Metric Conversions, Scientific Notation, and Dimensional Analysis

International System of Units Built on a set of seven metric units, called base units (base units contain no prefix…examples are grams, meter, and liter) Prefixes are added to the names of SI base units to represent quantities that are larger or smaller than the base units (examples are kilogram, centimeter, and milliliter)

Units of Measurement Length – meter (m), kilometer (km) Mass – kilogram (kg), gram (g) Time – second (s) Temperature – Kelvin (K) or Celsius (C) Amount of substance – mole (mol) Volume- liter (L), milliliter (mL)

Metric Prefixes and Symbols Kilo – k Hecto – h Deka – da BASE Deci – d Centi – c Milli – m K ing H enry D ied B y D rinking C hocolate M ilk Example Problems (hyperlink)

Derived SI Units Units derived from multiplying, dividing units Examples: Volume – cubic meter (m 3 ) Density – kg per cubic meter (kg/m 3 )

Unit Conversions Tutorial – Home Unit Conversions Tutorial – Home 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

Example Problems A baker uses 1.5 tsp of vanilla extract in each cake. How much vanilla in liters is consumed to make 800 cakes? (1tsp = 5mL) Answer  6 L A person drinks eight glasses of water a day. Each glass contains 300 mL. How many liters will a person drink in 1 yr? Answer  876 L

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 Numbers less than 1 will have negative exponents Ex will be written as 1 x (hyperlink)