Metric Conversions, Scientific Notation, and Dimensional Analysis

Metric Conversions, Scientific Notation, and Dimensional Analysis

Scientific Notation Steps for converting: Put the decimal after the first digit and drop the zeros Ex. 123,000,000,000 1.23 To find the exponent, count the number of places from the decimal to the end of the number. Ex. In 123,000,000,000 there are 11 places therefore we write it as 1.23 x 1011 Numbers less than 1 will have negative exponents Ex. 0.000001 will be written as 1 x 10-6

Examples Convert: 0.005 5,050 0.0008 1,000 1,000,000 0.25 0.025 0.0025 500 5,000

International System of Units Built on a set of seven metric units, called base units Prefixes are added to the names of SI base units to represent quantities that are larger or smaller than the base units

SI Base Units Length – meter (m) Mass – kilogram (kg) Time – second (s) Temperature – Kelvin (K) Amount of substance – mole (mol) Electric current – ampere (A) Luminous intensity – candela (cd)

Metric Prefixes and Symbols Kilo – k Hecto – h Deka – da BASE Deci – d Centi – c Milli – m King Henry Died By Drinking Chocolate Milk

Metric Conversions Practice Problems 1. 2. 3. 4. 5. 6. 7. 8. 100m km 3m mm 230cm m 461mm m 2500m km 4500mg g 2000g mg 200g kg 9. 10. 11. 12. 13. 14. 15. 23L mL 0.14mm m 1550mm m 4000mL L 1.4kg g 1452mg g 9.5m cm

Derived SI units Area – sq. meter (m2) Volume – cubic meter (m3) Density – kg per cubic meter (kg/m3) Molar mass – kg per mole (kg/mol) Concentration – moles per liter (M) Molar volume – cubic meters per mol (m3/mol)

Dimensional Analysis The technique of converting between units Uses: 1. Unit equalities – an equation that shows how different units are related (ex. 1cm 0.01m) 2. Conversion factors – equation that always equals one (ex. 1cm/0.01m) *Multiply the conversion factor so that units you do not want cancel and the unit that you do want ends up on top

Homework Problems 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 64.5dm mm 91.2m km 96.5in yds 1.235ft cm 8.95kJ cal 34.5miles m 52.3cm ft 6.98m/min km/hr 59.63cal J 96.5kJ cal 1year sec