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Dimensional Analysis

Dimensional Analysis. Dimensional Analysis. Unit conversion using conversion factors Conversion factor- a fraction based on a definition and equal to 1 Example: Definition (from the prefixes chart) 1 cm = 0.01 m Conversion factors possible: 1 cm 0.01 m 0.01 m OR 1 cm. Intro.

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Dimensional Analysis

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  1. Dimensional Analysis

  2. Dimensional Analysis • Unit conversion using conversion factors • Conversion factor- a fraction based on a definition and equal to 1 • Example: • Definition (from the prefixes chart) 1 cm = 0.01 m • Conversion factors possible: 1 cm0.01 m0.01 m OR 1 cm

  3. Intro • How long can you hold your breath? • Convert it to DAYS!

  4. To Convert between Units Convert from 5.8 m to cm • Write your given: 5.8 m • Write your definition (based on the prefixes chart)- how are your units related? 1 cm = 0.01 m 3. Setup your conversion factor like this:

  5. Converting between units- continued • (still step 3) & Step 4- solve. Cancel unit that occur on both the top and the bottom.

  6. Conversion Factor The larger number goes with the smaller unit The smaller number goes with the larger unit

  7. Examples of dimensional analysis For significant figures, look at the original number, so the answer should be 15.9 cm. The conversion factor should generally not be considered when determining significant figures because it is a definition, an exact value. Exception- when you calculated the number to use in the conversion factor.

  8. Examples of dimensional analysis • Convert 2.6 km to mm • First- what is the desired unit? • Answer- mm • Second- how to we get from km 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

  9. More examples

  10. 3.3 Section Quiz • 1. 1 Mg = 1000 kg. Which of the following would be a correct conversion factor for this relationship? •  1000. •  1/1000. • ÷ 1000. • 1000 kg/1Mg.

  11. 3.3 Section Quiz • 2. The conversion factor used to convert joules to calories changes • the quantity of energy measured but not the numerical value of the measurement. • neither the numerical value of the measurement nor the quantity of energy measured. • the numerical value of the measurement but not the quantity of energy measured. • both the numerical value of the measurement and the quantity of energy measured.

  12. 3.3 Section Quiz • 3. How many  g are in 0.0134 g? • 1.34  10–4 • 1.34  10–6 • 1.34  106 • 1.34  104

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