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What is Scientific Notation? Scientific notation is a way of expressing really big numbers or really small numbers. Scientific notation is a way of expressing really big numbers or really small numbers. It is most often used in scientific calculations where the analysis must be very precise. It is most often used in scientific calculations where the analysis must be very precise. For very large and very small numbers, scientific notation is more concise. For very large and very small numbers, scientific notation is more concise.

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Scientific notation consists of two parts: A number between 1 and 10 A number between 1 and 10 A power of 10 A power of 10 N x 10 x

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To change standard form to scientific notation… Place the decimal point so that there is one non-zero digit to the left of the decimal point. Place the decimal point so that there is one non-zero digit to the left of the decimal point. Count the number of decimal places the decimal point has moved from the original number. This will be the exponent on the 10. Count the number of decimal places the decimal point has moved from the original number. This will be the exponent on the 10. If the original number was less than 1, then the exponent is negative. If the original number was greater than 1, then the exponent is positive. If the original number was less than 1, then the exponent is negative. If the original number was greater than 1, then the exponent is positive.

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Examples Given: 289,800,000 Given: 289,800,000 Use: (moved 8 places) Use: (moved 8 places) Answer: x 10 8 Answer: x 10 8 Given: Given: Use: 5.67 (moved 4 places) Use: 5.67 (moved 4 places) Answer: 5.67 x Answer: 5.67 x 10 -4

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To change scientific notation to standard form… Simply move the decimal point to the right for positive exponent 10. Simply move the decimal point to the right for positive exponent 10. Move the decimal point to the left for negative exponent 10. Move the decimal point to the left for negative exponent 10. (Use zeros to fill in places.)

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Example Answer: 5,093,000 (moved 6 places to the right) Answer: 5,093,000 (moved 6 places to the right) Given: x Given: x Answer: (moved 4 places to the left) Answer: (moved 4 places to the left) Given: x 10 6 Given: x 10 6

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Learning Check Express these numbers in Scientific Notation: Express these numbers in Scientific Notation: 1) ) ) ) 2 5)

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Chapter 5 - Chemistry I Working with Numbers

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Significant Digits In science numbers are not just numbers they are measurements, and as we have already discovered ALL measurements have some degree of uncertainty inherently in them. Because of this, when we combine certain measurements we must have the ability to reflect are uncertainty in our final results. Scientists Answer: SIGNIFICANT DIGITS

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Significant Digits (Cont.) Significant Digits are determined in measurements by following four distinct rules. Rule 1: ALL non-zero digits are significant. (1-9) Rule 2: Zeros preceding (coming before) the first non-zero number are NEVER significant. (Leading Zeros) Rule 3: Zeros in between non-zero numbers are ALWAYS significant. (Trapped Zeros) Rule 4: Trailing zeros (zeros at the end of a number) are only significant if a decimal is present.

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Rule 1: ALL non-zero digits are significant. Example: has 5 significant digits since all numbers are non-zero numbers.

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Rule 2: Zeros preceding (coming before) the first non-zero number are NEVER significant. (Leading) Zeros Example: has only 3 significant digits. The zeros preceding the number 1 are just keeping space in the number.

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Rule 3: Zeros in between non-zero numbers are ALWAYS significant. (Trapped Zeros) Example: 10,023 has only 5 significant digits. The zeros between the numbers 1 and 2 are a part of the measurement and must be counted.

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Rule 4: Trailing zeros (zeros at the end of a number) are only significant if a decimal is present. Example: 100 has only one significant digit since there is no decimal present in the number Has three significant digits, however, since there is a decimal present. WHY?

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How Many Sig. Digs. Do the following numbers have? How Many Sig. Digs. Do the following numbers have? m m kg kg 3500 V 3500 V 1,809,000 L 1,809,000 L Answers Answers 6 significant digits 6 significant digits 2 significant digits 2 significant digits 4 significant digits 4 significant digits

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Significant Digits (Cont.) In scientific calculations we must account for significant digits because of our uncertainty in measurement. In scientific calculations we must account for significant digits because of our uncertainty in measurement. We have two separate rules for Addition/Subtraction and Multiplication/Division We have two separate rules for Addition/Subtraction and Multiplication/Division

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Significant Digits (Cont.) Rule for Addition/Subtraction Rule for Addition/Subtraction The number of significant digits allowed in our calculated answer depends on the number with the largest uncertainty. The number of significant digits allowed in our calculated answer depends on the number with the largest uncertainty. Example: g Example: g g g g g g g g g

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Significant Digits (Cont.) g g g g g g g g g g 4 sig digs 4 sig digs 5 sig digs 5 sig digs 7 sig digs 7 sig digs The answer is g with 4 sig digs. We can only express our answer to the most uncertain measurement that we have. In this case, the ones spot.

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Significant Digits (Cont.) Rule for Multiplication/Division Rule for Multiplication/Division The measurement with the smallest number of significant digits determines the number of significant digits in the answer. The measurement with the smallest number of significant digits determines the number of significant digits in the answer. Example: V = (3.052 m)(2.10 m)(0.75 m) Example: V = (3.052 m)(2.10 m)(0.75 m)

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Significant Digits (Cont.) V = (3.052 m) x (2.10 m) x (0.75 m) V = (3.052 m) x (2.10 m) x (0.75 m) (4 sig figs)(3 sig figs)(2 sig figs) (4 sig figs)(3 sig figs)(2 sig figs) V = m 3 (5 sig figs) V = m 3 (5 sig figs) V = 4.8 m 3 V = 4.8 m 3

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Significant Digits (Cont.) One Last Rule One Last Rule Any numbers that are exact, do not affect the number of significant digits in the final answer. Any numbers that are exact, do not affect the number of significant digits in the final answer. Exact numbers are constants: Exact numbers are constants: 12 inches/foot; 3.14, 2.54 cm/inch 12 inches/foot; 3.14, 2.54 cm/inch

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Dimensional Analysis in Chemistry

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UNITS OF MEASUREMENT Use SI units based on the metric system LengthMassVolumeTimeTemperature Meter, m Kilogram, kg Seconds, s Celsius degrees, ˚C kelvins, K Liter, L

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Some Tools for Measurement Which tool(s) would you use to measure: A. temperature B. volume C. time D. weight

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Learning Check Match L) length M) mass V) 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. M L M V

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Learning Check What are some U.S. units that are used to measure each of the following? A. length B. volume C. weight D. temperature

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Solution Some possible answers are A. length inch, foot, yard, mile B. volume cup, teaspoon, gallon, pint, quart C. weight ounce, pound (lb), ton D. temperature F

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Metric Prefixes Kilo- means 1000 of that unit Kilo- means 1000 of that unit –1 kilometer (km) = 1000 meters (m) Centi- means 1/100 of that unit Centi- means 1/100 of that unit –1 meter (m) = 100 centimeters (cm) –1 dollar = 100 cents Milli- means 1/1000 of that unit Milli- means 1/1000 of that unit –1 Liter (L) = 1000 milliliters (mL)

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Metric Prefixes

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Units of Length ? kilometer (km) = 500 meters (m) ? kilometer (km) = 500 meters (m) 2.5 meter (m) = ? centimeters (cm) 2.5 meter (m) = ? centimeters (cm) 1 centimeter (cm) = ? millimeter (mm) 1 centimeter (cm) = ? millimeter (mm) 1 nanometer (nm) = 1.0 x meter 1 nanometer (nm) = 1.0 x meter OH distance = 9.4 x m 9.4 x cm nm OH distance = 9.4 x m 9.4 x cm nm

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Learning Check Select the unit you would use to measure 1. Your height a) millimeters b) meters c) kilometers 2. Your mass a) milligramsb) grams c) kilograms 3. The distance between two cities a) millimetersb) meters c) kilometers 4. The width of an artery a) millimetersb) meters c) kilometers

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Solution 1. Your height b) meters 2. Your mass c) kilograms 3. The distance between two cities c) kilometers 4. The width of an artery a) millimeters

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

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m = 1 ___a) mm b) km c) dm g = 1 ___ a) mg b) kg c) dg L = 1 ___a) mL b) cL c) dL m = 1 ___ a) mm b) cm c) dm Learning Check

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Conversion Factors Fractions in which the numerator and denominator are EQUAL quantities expressed in different 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: 1. Liters and mL 2. Hours and minutes 3. Meters and kilometers

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How many minutes are in 2.5 hours ? Conversion factor Conversion factor 2.5 hr x 60 min = 150 min 2.5 hr x 60 min = 150 min 1 hr 1 hrcancel By using dimensional analysis / factor-label method, the UNITS ensure that you have the conversion right side up, and the UNITS are calculated as well as the numbers!

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Sample Problem You have $7.25 in your pocket in quarters. How many quarters do you have? You have $7.25 in your pocket in quarters. How many quarters do you have? 7.25 dollars 4 quarters 7.25 dollars 4 quarters 1 dollar 1 dollar X = 29 quarters

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Learning Check A rattlesnake is 2.44 m long. How long is the snake in cm? a) 2440 cm b)244 cm c)24.4 cm

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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 1 day

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

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Wait a minute! 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 24 hr 1 hr 1 min

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English and Metric Conversions If you know ONE conversion for each type of measurement, you can convert anything! If you know ONE conversion for each type of measurement, you can convert anything! You will need to know and use these conversions: You will need to know and use these conversions: –Mass: 454 grams = 1 pound –Length: 2.54 cm = 1 inch –Volume: L = 1 quart

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Learning Check Learning Check An adult human has 4.65 L of blood. How many gallons of blood is that? Unit plan: L qt gallon Unit plan: L qt gallon Equalities:1 quart = L 1 gallon = 4 quarts 1 gallon = 4 quarts Your Setup:

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

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Dealing with Two Units – Honors Only 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? 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 1 ft 1 in. 100 cm x 1 min x 60 sec = 2400 sec x 1 min x 60 sec = 2400 sec 65 m 1 min 65 m 1 min Solution

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Temperature Scales Fahrenheit Fahrenheit Celsius Celsius Kelvin Kelvin Anders Celsius Lord Kelvin (William Thomson)

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Temperature Scales 1 kelvin = 1 degree Celsius Notice that 1 kelvin = 1 degree Celsius Boiling point of water Freezing point of water Celsius 100 ˚C 0 ˚C 100˚C Kelvin 373 K 273 K 100 K Fahrenheit 32 ˚F 212 ˚F 180˚F

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Calculations Using Temperature Generally require temps in kelvins Generally require temps in kelvins T (K) = t (˚C) T (K) = t (˚C) Body temp = 37 ˚C = 310 K Body temp = 37 ˚C = 310 K Liquid nitrogen = -196 ˚C = 77 K Liquid nitrogen = -196 ˚C = 77 K Generally require temps in kelvins Generally require temps in kelvins T (K) = t (˚C) T (K) = t (˚C) Body temp = 37 ˚C = 310 K Body temp = 37 ˚C = 310 K Liquid nitrogen = -196 ˚C = 77 K Liquid nitrogen = -196 ˚C = 77 K

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