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**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

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**Any equivalence statement can be made into two (conversion factors) **

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 km Note: both of these = 1 1 km m Which one to use? Depends on which direction you are trying to go.

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**Use the conversion factor that allows units to cancel. Which one? **

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

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**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

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**given conversion factor**

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

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**5.54 inch X 2.54 cm = 14.1 cm Three sig figs**

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

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**Ex #2. How many kilometers is the 26.2 mile marathon?**

Definition: 1 mi = km or 1 km = mi 26.2 mi x km = 42.2km 1 mi given conversion factor

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**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 meters X 100 cm X inch = ??? 1 meter cm given conversion conversion factor factor

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**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 = km; 1 gal = L 7.2 km x 1mi x L = 1L km 1 gal 17.0 mpg Are the Sig Figs right? NO!! 17 mpg

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**89.0 mph Big League speed! 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!

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**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 yd2 X 3 ft X 3 ft = 3.3 yd2 x 3ft 2 = 1 yd yd yd Answer = 29.7 sq ft = 3.0x101 sq ft (sig figs!)

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**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 cm3 X 1m X 1m X 1m = cm3 x 1m 3 100 cm cm 100cm cm Answer = 3.57x10-6 cubic meters

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**Homework Paddy’s Pool Procedure (Your individual best!)**

Conversion WS #3

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

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Solution ( ) 1000 cm 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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Using the Factor Label Method. 34,000,000 = 7.29 x 10 5 = 0.3254 = 5.6 x 10 -3 = 3.4 x 10 7 729,000 3.254 x 10 -1 0.005600.

Using the Factor Label Method. 34,000,000 = 7.29 x 10 5 = 0.3254 = 5.6 x 10 -3 = 3.4 x 10 7 729,000 3.254 x 10 -1 0.005600.

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