 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.

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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

First- learn the metric prefixes  http://www.essex1.com/people/speer/large.ht ml http://www.essex1.com/people/speer/large.ht ml  You should memorize: 3 base units or 1000 base units  Kilo 1 x 10 3 base units or 1000 base units  So 1 km = 1000 m  Centi 1 x 10 -2 base units or 0.01 base units  So 1 cm = 0.01 m OR 100 cm = 1 m  Milli 1 x 10 -3 base units or 0.001 base units  So 1 mm = 0.001 m OR 1000 mm = 1m  Be able to use a chart for the others!  On the chart, use 1 with the prefix. Use the other number with the base unit (L, m, g)

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) = 2600000 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 0.00000000000000000000876  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 10 -3 = 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 = 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  0.0000045 = 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 10 -2 = 0.056

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