Presentation on theme: "What is Scientific Notation?"— Presentation transcript:
1 What is Scientific Notation? 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.For very large and very small numbers, scientific notation is more concise.
2 Scientific notation consists of two parts: A number between 1 and 10A power of 10N x 10x
3 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.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.
4 Examples Given: 289,800,000 Use: 2.898 (moved 8 places) Answer: x 108Given:Use: 5.67 (moved 4 places)Answer: 5.67 x 10-4
5 To change scientific notation to standard form… Simply move the decimal point to the right for positive exponent 10.Move the decimal point to the left for negative exponent 10.(Use zeros to fill in places.)
6 Example Answer: 5,093,000 (moved 6 places to the right) Given: x 10-4Answer: (moved 4 places to the left)Given: x 106
7 Learning Check Express these numbers in Scientific Notation: 405789 2
9 Significant DigitsIn 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
10 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.
11 Significant Digits (Cont.) Rule 1: ALL non-zero digits are significant.Example:has 5 significant digits since all numbers are non-zero numbers.
12 Significant Digits (Cont.) Rule 2: Zeros preceding (coming before) the first non-zero number are NEVER significant. (Leading) ZerosExample:has only 3 significant digits. The zeros preceding the number 1 are just keeping space in the number.
13 Significant Digits (Cont.) 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.
14 Significant Digits (Cont.) 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.100. Has three significant digits, however, since there is a decimal present.WHY?
15 Significant Digits (Cont.) How Many Sig. Digs. Do the following numbers have?mkg3500 V1,809,000 LAnswers6 significant digits2 significant digits4 significant digits
16 Significant Digits (Cont.) 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
17 Significant Digits (Cont.) Rule for Addition/SubtractionThe number of significant digits allowed in our calculated answer depends on the number with the largest uncertainty.Example: ggggg
18 Significant Digits (Cont.) 4 sig digs5 sig digs7 sig digsThe 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.
19 Significant Digits (Cont.) Rule for Multiplication/DivisionThe 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)
20 Significant Digits (Cont.) V = (3.052 m) x (2.10 m) x (0.75 m)(4 sig figs)(3 sig figs)(2 sig figs)V = m3 (5 sig figs)V = 4.8 m3
21 Significant Digits (Cont.) One Last RuleAny numbers that are exact, do not affect the number of significant digits in the final answer.Exact numbers are constants:12 inches/foot; 3.14, 2.54 cm/inch
23 UNITS OF MEASUREMENT Use SI units — based on the metric system Length MassVolumeTimeTemperatureMeter, mKilogram, kgLiter, LSeconds, sCelsius degrees, ˚Ckelvins, K
24 Some Tools for Measurement Which tool(s) would you use to measure:A. temperatureB. volumeC. timeD. weight
25 Learning Check M L M V 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.MLMV
26 Learning CheckWhat are some U.S. units that are used to measure each of the following?A. lengthB. volumeC. weightD. temperature
27 Solution Some possible answers are A. length inch, foot, yard, mile B. volume cup, teaspoon, gallon, pint, quartC. weight ounce, pound (lb), tonD. temperature °F
28 Metric Prefixes Kilo- means 1000 of that unit 1 kilometer (km) = meters (m)Centi- means 1/100 of that unit1 meter (m) = 100 centimeters (cm)1 dollar = 100 centsMilli- means 1/1000 of that unit1 Liter (L) = milliliters (mL)
31 Units of Length ? kilometer (km) = 500 meters (m) 2.5 meter (m) = ? centimeters (cm)1 centimeter (cm) = ? millimeter (mm)1 nanometer (nm) = 1.0 x 10-9 meterO—H distance =9.4 x m9.4 x 10-9 cm0.094 nm
32 Learning Check Select the unit you would use to measure 1. Your height a) millimeters b) meters c) kilometers2. Your massa) milligrams b) grams c) kilograms3. The distance between two citiesa) millimeters b) meters c) kilometers4. The width of an artery
33 Solution 1. Your height a) millimeters b) meters 2. Your mass c) kilograms3. The distance between two citiesc) kilometers4. The width of an arterya) millimeters
34 Equalities State the same measurement in two different units length 25.4 cm
35 Learning Check 1. 1000 m = 1 ___ a) mm b) km c) dm g = 1 ___ a) mg b) kg c) dgL = 1 ___ a) mL b) cL c) dLm = 1 ___ a) mm b) cm c) dm
36 Conversion FactorsFractions in which the numerator and denominator are EQUAL quantities expressed in different unitsExample: in. = 2.54 cmFactors: 1 in and cm2.54 cm in.
37 Learning Check 1. Liters and mL 2. Hours and minutes Write conversion factors that relate each of the following pairs of units:1. Liters and mL2. Hours and minutes3. Meters and kilometers
38 How many minutes are in 2.5 hours? Conversion factor2.5 hr x min = min1 hrcancelBy 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!
39 Sample ProblemYou have $7.25 in your pocket in quarters. How many quarters do you have?7.25 dollars quarters1 dollarX= 29 quarters
40 Learning CheckA rattlesnake is 2.44 m long. How long is the snake in cm?a) 2440 cmb) 244 cmc) 24.4 cm
41 Learning Check How many seconds are in 1.4 days? Unit plan: days hr min seconds1.4 days x 24 hr x ??1 day
42 = 1.2 x 105 sec Solution Unit plan: days hr min seconds 1.4 day x 24 hr x 60 min x 60 sec1 day hr min= 1.2 x 105 sec
43 Wait a minute! What is wrong with the following setup? 1.4 day x 1 day x min x 60 sec24 hr hr min
44 English and Metric Conversions If you know ONE conversion for each type of measurement, you can convert anything!You will need to know and use these conversions:Mass: 454 grams = 1 poundLength: cm = 1 inchVolume: L = 1 quart
45 An adult human has 4.65 L of blood. How many gallons of blood is that? Learning CheckAn adult human has 4.65 L of blood. How many gallons of blood is that?Unit plan: L qt gallonEqualities: 1 quart = L1 gallon = 4 quartsYour Setup:
46 Steps to Problem Solving Read problemIdentify dataMake a unit plan from the initial unit to the desired unitSelect conversion factorsChange initial unit to desired unitCancel units and checkDo math on calculatorGive an answer using significant figures
47 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 feet?
48 Solution 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 = sec65 m min
49 Temperature Scales Fahrenheit Celsius Kelvin Anders Celsius 1701-1744 Lord Kelvin(William Thomson)
50 Temperature Scales Fahrenheit Celsius Kelvin 32 ˚F 212 ˚F 180˚F 100 ˚C Boiling point of water32 ˚F212 ˚F180˚F100 ˚C0 ˚C100˚C373 K273 K100 KFreezing point of waterNotice that 1 kelvin = 1 degree Celsius
51 Calculations Using Temperature Generally require temp’s in kelvinsT (K) = t (˚C)Body temp = 37 ˚C = 310 KLiquid nitrogen = ˚C = 77 K