figures**

3/28/2017 Measurements Measured Numbers and Significant Figures

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3/28/2017 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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3/28/2017 Reading a Meterstick . l I I I I cm First digit (known) = ?? cm Second digit (known) = ? cm Third digit (estimated) between Length reported = cm or cm or cm

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**Known + Estimated Digits**

3/28/2017 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 . l8. . . . I . . . . I9. . . .I . . . . I10. . cm**

3/28/2017 Learning Check . l I I I I cm What is the length of the line? 1) cm 2) cm 3) cm How your answer compare with your neighbor’s answer? Why or why not?

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**Learning Check l5. . . . I . . . . I6. . . .I . . . . I7. . cm**

3/28/2017 Learning Check l I I I I cm What is the length of the line? 1) 6.0 cm 2) cm 3) cm

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**Zero as a Measured Number**

3/28/2017 Zero as a Measured Number . l I I I I cm What is the length of the line? First digit ?? cm Second digit ? cm Last (estimated) digit is cm (not to the left or right of .5)

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**Exact Numbers Obtained when you count objects 1 watch 4 pizzas**

3/28/2017 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 1. measuring 2. counting 3. definition**

3/28/2017 Learning Check A. Exact numbers are obtained by 1. measuring 2. counting 3. definition B. Measured numbers are obtained by A = 2 & 3; B = 1

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**Learning Check Classify each of the following as an exact (1)**

3/28/2017 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 10-4 cm D.___There were 6 hats on the shelf E.___A can of soda contains 355 mL of soda 2, 1, 2, 1, 2

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**Significant Figures in Measurement**

3/28/2017 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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**Significant Figures Summary**

3/28/2017 Any digit that is not zero is significant 1.234 kg significant figures Zeros between nonzero digits are significant 606 m significant figures Zeros to the left of the first nonzero digit are not significant 0.08 L significant figure If a number is greater than 1, then all zeros to the right of the decimal point are significant 2.0 mg 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 1.8

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**Counting Significant Figures**

3/28/2017 Counting Significant Figures Number of Significant Figures 38.15 cm 4 5.6 ft 2 65.6 lb ___ m ___ Complete: All non-zero digits in a measured number are (significant or not significant).

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**Leading Zeros 0.008 mm 1 0.0156 oz 3 0.0042 lb ____ 0.000262 mL ____**

3/28/2017 Leading Zeros Number of Significant Figures 0.008 mm 1 oz 3 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 3 2001 min 4**

3/28/2017 Sandwiched Zeros Number of Significant Figures 50.8 mm 3 2001 min 4 0.702 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. 2 200 yr 1**

3/28/2017 Trailing Zeros Number of Significant Figures 25,000 in 200 yr 1 48,600 gal 3 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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3/28/2017 Learning Check A. Which answers contain 3 significant figures? 1) ) ) 4760 B. All the zeros are significant in 1) ) ) x 103 C. 534,675 rounded to 3 significant figures is 1) ) 535, ) 5.35 x 105 A: 2, 3; B: 2, 3; C: 2, 3

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**Learning Check 2) 400.0 and 40 3) 0.000015 and 150,000**

3/28/2017 Learning Check In which set(s) do both measured numbers contain the same number of significant figures? 1) and 22.00 2) and 40 3) and 150,000 Only 3)

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**Learning Check SF3 A. 0.030 m 1 2 3 B. 4.050 L 2 3 4 C. 0.0008 g 1 2 4**

3/28/2017 Learning Check SF3 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 A: 2; b: 4; c: 1; d: 3; e: 3

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**Significant Numbers in Calculations**

3/28/2017 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**

3/28/2017 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 26.54 answer one decimal place E.g., = 31 should be 26 (assume all numbers are measured numbers)

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3/28/2017 Learning Check In each calculation, round the answer to the correct number of significant figures. A = 1) ) ) 257 B = 1) ) ) 40.7 A: 2; B: 3

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**Multiplying and Dividing**

3/28/2017 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. 2.19 X 4.2 = 1) 9 2) 9.2 3) 9.198 B. 4.311 ÷ 0.07 =**

3/28/2017 Learning Check A X = 1) ) ) B ÷ = 1) ) ) 60 C X = X 0.060 1) ) ) A: 2; B: 3; C: 2

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3/28/2017 Measurements Prefixes and Equalities

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**Metric Prefixes Increase or decrease basic unit by 10**

3/28/2017 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 = meters 1 kilogram = grams

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**Prefixes that Increase A Unit**

3/28/2017 Prefixes that Increase A Unit Prefix Symbol Value giga- G mega- M kilo- k

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**Prefixes that Decrease A Unit**

3/28/2017 Prefixes that Decrease A Unit Prefix Symbol Value deci- d 0.1 centi- c milli- m micro- (mu) nano n

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**Learning Check Match 1) length 2) mass 3) volume**

3/28/2017 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. A: 2; B: 1; C: 2; D: 3

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**Learning Check 1) millimeters 2) meters 3) kilometers**

3/28/2017 Learning Check Select the unit you would use to measure A. Your height 1) millimeters 2) meters 3) kilometers B. Your mass 1) milligrams 2) grams 3) kilograms C. The distance between two cities 1) millimeters 2) meters 3) kilometers D. The width of an artery A: 2; B: 3; C: 3; D: 1

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**Learning Check Indicate the prefix to use for**

3/28/2017 Learning Check Indicate the prefix to use for 1. A mass that is 1000 times greater than 1 gram 1) kilo 2) milli 3) mega 2. A length that is 1/100 of 1 meter? 1) deci 2) centi 3) milli 3. A unit of time that is 1/1000 of a second. 1) nanosecond 2) microsecond 3)millisecond 1: 1; 2: 2; 3: 3

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**Equalities State the same measurement in two different units length**

3/28/2017 Equalities State the same measurement in two different units length 10.0 in. 25.4 cm

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**Fundamental & Derived SI units and Metric Equalities**

3/28/2017 Length 1 km = 1000 m 1m = 100 cm 1m = 1000 mm Mass 1 kg = g 1 g = Volume 1 kL = 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 (m3)**

3/28/2017 Volume – SI derived unit for volume is cubic meter (m3) 1 cm3 = (1 x 10-2 m)3 = 1 x 10-6 m3 1 dm3 = (1 x 10-1 m)3 = 1 x 10-3 m3 1 L = 1000 mL = 1000 cm3 = 1 dm3 1 mL = 1 cm3

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**Learning Check C. 0.1 L = 1 ___ 1) mL 2) cL 3) dL**

3/28/2017 Learning Check A m = 1 ___ 1) mm 2) km 3) dm B g = 1 ___ 1) mg 2) kg 3) dg C L = 1 ___ 1) mL 2) cL 3) dL D m = 1 ___ 1) mm 2) cm 3) dm A: 2; B: 1; C: 3; D: 2

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**Learning Check Give the value of the following units: A. 1 kg = ____ g**

3/28/2017 Learning Check Give the value of the following units: A. 1 kg = ____ g 1) 10 g 2) 100 g 3) g B. 1 mm = ____ m 1) m 2) m 3) 0.1 m A: 3; B: 1

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**Some American Equalities**

3/28/2017 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? 1 ft = 12 in; 1 qt = 2 pints

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**Some Metric-American Equalities**

3/28/2017 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**

3/28/2017 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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3/28/2017 Accuracy vs. Precision Accuracy – how close a measurement is to the true value Precision – how close a set of measurements are to each other accurate & precise precise but not accurate not accurate & not precise

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3/28/2017 Conversion Factors Fractions in which the numerator and denominator are quantities expressed in an equality between those units Example: in. = 2.54 cm Factors: 1 in and cm 2.54 cm in.

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**Learning Check A. Liters and mL B. Hours and minutes**

3/28/2017 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**

3/28/2017 Solution A. quarts and mL 1 L = 1000 mL 1 L and mL 1000 mL L B. hours and minutes 1 hr = 60 min 1 hr and min 60 min hr C. meters and kilometers 1 km = 1000 m 1 km and m 1000 m km

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**Problem Solving Using Conversion Factors**

3/28/2017 Measurements Problem Solving Using Conversion Factors

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**Initial and Final Units**

3/28/2017 Initial and Final Units 1. A person has a height of 2.0 meters. What is that height in inches? Initial unit = m Final 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 = pints Final unit = _______ inches 1: in; 2: oz ounces

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**How many minutes are in 2.5 hours?**

3/28/2017 How many minutes are in 2.5 hours? Initial unit 2.5 hr Conversion Final factor unit 2.5 hr x min = min 1 hr cancel Answer (2 SF)

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3/28/2017 Learning Check A rattlesnake is 2.44 m long. How long is the snake in cm? 1) 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?**

3/28/2017 Solution A rattlesnake is 2.44 m long. How long is the snake in cm? 2) 244 cm 2.44 m x cm = 244 cm 1 m

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**Learning Check How many seconds are in 1.4 days?**

3/28/2017 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**

3/28/2017 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 hr min = 1.2 x 105 sec

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**Unit Check What is wrong with the following setup?**

3/28/2017 Unit Check What is wrong with the following setup? 1.4 day x 1 day x min x 60 sec 24 hr hr 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**

3/28/2017 Unit Check 1.4 day x 1 day x min x 60 sec 24 hr hr min Units = day2-sec/hr2 Not the final unit needed

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3/28/2017 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:**

3/28/2017 Solution Unit plan: mL qt gallon Setup: 4650 mL x qt x 1 gal = gal 946 mL qt 3 SF equality exact SF

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**Steps to Problem Solving**

3/28/2017 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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3/28/2017 Learning Check If the ski pole is 3.0 feet in length, how long is the ski pole in mm?

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3/28/2017 Solution 3.0 ft x 12 in x cm x 10 mm = 1 ft in cm

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3/28/2017 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 feet?

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**Solution Initial 8450 ft x 12 in. x 2.54 cm x 1 m 1 ft 1 in. 100 cm**

3/28/2017 Solution Initial 8450 ft x 12 in. x cm x 1 m 1 ft in cm x 1 min x 60 sec = sec 65 m min final (2 SF)

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3/28/2017 Measurements Density

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**Density Density compares the mass of an object to its volume**

3/28/2017 Density Density compares the mass of an object to its volume D = mass = g or g volume mL cm3 Note: 1 mL = 1 cm3

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**Learning Check D1 Osmium is a very dense metal. What is its**

3/28/2017 Learning Check D1 Osmium is a very dense metal. What is its density in g/cm3 if g of the metal occupies a volume of 2.22cm3? 1) g/cm3 2) 22.5 g/cm3 3) 111 g/cm3

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3/28/2017 Solution 2) Placing the mass and volume of the osmium metal into the density setup, we obtain D = mass = g = volume 2.22 cm3 = g/cm3 = g/cm3

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3/28/2017 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 1) 0.2 g/ cm3 2) 6 g/m3 3) 252 g/cm3**

3/28/2017 Learning Check What is the density (g/cm3) 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 ) 6 g/m ) g/cm3 33 mL 25 mL

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**Solution 2) 6 g/cm3 Volume (mL) of water displaced**

3/28/2017 Solution 2) 6 g/cm3 Volume (mL) of water displaced = mL mL = mL Volume of metal (cm3) = 8 mL x 1 cm3 = cm3 1 mL Density of metal = mass = 48 g = 6 g/cm3 volume cm3

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**Learning Check3 K V W V K W W V K 1) 2) 3)**

3/28/2017 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) ) ) Answer: 1; K V W K V W W V K

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**Density as Conversion Factors**

3/28/2017 Density as Conversion Factors A substance has a density of 3.8 g/mL. Density = 3.8 g/mL Equality g = 1 mL Conversion factors. 3.8 g and mL 1 mL g

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3/28/2017 Density Connections Mass Volume kg L g mL (cm3) mg

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3/28/2017 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) 0.614 kg Unit plan: mL g kg**

3/28/2017 Solution 1) kg Unit plan: mL g kg Equalities: 1 mL = g and 1 kg = 1000 g Setup: 875 mL x g x kg = kg 1 mL g density metric factor factor

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3/28/2017 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) L 3) L

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**Solution Unit Plan: g mL L 575 g x 1 mL x 1 L = 0.548 L 1.05 g 1000 mL**

3/28/2017 Solution 1) Unit Plan: g mL L 575 g x mL x 1 L = L 1.05 g mL

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3/28/2017 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/cm3) are obtained from the cans? 1) 1.0 L 2) 2.0 L 3) 4.0 L

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**Solution 1 cm3 1000 mL 1) 1.0 L 125 cans x 1.0 lb x 454 g x 1 cm3**

3/28/2017 Solution 1) 1.0 L 125 cans x 1.0 lb x 454 g x 1 cm3 21 cans lb g x 1 mL x L = 1.0 L 1 cm mL

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3/28/2017 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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3/28/2017 Solution 1) 25 g Al x mL = mL g 25 g Al 2.70 g/mL

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**Measuring Temperature**

3/28/2017 Chapter 1 Measuring Temperature

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**Temperature Particles are always moving.**

3/28/2017 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.**

3/28/2017 Learning Check Suppose you place water in a freezer. A. The water particles move 1) faster 2) slower ) the same B. The water will get 1) hotter 2) colder ) stay the same C. The temperature of the water will be 1) higher 2) lower ) the same A: 2; b: 2; c: 2

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**Temperature Measures the hotness or coldness of an object**

3/28/2017 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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3/28/2017 Temperature Scales

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**Units of Temperature between Boiling and Freezing**

3/28/2017 Units of Temperature between Boiling and Freezing Fahrenheit Celsius Kelvin Water boils °F °C K 180° 100°C K Water freezes 32°F °C K

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**Learning Check A. Temperature of freezing water 1) 0°F 2) 0°C 3) 0 K**

3/28/2017 Learning Check A. Temperature of freezing water 1) 0°F ) 0°C ) 0 K B. Temperature of boiling water 1) 100°F ) 32°F ) 373K C. Number of Celsius units between the boiling and freezing points of water 1) ) ) 273 A: 2; B: 3; C: 1

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**Fahrenheit Formula 180°F = 9°F = 1.8°F 100°C 5°C 1°C**

3/28/2017 Fahrenheit Formula 180°F = °F = 1.8°F °C °C 1°C Zero point: 0°C = 32°F °F = 9/5 (T°C) or °F = 1.8 (T°C)

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**Celsius Formula Rearrange to find T°C °F = 1.8 T°C + 32**

3/28/2017 Celsius Formula Rearrange to find T°C °F = 1.8 T°C °F = 1.8 T°C ( ) °F = 1.8 T°C °F = T°C 1.8

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**Temperature Conversions**

3/28/2017 Temperature Conversions A person with hypothermia has a body temperature of 29.1°C. What is the body temperature in °F? °F = (29.1°C) exact tenth's exact = = 84.4°F tenth’s

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**Learning Check 1) 73.8 °C 2) 58.8 °C 3) 41.0 °C**

3/28/2017 Learning Check The normal temperature of a chickadee is 105.8°F. What is that temperature in °C? 1) °C 2) °C 3) °C

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**Solution Solution: °C = (°F - 32) 1.8 = (105.8 - 32) = 73.8°F**

3/28/2017 Solution 3) 41.0 °C Solution: °C = (°F - 32) 1.8 = ( ) = 73.8°F 1.8° = °C

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**Learning Check Pizza is baked at 455°F. What is that in °C? 1) 437 °C**

3/28/2017 Learning Check Pizza is baked at 455°F. What is that in °C? 1) 437 °C 2) 235°C 3) 221°C Answer: 2

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**Learning Check 1) 19 °F 2) 59°F 3) 5°F**

3/28/2017 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 Answer: 3

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**Kelvin Scale On the Kelvin Scale 1K = 1°C**

3/28/2017 Kelvin Scale On the Kelvin Scale 1K = 1°C 0 K is the lowest temperature 0 K = °C K °C K = °C

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3/28/2017 Learning Check What is normal body temperature of 37°C in kelvins? 1) 236 K 2) K 3) 342 K Answer: 2

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3/28/2017 Three States of Matter solid liquid gas

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3/28/2017 Physical or Chemical? A physical change does not alter the composition or identity of a substance. ice melting sugar dissolving in water Phase Change A chemical change alters the composition or identity of the substance(s) involved. hydrogen burns in air to form water

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**Extensive and Intensive Properties**

3/28/2017 Extensive and Intensive Properties An extensive property of a material depends upon how much matter is is being considered. mass length volume An intensive property of a material does not depend upon how much matter is being considered. density temperature color

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**Matter - anything that occupies space and has mass.**

3/28/2017 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 103 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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1 Chapter 2 - Measurements Section 2.1 Units of Measurement.

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