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3.2-3.3 - Dimensional Analysis

3.2-3.3 - Dimensional Analysis. Use the equivalence statement/conversion factor that relates the two units. Choose the appropriate conversion factor to make the required change (make sure unwanted units cancel) Multiply the quantity to be converted by the conversion factor.

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3.2-3.3 - Dimensional Analysis

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  1. 3.2-3.3- Dimensional Analysis

  2. Use the equivalence statement/conversion factor that relates the two units. Choose the appropriate conversion factor to make the required change (make sure unwanted units cancel) Multiply the quantity to be converted by the conversion factor. Check to make sure you have correct sig figs and the units that you wanted. Converting from One Unit to Another

  3. Conversion factor: • A numerical factor used to multiply or divide a quantity when converting from one system of units to another. • Conversion factors are always equal to 1 • Dimensional analysis: • A fancy way of saying “converting units” by using conversion factors Dimensional Analysis

  4. Suppose you want to know how many meters are in 48 km. You have to choose a conversion factor that relates kilometers to meters. You know that for every 1 kilometer there is 1000 meters. What will your conversion factor be? 1000m/1km Now that you know your conversion factor, you can multiply it by your known…BUT you want to make sure you set it up so that kilometers cancels out. How would you do this? Dimensional analysis uses conversion factors

  5. 48km x 1000m 1km =48,000 m TIP: Put the units you already have on the bottom of the conversion factor and the units you want on top.

  6. Practice*you can find conversion factors in the back cover of your book! Convert the following measurements: • 2.85 cm  ? in • 26.2 miles  ? Km • 15.6 kg  ? Lbs • 5.80 gal  ? Quarts Answers: • 2.85 cm = 1.12 in • 26.2 miles = 42.1 km • 15.6 kg = 34.4 lbs • 5.80 gal = 23.2 qts

  7. Temperature conversions

  8. Fahrenheit Scale • Water boils at 212°F • Water freezes at 32°F • Celsius Scale • Water boils at 100°C • Water freezes at 0°C • Kelvin Scale • Water boils at 373 K • Water freezes at 273 K Temperature Scales

  9. The size of each temperature unit (each degree) is the same for the Celsius and Kelvin scales. The Fahrenheit degree is smaller than the Celsius and Kelvin unit. Temperature scales (cont’d)

  10. The easier of the conversions To convert from Celsius to Kelvin: °C + 273 = K To convert from Kelvin to Celsius: K -273 = °C Converting between kelvin and celsius scales

  11. practice • Convert the following: • 987 K = __________ °C • 45 K = ___________ °C • 125°C = _________ K • -25 °C = _________ K Answers • 987 K = _714___ °C • 45 K = __-228__ °C • 125°C = __398___ K • -25 °C = __248___ K

  12. To convert from Celsius to Fahrenheit 1.80(°C )+ 32 = °F To convert from Fahrenheit to Celsius (°F – 32) / 1.80 = °C Converting betweencelsius and fahrenheit

  13. practice • Convert the following: • 98.6 °F= _______ °C • 45 °F = _______ °C • 125°C = ______ °F • -25 °C = ______ °F • Answers: • 98.6 °F= __37___ °C • 45 °F = __7.2___ °C • 125°C = _257___ °F • -25 °C = _-13__ °F

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