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Unit 2:SCIENTIFIC MEASUREMENT

Unit 2:SCIENTIFIC MEASUREMENT. OBJECTIVES (Don’t Copy!) Convert Between Standard Notation to Scientific Notation Identify Significant Figures & Uncertainty in Measurements Perform Operations with Significant Figures Addition & Subtraction Multiplication & Division

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Unit 2:SCIENTIFIC MEASUREMENT

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  1. Unit 2:SCIENTIFIC MEASUREMENT OBJECTIVES (Don’t Copy!) • Convert Between Standard Notation to Scientific Notation • Identify Significant Figures & Uncertainty in Measurements • Perform Operations with Significant Figures • Addition & Subtraction • Multiplication & Division NOTE: PLEASE COPY EXAMPLES IN THIS SLIDESHOW

  2. What is Scientific Notation? • a way of expressing really big numbers or really small numbers. • For some numbers, scientific notation is more concise.

  3. Scientific notation consists of two parts: • A number between 1 and 10 (the “coefficient”) • A power of 10 • Ex: 7.01 x 108

  4. Converting from StandardScientific Notation EX: Convert 289,800,000 to scientific notation. _______ x 10___ 8 2.898 STEP 1: Moving the decimal, convert this number so that it falls between 1 and 10. STEP 2: Count the number of places you moved the decimal. This is the exponent. • If the number was large to start with, exponent is positive • If the number was small to start with, exponent is negative

  5. Examples • Given: 0.000567 NOTE: This is a very small number, so the exponent is SMALL (negative) 5.67 -4 x 10 ___ ___________ STEP 1 STEP 2

  6. Converting Scientific Notation to Standard • Ex: 9.301 x 10 -7 • STEP1 : Using the sign on the exponent, decide which way to move your decimal. • Negative sign, move to the left (negative direction) • Positive sign, move to the right (positive direction) STEP 2: Move the decimal the same number of spaces as the exponent indicates. Use zeros to hold “empty” spaces.

  7. Scientific Notation & Your Calculator • Video Instructions- Using Calculator

  8. Plugging Scientific Notation into My Calculator • Find the button on your calculator that is used to enter SCIENTIFIC NOTATION. Write it HERE___ OR • (Do Not Copy) Note: If you find one of the symbols ABOVE a key, rather than ON a key, you must push OR EE EXP 2nd EE 2nd EXP

  9. Plugging Scientific Notation Into My Calculator • Ex: Plug this number into your calculator: 8.93 x 1o-13 • (leave the blanks empty for now) • Write the steps you used below • Type 8.93 • Push ______ button. • Type_____13_____ • Push ____OR____ button • What I see on the screen is _________ NOTE: Use your calculator’s keys if they differ from what is written here EE NOTE: Sometimes these 2 steps can be reversed (-) +/- 8.93 -13

  10. Scientific Notation: Doing Calculations Ex: 3 x 104 + 2.5 x 105 USE CALCULATOR: NOTE: Use your calculator’s keys if they differ from what is written in table & fill them in NOTE: Answers must be in scientific notation! Calculator says: 280000 Correct Answer: 2.8 x 105

  11. Practice • 9.1 x 10-3 + 4.3 x 10-2 Calculator says: 0.0521 ANSWER: 5.21 x 10-2

  12. Scientific Notation:Multiplying&Dividing Ex: (6.1 x 10-3) (7.2 x 109) USE CALCULATOR: NOTE: Use your calculator’s keys if they differ from what is written in table NOTE: Answers must be in scientific notation! Calculator says: 43920000 Correct Answer: 4.392 x 107

  13. Stating a Measurement In every measurement there is a • Number followed by a • Unit from a measuring device The number should also be as precise as the measuring device.

  14. Ex: Reading a Meterstick . l2. . . . I . . . . I3 . . . .I . . . . I4. . cm First digit (known) = 2 2.?? cm Second digit (known) = 0.7 2.7? cm Third digit (estimated) between 0.05- 0.07 Length reported =2.75 cm or 2.74 cm or 2.76 cm

  15. Significant Figures • 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

  16. Shortcuts to Sig Figs The Atlantic-Pacific Rule says: "If a decimal point is Present, ignore zeros on the Pacific (left) side. If the decimal point is Absent, ignore zeros on the Atlantic (right) side. Everything else is significant."

  17. Counting Significant Figures:Unlimited Sig Figs 2 instances in which there are an unlimited # of sig figs. • Counting. Ex: 23 people in our classroom. • Exactly defined quantities. Ex: 1hr = 60 min. • Both are exact values. There is no uncertainty. • Neither of these types of values affect the process of rounding an answer.

  18. Learning Check (Do Not Copy) A. Which answers contain 3 significant figures? 1) 0.4760 2) 0.00476 3) 4760 B. All the zeros are significant in 1) 0.00307 2) 25.300 3) 2.050 x 103 C. 534,675 rounded to 3 significant figures is 1) 535 2) 535,000 3) 5.35 x 105

  19. Learning Check (Do not copy) In which set(s) do both numbers contain the samenumber of significant figures? 1) 22.0 and 22.00 2) 400.0 and 40 3) 0.000015 and 150,000

  20. Rounding With Sig Figs • When rounding an answer, determine which is the last significant figure. This is where you will round your number. • If the digit immediately to the right of the last sig fig is less than 5, the value of the last sig fig remains the same. • 34, 231 rounded to 3 sig figs  • If it is 5 or greater, round up. • Ex: 0.09246 rounded to 3 sig figs  34,200 0.0925

  21. Practice Rounding (p 69) • Round off each measurement to the number of sig figs shown in parentheses. • 314.721 meters (four) • 0.001775 meter (two) • 8792 meters (two) • 25,599 (four) = 314.7 meters =0.0018 meter NOTE: The zeros are IMPORTANT place holders, but are not SIGNIFICANT b/c they don’t contribute to the precision of the answer. = 8800 meters = 2.560 x 10 4 NOTE: Sometimes the only way to show sig figs properly is to use scientific notation!

  22. 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 • If you must round to obtain the right # of sig figs, do so after all calcs are complete

  23. Adding and Subtracting The answer is rounded to the same PLACE as the LEAST PRECISE measurement . 25.2one decimal place + 1.34two decimal places 26.54 answer 26.5one decimal place

  24. Learning Check In each calculation, round the answer to the correct number of significant figures. A. 235.05 + 19.6 + 2.1 = 1) 256.75 2) 256.8 3) 257 B. 58.925 - 18.2 = 1) 40.725 2) 40.73 3) 40.7

  25. 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. Ex: 4.31 cm x 7.22 cm x 9 cm = 280.0638 cm3 = 300 cm3 3 SF 3 SF 1 SF 1 SF

  26. Learning Check A. 2.19 X 4.2 = 1) 9 2) 9.2 3) 9.198 B. 4.311 ÷ 0.07 = 1)61.582) 62 3) 60 C. 2.54 X 0.0028 = 0.0105 X 0.060 1) 11.3 2) 11 3) 0.041

  27. Practice in Teams Q#1: 8.3lb ÷ 9.102 in2 = 0.911887497 = 0.91 lb/in2 2 SF 4 SF ANSWER: 2 SF

  28. Practice in Teams 3 SF Q#2: 63.2 m2 - 2.38 m2 = 11.05617161 m 5.501 m 3 SF = 11.1 m 4 SF You only round once! (YORO). DON’T round after you subtract, then AGAIN after you divide. Answer: 3 SF NOTE: When you have a mixture of +/- & x/÷, the rule for x/÷ is used. This rule says, “round to the same # of SF as the measurement with the least # of SF.”

  29. You Practice: SF Review WS (Don’t Copy) • #21, 22, 25,27,30,31,32,35,36,37,38,39 (12 problems)

  30. Density = __Mass__ Volume Cover the variable you are solving for and perform the operation with the given amounts NOTE: Put this on your P. Table M D = _M_ V (Mass) ÷ V D X (Density) (Volume)

  31. Common Units for Density Probs (Copy onto P. Table) • Volume = L (mL), cm3 • NOTE: 1 mL = 1 cm3 • Mass = g (kg, mg, etc.), lbs

  32. Density Practice Problem #1 (p 91) QUESTION: A copper penny has a mass of 3.1 g and a volume of 0.35 cm3. What is the density of copper? SOLUTION: Givens: Unknown: • mass = 3.1 g density = ? • Volume = 0.35 cm3 • Find equation and solve D = m/v • D = 3.1 g /0.35 cm3 • D = 8.8571 g/cm3

  33. Density Practice Problem #2 (p 92) What is the volume of a pure silver coin that has a mass of 14 g? The density of silver (Ag) is 10.5 g/cm3. • Givens: Unknown: • Mass = 14 g volume = ? • Density = 10.5 g/cm3 • Find formula & derive it: D = M/V V = M/D • Substitute values & solve V = 14 g 10.5 g/cm3

  34. UNITS OF MEASUREMENT We use SI units — based on the metric system (SI means SystemeInternationale) Length Mass Volume Time Temperature Meter, m Kilogram, kg Liter, L Seconds, s Celsius degrees, ˚C kelvins, K

  35. Metric Prefixes Base unit (100) goes here (g, m, L)

  36. How to set up conversion factors in the metric system • If you always select the larger of the 2 units as your “1” unit, • Then the multiplier (on prefixes table) will have a positive exponent. Ex 1: Compare Megagrams & grams. Which is larger? Megagrams This is our “1” unit 1 Mg = 106 grams This is the multiplier from our table

  37. Ex: Compare meters & millimeters • Which is the larger of the 2 units? meters This is your “1” unit NOTE: when you look on your prefixes chart, the “milli-” multiplier is 10-3. When we use the method of making the larger unit the “1” unit, we always have a positive exponent for our multiplier. 1 meter = 103 mm

  38. Conversion Factors Fractions in which the numerator and denominator are EQUAL quantities expressed in different units Example: 1 km = 103 m Factors: 1 km and 103 m 103 m 1 km They don’t change the value of the measurement, just the units in which it is expressed.

  39. Conversion Factors Fractions in which the numerator and denominator are EQUAL quantities expressed in different units Example: 1 hr. = 60 min Factors: 1 hr. and 60 min 60 min 1 hr. They don’t change the value of the measurement, just the units in which it is expressed.

  40. Ex 1: How many millimeters in 1205 meters? 4. Place units of the unknown in the numerator of the conversion factor. (if you can find a relationship between the 2 units. We can! 1m = 103 mm) 1. Identify your given. Place it far left. 103 mm 1205 m = _____mm 1.205 x106 m 1 2. Identify your unknown. Place it far right. (The given units are in the NUMERATOR. Your goal is to get rid of the units of your given. How?) 5. Cancel units & do the math! (Sig figs!) 3. Place the units of the given in the denominator of the conversion factor!

  41. Ex: Convert your weight from pounds (lbs) to kg. 4. Place units of the unknown in the numerator of the conversion factor. (if you can find a relationship between the 2 units. We can! 1kg = 2.2lb) 1. Identify your given. Place it far left. 1 kg 150 lbs = _____kg 68 lbs 2.2 2. Identify your unknown. Place it far right. The given units are in the NUMERATOR. Your goal is to get rid of the units of your given. How? 5. Cancel units & do the math! (Sig figs!) 3. Place the units of the given in the denominator of the conversion factor!

  42. Ex 3: How many minutes are in 2.5 hours? Conversion factor 2.5 hr x 60 min = 150 min 1 hr cancel By using dimensional analysis, the UNITS ensure that you have the conversion right side up, and the UNITS are calculated as well as the numbers!

  43. Example #4: PLEASE COPY How many seconds are in 1.4 days? Unit plan: days hr min seconds 1.4 days x 24 hr x _60min x 60 s =___s 1 day 1 hr 1 min ANSWER: 120,960 s. FINAL ANSWER (in sig figs) = 120,000 s

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