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Mastering Unit Conversions: Factor-Label Method Explained

Learn how to convert between units using conversion factors and the Factor-Label method with step-by-step examples and explanations. Units are crucial to prevent mistakes and ensure accuracy in conversions. Practice with various conversion scenarios provided.

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Mastering Unit Conversions: Factor-Label Method Explained

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  1. Unit Conversions-Take II We use the Factor-Label method to convert from one unit to another. Key Idea: -Use “conversion factors” to convert between units. PAY ATTENTION TO UNITS so that they cancel. Units are your friends!!! They prevent mistakes

  2. 1 km = 1000 m (This is called an Equivalence Statement or Definition) Any equivalence statement can be made into two(conversion factors) • 1000 m=1 kmNote: both of these = 1 1 km 1000 m Which one to use? Depends on which direction you are trying to go.

  3. For example: Convert 25 km to meters • Use the conversion factor that allows units to cancel. Which one?  1000 m or 1 km 1 km 1000 m 25 km x 1000 m= 25000 m (or 2.5 x 104 m) 1 km given conversion factor

  4. Step-By-Step Method to Solving Problems. Example: How many centimeters are there in 5.54 inches? • Step 1: Find how many centimeters are equal to one inch (Equivalence Statement). 1 inch = 2.54 cm or 2.54 cm = 1 inch

  5. Step 2: Turn the statement into a “conversion factor” 1 inch = 1 or 2.54cm= 1 2.54 cm1 inch Step 3: Multiply the given by the conversion factor which will allow the unit to cancel out. 5.54 inchX 2.54 cm= 14.1 cm 1 inch given conversion factor

  6. Step 4: Check your sig figs and don’t forget units! 5.54 inchX 2.54 cm= 14.1 cm 1 inch Three sig figs

  7. Ex #2. How many kilometers is the 26.2 mile marathon? Definition: 1 mi = 1.6093 km or 1 km = .62137 mi 26.2 mi x 1.6093 km = 42.2km 1 mi given conversion factor

  8. You can do more than one conversion at a time. Example: How many inches in 4.2 meters? Definitions: 1 meter = 100 cm 1 inch = 2.54 cm Set up: 4.2 metersX100 cmX1 inch= ??? 1 meter 2.54 cm given conversion conversion factor factor

  9. Top and Bottom Conversions: Mr Clauson’s Durango gets 7.2 km/L of gas. How many miles per gallon is that? Logic: Need to go from km mi on top, and from L to gal on the bottom. 1 mi = 1.6093 km; 1 gal = 3.7854 L 7.2 km x 1mi x 3.7854 L = 1L 1.6093 km 1 gal 17.0 mpg NO!! 17 mpg Are the Sig Figs right?

  10. Another Top and Bottom example: This year in physics, the fastest baseball throw was 39.8 m/sec. What is the speed in miles/hour? • Logic: Need to go from m mi on top, and from sec to hr on the bottom. 1 m = 3.28 ft; 1mi = 5280 ft; 1 hr = 60 min; 1 min = 60 sec 89.0 mph Big League speed!

  11. Doing Area Conversions Use the conversion factors, but square them!! Example: How many square feet in 3.3 square yards? The linear conversion factor 1 yard = 3 feet Has to be squared! 3.3 yd2X3 ft X 3 ft= 3.3 yd2 x 3ft2= 1 yd 1 yd 1 yd Answer = 29.7 sq ft = 3.0x101 sq ft (sig figs!)

  12. Doing Volume Conversions Use the conversion factors, but cube them!! Example: How many cubic meters in 357 cm3? The linear conversion factor 1 m = 100 cm Has to be cubed! 3.57 cm3X1m X1m X1m = 3.57 cm3 x 1m 3 100 cm 100 cm 100cm 100 cm Answer = 3.57x10-6 cubic meters

  13. Homework • Paddy’s Pool Procedure (Your individual best!) • Conversion WS #3

  14. Learning Check A Nalgene water bottle holds 1000 cm3 of dihydrogen monoxide (H2O). How many cubic decimeters is that?

  15. Solution ( ) 1000 cm3 1 dm 3 10 cm = 1 dm3 So, a dm3 is the same as a Liter ! A cm3 is the same as a milliliter.

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