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Easy Dimensional Analysis: Methods & Examples

Learn about dimensional analysis, unit conversion, and scientific notation effortlessly. Understand how to multiply, divide, and convert units with cancelation techniques. Master converting from regular to scientific notation and vice versa.

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Easy Dimensional Analysis: Methods & Examples

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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. 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

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

  5. 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

  6. 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

  7. 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

  8. 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

  9. 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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