Chapter 2- Learning Outcome 1_Mathematics for Technologists
- 1. 21st Century Mathematics for the Industrial Technology Learners: Automotive Technology BABY 'RLENE I. BAYOC
- 2. Measurements and Scientific Notation Chapter II 21st Century Mathematics for the Industrial Technology Learners: Automotive Technology
- 3. CHAPTER II: Measurements and Scientific Notations Learning Outcome 1: Explain the concept of measurement and scientific notation.
- 4. Measurement is the assignment of a number to a characteristic of an object or event, which can be compared with other objects or events using measuring devices or tools. There are two acceptable systems of measure that are used internationally, the Metric (SI) and the English system. The basic units of measurements in the metric system are Meter (m) for linear, Gram (g) for weight and Liter (L) for volume. The English system uses inch, foot, and the yard in measuring length. CHAPTER II: Measurements and Scientific Notations
- 5. THE METRIC SYSTEM OF MEASUREMENTS LENGTH millimeter (mm) 1 centimeter =10mm 1 decimeter =100mm =10cm 1 meter =1000mm =100cm =10dm 1 dekameter =10000mm =1000cm =100dm = 10m 1 hectometer =100000mm =10000cm =1000dm = 100m =10dkm 1 kilometer =1000000mm =100000cm =10000dm =1000m =100dkm =10hm WEIGHT VOLUME TIME milligram milliliter seconds centigram centiliter 1 minute = 60 seconds decigram deciliter 1 hour = 60 minutes gram liter 1 day = 24 hours dekagram dekaliter 1 week = 7 days hectogram hectoliter 1 month = 30 days kilogram kiloliter 1 year = 365 days CHAPTER II: Measurements and Scientific Notations
- 6. THE METRIC SYSTEM OF MEASUREMENTS MEASURABLE QUANTITIES UNIT ABREVIATION Acceleration meter per second squared m/s2 Amount of substance Mole mol Angle Radian R Angular Acceleration radian per second squared r/s2 Angular Velocity radian per second r/s Area square meter m2 Density kilogram per cubic meter kg/m3 Electrical Current Ampere A Energy Joule J or N-m Force Newton N or kg-m/s2 Frequency Hertz Hz or 1/s Impulse Newton-second kg-m/s CHAPTER II: Measurements and Scientific Notations
- 7. THE METRIC SYSTEM OF MEASUREMENTS MEASURABLE QUANTITIES UNIT ABREVIATION Length Meter M Luminous intensity Candela cd Mass Kilogram kg Moment of a Force Newton-meter N-m Power Watt W or J/s Pressure Pascal Pa or N/m2 Stress Pascal Pa or N/m2 Temperature Kelvin K Time Second S Velocity meter per second m/s Volume (solids) cubic meter m3 Volume (liquids) Liter L or 10-3 m3 Work Joule J or N-m CHAPTER II: Measurements and Scientific Notations
- 8. ENG LISH SYSTEM O F M EASUREM ENTS Length Capacity (Dry) 12 inches = 1 foot 16 fluid ounces = 1 pint 3 feet = 1 yard 2 pints = 1 quart 220 yards = 1 furlong 8 quarts = 1 peck 8 furlongs = 1 mile 4 pecks = 1 bushel 5,280 feet = 1 mile Capacity (Liquid) 1,760 yards = 1 mile 4 gills = 1 pint Mass 2 pints = 1 quart 437.5 grains = 1 ounce 4 quarts = 1 gallon 16 ounces = 1 pound Troy Weights 14 pounds = 1 stone 24 grains = 1 pennyweight 100 pounds = 1 hundredweight 20 pennyweights = 1 ounce Area Apothecaries' Measures 144 square inches = 1 square foot 60 minims = 1 fluid dram 9 square feet = 1 square yard 8 fluid drams = 1 fluid ounce 4,840square yards = 1 acre 16 fluid ounces = 1 pint 640 acres = 1 square mile Apothecaries' Weights 1 square mile = 1 section 20 grains = 1 scruple 36 sections = 1 township 3 scruples = 1 dram Volume 8 drams = 1 ounce 1,728 cubic inches = 1 cubic foot 27 cubic feet = 1 cubic yard CHAPTER II: Measurements and Scientific Notations
- 9. SCIENTIFIC NOTATION A real number x is said to be expressed in scientific notation if it is written in the form x = ± a.b × 10n, where n is an integer and 1 ≤ a ≤ 9 and b is a decimal number or zero. The integer n is called the characteristic of x, the number a.b is called the mantissa of x, and the factor 10n is called the order of magnitude of x. To change a number from ordinary decimal form to scientific notation, move the decimal point to obtain a number between 1 ≤ x < 10 and multiply by 10n or by 10–n , where n is the number of times the point moved to the left or to the right. CHAPTER II: Measurements and Scientific Notations
- 10. NAMES AND SCIENTIFIC PREFIXES FOR SOME INTEGER POWERS OF 10 Let us consider the number of electrons passing by a point in a circuit every second with a steady electric current of 1 amp: 1 amp = 6,250,000,000,000,000,000 electrons per second. This can be change to scientific notation by moving the decimal point 18 places to the left to obtain 6.250,000,000,000,000,000 and multiply it by 1018, so that 6,250,000,000,000,000,000 =6.25×1018 electron per second. Another example is the Proton mass = 0.000 000 000 000 000 000 000 00167 grams. To change it to scientific notation, we move the decimal point 25 places to the right to obtain 1.67 then multiply it by 10–25, so that we have 1.67×10–25 grams. CHAPTER II: Measurements and Scientific Notations
- 11. NAMES AND SCIENTIFIC PREFIXES FOR SOME INTEGER POWERS OF 10 Power of 10 Names Numeral Prefix Abbreviation 1018 Quintillion 1,000,000,000,000,000,000 Exa E 1015 Quadrillion 1,000,000,000,000,000 Peta P 1012 Trillion 1,000,000,000,000 Tera T 109 Billion 1,000,000,000 Giga G 106 Million 1,000,000 Mega M 103 Thousand 1,000 Kilo k 102 Hundred 100 Hecto h 101 Ten 10 Deka da 100 Unit 1 10–1 Tenth 0.1 Deci d 10–2 Hundredth 0.01 Centi c 10–3 Thousandth 0.001 Milli m 10–6 Millionth 0.000 001 Micro µ 10–9 Billionth 0.000 000 001 Nano n 10–12 Trillionth 0.000 000 000 001 Pico p 10–15 Quadrillionth 0.000 000 000 000 001 Femto f 10–18 Quintillionth 0.000 000 000 000 000 001 Atto A CHAPTER II: Measurements and Scientific Notations
- 13. CHAPTER II: Measurements and Scientific Notations Thank you