Dimensional Analysis  What happens when you divide a number by itself?  What happens when you divide a unit by itself?  In both cases, you get the number 1.  Dimensional analysis involves multiplication and division.  Focus on cancelation of UNITS  Just another method of unit conversion

Conversion factors  To convert between units:  Figure out what CONVERSION FACTOR you need to perform your calculation  Conversion factors – take a definition and turn it into a fraction equal to one – for example:  There are 12 inches in 1 foot  12 inches or 1 foot 1 foot 12 inches

Examples of dimensional analysis Multiply across the top. Divide by whatever’s on the bottom

Examples of dimensional analysis  Convert 2.6 km to mm  First- what is the desired unit?  Answer- mm  Second- how to we get from m to mm?  We know that 1 km = 1000 m  We know that 1 m = 1000 mm  2.6 km( 1000 m )(1000 mm) = m 1 km 1 m

Scientific Notation  Why do we need to know this?  It’s hard to work with numbers like this:  6,000,000,000,000,000,000,000  Or this  What is scientific notation?  Simplifying large or small numbers by converting them to a number between 1 and 10 multiplied by powers of 10

Scientific Notation  Powers of 10?  10 x 10 x 10 = 1000 or 10 3  10 -n = 1/10 n  So = 1/10 3 = 1/1000 = 0.001

Converting regular notation to Scientific Notation  Always move the decimal so there is one number LEFT of the decimal  If the original number is LARGER than 1 and the decimal is moved to the LEFT, use a positive exponent  1,567 = x 10 3  If the original number is SMALLER than 1 and the decimal is moved to the RIGHT, use a negative exponent  = 4.5 x 10 -6

Converting from scientific notation to regular notation  Move the decimal the number of places indicated by the exponent.  If the exponent is positive, your final number should be larger than 1  5.6 x 10 2 = 560  I f the exponent is negative, your final number should be smaller than 1  5.6 x = 0.056