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Dimensional Analysis

Dimensional Analysis. 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

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Dimensional Analysis

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  1. Dimensional Analysis

  2. 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

  3. First- learn the metric prefixes • http://www.essex1.com/people/speer/large.html • You should memorize: • Kilo 1 x 103 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)

  4. 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

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

  6. 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

  7. 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

  8. Scientific Notation • Powers of 10? • 10 x 10 x 10 = 1000 or 103 • 10-n = 1/10n • So 10-3 = 1/103 = 1/1000 = 0.001

  9. 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 103 • 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

  10. 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 102 = 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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