Chabot Mathematics 1 7 Sci Notat Using

Chabot Mathematics § 1. 7 Sci. Notat Using Units Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@Chabot. College. edu Chabot College Mathematics 1 Bruce Mayer, PE BMayer@Chabot. College. edu • MTH 55_Lec-03_sec_1 -7_Sci. Not_Units_Rules. ppt

Review § 1. 6 MTH 55 § Any QUESTIONS About • § 1. 6 → Exponent Properties § Any QUESTIONS About Home. Work • § 1. 6 → HW-02 Chabot College Mathematics 2 Bruce Mayer, PE BMayer@Chabot. College. edu • MTH 55_Lec-03_sec_1 -7_Sci. Not_Units_Rules. ppt

Scientific Notation § Scientific notation for a number is an expression of the type N × 10 m • Where: N is at least 1 but less than 10 (that is, 1 ≤ N < 10), • N is expressed in decimal notation • m is an integer. Chabot College Mathematics 3 Bruce Mayer, PE BMayer@Chabot. College. edu • MTH 55_Lec-03_sec_1 -7_Sci. Not_Units_Rules. ppt

Scientific Notation § Scientific notation for a number is an expression of the type N × 10 m § Note that when • m is positive the decimal point moves right m places in decimal notation • m is negative, the decimal point moves left |m| places. Chabot College Mathematics 4 Bruce Mayer, PE BMayer@Chabot. College. edu • MTH 55_Lec-03_sec_1 -7_Sci. Not_Units_Rules. ppt

Example Scientific Notation § Example - Convert to decimal notation: a) 3. 842 106 b) 5. 3 10− 7 § Solution: a) Since the exponent is positive, the decimal point moves right 6 places. 3. 842000 → 3. 842 106 = 3, 842, 000 b) Since the exponent is negative, the decimal point moves left 7 places. 0. 0000005. 3 → 5. 3 10− 7 = 0. 00000053 Chabot College Mathematics 5 Bruce Mayer, PE BMayer@Chabot. College. edu • MTH 55_Lec-03_sec_1 -7_Sci. Not_Units_Rules. ppt

Example Scientific Notation § Write in scientific notation: a) 94, 000 b) 0. 0423 § Solution a) We need to find m such that 94, 000 = 9. 4 10 m. § This requires moving the decimal point 4 places to the right. § 94, 000 = 9. 4 104 Chabot College Mathematics 6 Bruce Mayer, PE BMayer@Chabot. College. edu • MTH 55_Lec-03_sec_1 -7_Sci. Not_Units_Rules. ppt

Example Scientific Notation § Write in scientific notation: a) 94, 000 b) 0. 0423 § Solution b) To change 0. 0423 to 4. 23 we move the decimal point 2 places to the left. § 0. 0423 = 4. 23 10– 2 Chabot College Mathematics 7 Bruce Mayer, PE BMayer@Chabot. College. edu • MTH 55_Lec-03_sec_1 -7_Sci. Not_Units_Rules. ppt

Multiplying and Dividing Using Scientific Notation § Products and quotients of numbers written in scientific notation are found using the rules for exponents. Example - Simplify: (1. 7 108)(2. 2 10− 5) Solution (1. 7 108)(2. 2 10− 5) = (1. 7 2. 2) (108 10− 5) = 3. 74 108 +(− 5) = 3. 74 103 Chabot College Mathematics 8 Bruce Mayer, PE BMayer@Chabot. College. edu • MTH 55_Lec-03_sec_1 -7_Sci. Not_Units_Rules. ppt

Example Divide § Simplify (6. 2 10− 9) (8. 0 108) § Solution (6. 2 10− 9) (8. 0 108) = Chabot College Mathematics 9 Bruce Mayer, PE BMayer@Chabot. College. edu • MTH 55_Lec-03_sec_1 -7_Sci. Not_Units_Rules. ppt

Multiply & Divide Summary § If Multiplying in Scientific Notation, then • MULTIPLY Decimal Numbers • ADD Exponent Numbers § If Dividing in Scientific Notation, then • DIVIDE Decimal Numbers • SUBTRACT Exponent Numbers Chabot College Mathematics 10 Bruce Mayer, PE BMayer@Chabot. College. edu • MTH 55_Lec-03_sec_1 -7_Sci. Not_Units_Rules. ppt

Scientific Notation Procedure § Move the decimal point to the right or left until you have a number that is greater than or equal to 1, but less than 10. § Count how many places you moved the decimal point. This number will become the absolute value of the exponent. § If you moved the decimal point to the left, the exponent will be positive. § If you moved the decimal point to the right, make the exponent negative. Chabot College Mathematics 11 Bruce Mayer, PE BMayer@Chabot. College. edu • MTH 55_Lec-03_sec_1 -7_Sci. Not_Units_Rules. ppt

Left↔Right? Top↨Bottom? What? ? ? § When deciding on the SIGN for the Exponent in Scientific Notation § If the Number is ≥ 10, then the Exponent is POSTIVE § If the Number is <1, then the Exponent is NEGATIVE § If the Number is ≥ 1 & <10, then the Exponent is ZERO • i. e. , NO “x 10 n” needed Chabot College Mathematics 12 Bruce Mayer, PE BMayer@Chabot. College. edu • MTH 55_Lec-03_sec_1 -7_Sci. Not_Units_Rules. ppt

More Examples § Write in Scientific Notation: a) 1043 b) 2. 5 c) 0. 000495 § Scientific Notation Solutions a) 1. 043 103 b) 2. 5 100 = 2. 5 1 = 2. 5 c) 4. 95 10− 4 a) The decimal is to the right of the 3. Move it LEFT 3 places. b) This number is already greater than or equal to one and less than 10. Therefore, the decimal does NOT have to be moved and the exponent will be 0 c) Move the decimal RIGHT 4 places. Chabot College Mathematics 13 Bruce Mayer, PE BMayer@Chabot. College. edu • MTH 55_Lec-03_sec_1 -7_Sci. Not_Units_Rules. ppt

Example Mass of an Atom § As you will learn § The Primary when you take Sub. Atomic Particles CHEM 1 A & and their masses ENGR 45 all matter • Protons → 1. 67 10− 27 kg is made of VERY small particles called • Neutrons → 1. 67 10− 27 kg ATOMS • Electrons → § Atoms are, in turn, 9. 11 10− 31 kg composed of SUB-atomic Particles Chabot College Mathematics 14 Bruce Mayer, PE BMayer@Chabot. College. edu • MTH 55_Lec-03_sec_1 -7_Sci. Not_Units_Rules. ppt

Example Mass of 107 Ag § Now take the Metal Silver (Chem Symbol Ag). § The 107 Ag atom “Isotope” contains • 47 Protons • 47 Electrons • 60 Neutrons § Find the Mass of a 107 Ag atom Chabot College Mathematics 15 Bruce Mayer, PE BMayer@Chabot. College. edu • MTH 55_Lec-03_sec_1 -7_Sci. Not_Units_Rules. ppt

Example Mass of 107 Ag 1. Find Total PROTON Mass 2. Find Total ELECTRON Mass 3. Find Total NEUTRON Mass Chabot College Mathematics 16 Bruce Mayer, PE BMayer@Chabot. College. edu • MTH 55_Lec-03_sec_1 -7_Sci. Not_Units_Rules. ppt

Example Mass of 107 Ag § Add the Total Masses of the all the Sub. Atomic particles Chabot College Mathematics 17 Bruce Mayer, PE BMayer@Chabot. College. edu • MTH 55_Lec-03_sec_1 -7_Sci. Not_Units_Rules. ppt

Chabot Mathematics Chp 1 Extra Using Units Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@Chabot. College. edu Chabot College Mathematics 18 Bruce Mayer, PE BMayer@Chabot. College. edu • MTH 55_Lec-03_sec_1 -7_Sci. Not_Units_Rules. ppt

Physical Quantities § Anything that we can “Feel” or “See” or “Sense” can be MEASURED. These Things are PHYSICAL Quantities • e. g. ; Time, Temperature, Length, Angle § To “Measure” a physical quantity We need a “Ruler” that describes the “Size” of the Quantity. This “Sizing” leads to the concept of UNITS Chabot College Mathematics 19 Bruce Mayer, PE BMayer@Chabot. College. edu • MTH 55_Lec-03_sec_1 -7_Sci. Not_Units_Rules. ppt

Units Introduction § People MEASURE quantities through COMPARISONS with STANDARDS. § Every measured quantity has an associated “UNIT” Which is the NAME of the Standard. § Need to define SENSIBLE and PRACTICAL "units" and "standards" that People everywhere can AGREE upon § Even though there exist an almost INFINITE number of different physical quantities, we need no more than a handful of “BASE” standards. Chabot College Mathematics 20 Bruce Mayer, PE BMayer@Chabot. College. edu • MTH 55_Lec-03_sec_1 -7_Sci. Not_Units_Rules. ppt

SI System of Units § Système International d'Unités (International System of Units) § A Completely Consistent Set of Basic Units • Requires NO Conversion factors – e. g. , 18 inches = 1. 5 feet • Defined by UNCHANGING Physical Phenomena – Except for one. . . Chabot College Mathematics 21 http: //www. bipm. org/en/si/ Bruce Mayer, PE BMayer@Chabot. College. edu • MTH 55_Lec-03_sec_1 -7_Sci. Not_Units_Rules. ppt

SI Base Units § From this List Observe SI Base Units Base quantity Name Symbol length meter m mass kilogram kg time second s electric current ampere A thermodynamic temperature kelvin K amount of substance mol candela cd luminous intensity § All But the kg are defined by Physical Phenomena • Examine the Defs Chabot College Mathematics 22 • Very common Units – Mass (kg) – Length (m) – Time (s) • Some Not so Common Units – Current (A) – Temperature (K) • Some Uncommon units – Substance amt (mol) – Luminous Int (cd) Bruce Mayer, PE BMayer@Chabot. College. edu • MTH 55_Lec-03_sec_1 -7_Sci. Not_Units_Rules. ppt

Second Defined § Time (Second) § The duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom • This is the Definition of an “Atomic” Clock – more than 200 atomic clocks are located in metrology institutes and observatories in more than 30 countries around the world Chabot College Mathematics 23 Bruce Mayer, PE BMayer@Chabot. College. edu • MTH 55_Lec-03_sec_1 -7_Sci. Not_Units_Rules. ppt

Meter Defined § Length or Distance (meter) § “The path traveled by light in vacuum during a time interval of 1/299792458 of a second. ” 1 meter Laser photon Chabot College Mathematics 24 1/299792458 s Bruce Mayer, PE BMayer@Chabot. College. edu • MTH 55_Lec-03_sec_1 -7_Sci. Not_Units_Rules. ppt

Kilogram Defined § Mass (Kilogram) § a cylinder of PLATINUMIRIDIUM alloy maintained under vacuum conditions by the International Bureau of Weights and Measures in Paris If The Proto. Type Were Cubic, its Edge Length would be About 36. 2 mm (1. 42”); quite small Chabot College Mathematics 25 Bruce Mayer, PE BMayer@Chabot. College. edu • MTH 55_Lec-03_sec_1 -7_Sci. Not_Units_Rules. ppt

Amp Defined § Electric Current (ampere) § That constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 m apart in vacuum, would produce between these conductors a force equal to 2 x 10− 7 Newton per metre of length. • What’s a Newton? → 1 kg-m/(s 2) Chabot College Mathematics 26 Bruce Mayer, PE BMayer@Chabot. College. edu • MTH 55_Lec-03_sec_1 -7_Sci. Not_Units_Rules. ppt

Kelvin (Temperature) Defined § § Thermodynamic temperature (Kelvin) The unit of thermodynamic temperature, is the fraction 1/273. 16 of thermodynamic temperature of the triple point of water. § 273. 16 K = 0. 0098 °C § Room Temperature (72 °F) is about 295. 5 Kelvins § NO “Degree” Sign Used with the Kelvin Unit Chabot College Mathematics 27 Bruce Mayer, PE BMayer@Chabot. College. edu • MTH 55_Lec-03_sec_1 -7_Sci. Not_Units_Rules. ppt

mole (amt of Substance) Defined § Amount of § The mole is the amount of substance of a system which Substance contains as many elementary (mole) entities as there atoms in 0. 012 kilogram of carbon 12. § 1 mol = 6. 023 x 1023 entities • entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles. Chabot College Mathematics 28 Bruce Mayer, PE BMayer@Chabot. College. edu • MTH 55_Lec-03_sec_1 -7_Sci. Not_Units_Rules. ppt

Luminous Intensity Defined § The luminous intensity, in a given § Light direction, of a source that emits Brightness monochromatic radiation (one(candela) color light) of frequency 540 x 1012 Hertz (λ = 555. 5 nm) and that has a radiant intensity in that direction of 1/683 watt per steradian § The are 4 (12. 57) Steradians in a sphere • 1 Str = 7. 96% of the Sphere Surface Chabot College Mathematics 29 Bruce Mayer, PE BMayer@Chabot. College. edu • MTH 55_Lec-03_sec_1 -7_Sci. Not_Units_Rules. ppt

Units Have Evolved § Candela Predecessor based on a Flame • Hence the Name § Temperature Based on Freezing points • Water • Platinum § Second Based on the Sidereal (standard) day Chabot College Mathematics 30 Bruce Mayer, PE BMayer@Chabot. College. edu • MTH 55_Lec-03_sec_1 -7_Sci. Not_Units_Rules. ppt

Units Have Evolved § History of the Meter (or Metre) • One ten millionth of the distance from the North pole to the equator. • The distance between two fine lines engraved near the ends of a platinum-iridium bar • 1 650 763. 73 wavelengths of a particular orange-red light emitted by atoms of krypton-86 (86 Kr). • The length of the path traveled by light in a vacuum during a time interval of 1/299 792 458 of a second. Chabot College Mathematics 31 Bruce Mayer, PE BMayer@Chabot. College. edu • MTH 55_Lec-03_sec_1 -7_Sci. Not_Units_Rules. ppt

SI Derived Units § The Seven Base Units May be Arithmetically Combined to Produce “Derived Units” • e. g. : § Several Derived Units have Special Usefulness And Given their OWN Names Chabot College Mathematics 32 Bruce Mayer, PE BMayer@Chabot. College. edu • MTH 55_Lec-03_sec_1 -7_Sci. Not_Units_Rules. ppt

Some Derived Units Derived quantity Name Symbol Expression in terms of other SI units Expression in terms of SI base units plane angle radian (a) rad - m·m-1 = 1 (b) solid angle steradian (a) sr (c) - m 2·m-2 = 1 (b) frequency hertz Hz - s-1 force newton N - m·kg·s-2 pressure, stress pascal Pa N/m 2 m-1·kg·s-2 energy, work, quantity of heat joule J N·m m 2·kg·s-2 power, radiant flux watt W J/s m 2·kg·s-3 electric charge, quantity of electricity coulomb C - s·A Chabot College Mathematics 33 Bruce Mayer, PE BMayer@Chabot. College. edu • MTH 55_Lec-03_sec_1 -7_Sci. Not_Units_Rules. ppt

Some (more) Derived Units Derived quantity Name Symbol Expression in terms of other SI units Expression in terms of SI base units electric potential difference, volt electromotive force V W/A m 2·kg·s-3·A-1 capacitance farad F C/V m-2·kg-1·s 4·A 2 electric resistance ohm V/A m 2·kg·s-3·A-2 electric conductance siemens S A/V m-2·kg-1·s 3·A 2 magnetic flux Weber Wb V·s m 2·kg·s-2·A-1 magnetic flux density tesla T Wb/m 2 kg·s-2·A-1 inductance henry H Wb/A m 2·kg·s-2·A-2 Celsius temperature degree Celsius °C - K luminous flux lumen lm cd·sr (c) m 2·m-2·cd = cd illuminance lux lx lm/m 2 Chabot College Mathematics 34 m 2·m-4·cd = m 2·cd Bruce Mayer, PE BMayer@Chabot. College. edu • MTH 55_Lec-03_sec_1 -7_Sci. Not_Units_Rules. ppt

Old (and Tired) Unit Sets § MKS • Stands for Meter-Kilogram-Second in the Most Common Units – Predecessor to The SI Units § CGS • Means Centimeter-Gram-Second – Still Widely Used § IPS, FPM, FPH • Inch-Pound-Sec, Foot-Lb-Min, Ft-Lb-Hour Chabot College Mathematics 35 Bruce Mayer, PE BMayer@Chabot. College. edu • MTH 55_Lec-03_sec_1 -7_Sci. Not_Units_Rules. ppt

American Engineering System, AES – Still in (declining) Use Fundamental Dimension Base Unit So length foot (ft) mass pound (lbm) force pound (lbf) time second (sec) electric charge [Q] coulomb (C) absolute temperature degree Rankine (o. R) luminous intensity candela (cd) amount of substance mole (mol) Chabot College Mathematics 36 m SA e A M re t E h SI e Bruce Mayer, PE BMayer@Chabot. College. edu • MTH 55_Lec-03_sec_1 -7_Sci. Not_Units_Rules. ppt

Conservation of Units § Principle of conservation of units: • Units on the LEFT side of an equation MUST be the SAME as those on the RIGHT side of an Equation § Then Have Dimensional homogeneity • Needed to Prevent “Apples & Oranges” Confusion – e. g. , I Buy 100 ft of Wire at One Store and 50 m at another; how much total Wire do I have? Ø It’s NOT “ 150” Chabot College Mathematics 37 Bruce Mayer, PE BMayer@Chabot. College. edu • MTH 55_Lec-03_sec_1 -7_Sci. Not_Units_Rules. ppt

Unit Conversion by Chain-Link § To Determine the Amount of Wire I have Need to Convert to Consistent (Homogeneous) Units § Start by Thinking About the Definition of “ 1” • Now Consider a “minute” § Read as “ 60 Seconds per minute” Chabot College Mathematics 38 Bruce Mayer, PE BMayer@Chabot. College. edu • MTH 55_Lec-03_sec_1 -7_Sci. Not_Units_Rules. ppt

Chain-Link Unit Conversion § Also Units can be Multiplied and Divided in a manner similar to Numbers • This how we get, say, “Square Feet” – e. g. ; Consider an 8 ft x 10 ft Engineer’s Cubicle in Dilbert-Land. How Much Work. Space Does the Engineer Have? § Now Back to the Wire • Want to Know how many FEET of Wire I have in Total Chabot College Mathematics 39 Bruce Mayer, PE BMayer@Chabot. College. edu • MTH 55_Lec-03_sec_1 -7_Sci. Not_Units_Rules. ppt

Chain-Link Unit Conversion cont. § Check on the Internet and Find that there are 3. 2808 ft in one meter • Multiply the 50 m by this special Value of 1 § Can “Cancel” The Units by Division § So then the Total Wire = 100 ft + 164 ft = 264 ft Chabot College Mathematics 40 Bruce Mayer, PE BMayer@Chabot. College. edu • MTH 55_Lec-03_sec_1 -7_Sci. Not_Units_Rules. ppt

Chain Link Examples § A World-Class Sprinter can Run 100 m in 10 s. • How Fast is this in MPH? § Gasoline In Hamburg Germany Costs 1. 10 € for one Liter of Regular Unleaded • How Much is this in $ per Gallon – Find Currency Exchange Rate → $1 = 0. 787 € Chabot College Mathematics 41 Bruce Mayer, PE BMayer@Chabot. College. edu • MTH 55_Lec-03_sec_1 -7_Sci. Not_Units_Rules. ppt

Some Unit Conversions § See Also http: //www. onlineconversion. com/ Chabot College Mathematics 42 Bruce Mayer, PE BMayer@Chabot. College. edu • MTH 55_Lec-03_sec_1 -7_Sci. Not_Units_Rules. ppt

White. Board Work § Problems From § 1. 7 Exercise Set • 64, 66, 68 § “Seward’s Folly” ≡ 1868 Purchase of Alaska from Russia For $7. 2 M Chabot College Mathematics 43 Bruce Mayer, PE BMayer@Chabot. College. edu • MTH 55_Lec-03_sec_1 -7_Sci. Not_Units_Rules. ppt

White Board Example § The USA FDA recommends that Adults consume 2200 Calories per Day • What then is the “Power Rating” of a Grown Human Being? – Note that are TWO types of “Calories” 1. The Amount of Heat Required to Raise the Temperature of 1 GRAM of water by 1 °C (or 1 Kelvin) Ø Often Called the Gram-CAL; used in the CGS system 2. The Amount of Heat Required to Raise the Temperature of 1 KILOgram of water by 1 °C Ø Often Called the Kg. CAL; This is what you read on the side of Food Packaging Chabot College Mathematics 44 Bruce Mayer, PE BMayer@Chabot. College. edu • MTH 55_Lec-03_sec_1 -7_Sci. Not_Units_Rules. ppt

White Board Examples § A 1966 Dodge Hemi Engine • 426 Cubic Inch V 8 – What is the Engine Displacement in Litres? • Develops 425 HP – What is the Power in Watts? § The 2006 Toyota Prius Hybrid Synergy Drive System has a Torque rating of 400 Newton-Meters (Nm) • What is this Torque in Ft-Lbs? Chabot College Mathematics 45 Bruce Mayer, PE BMayer@Chabot. College. edu • MTH 55_Lec-03_sec_1 -7_Sci. Not_Units_Rules. ppt

All Done for Today More Info on Silver Isotopes Atomic Relative Isotope Mass Abundance (g/mol) (at %) 107 Ag 106. 905 51. 839 109 Ag 108. 905 48. 161 § http: //www. webelements. com/webelements/el ements/text/Ag/isot. html Chabot College Mathematics 46 Bruce Mayer, PE BMayer@Chabot. College. edu • MTH 55_Lec-03_sec_1 -7_Sci. Not_Units_Rules. ppt

All Done for Today Cooking Conversions Chabot College Mathematics 47 • 16 tablespoons = 1 cup • 12 tablespoons = 3/4 cup • 10 tablespoons + 2 teaspoons = 2/3 cup • 8 tablespoons = 1/2 cup • 6 tablespoons = 3/8 cup • 5 tablespoons + 1 teaspoon = 1/3 cup • 4 tablespoons = 1/4 cup • 2 tablespoons = 1/8 cup • 1 tablespoon = 1/16 cup • 2 cups = 1 pint • 2 pints = 1 quart • 3 teaspoons = 1 tablespoon • 48 teaspoons = 1 cup Bruce Mayer, PE BMayer@Chabot. College. edu • MTH 55_Lec-03_sec_1 -7_Sci. Not_Units_Rules. ppt

Chabot Mathematics Appendix Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@Chabot. College. edu – Chabot College Mathematics 48 Bruce Mayer, PE BMayer@Chabot. College. edu • MTH 55_Lec-03_sec_1 -7_Sci. Not_Units_Rules. ppt