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Published byAdrian Gibson Modified over 2 years ago

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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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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 1000 m Which one to use? Depends on which direction you are trying to go.

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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 = m (or 2.5 x 10 4 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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Step 2:2: Turn the statement into a conversion factor 1 inch = 1 or 2.54 cm = cm 1 inch Step 3 : Multiply the given by the conversion factor which will allow the unit to cancel out inch X 2.54 cm = 14.1 cm 1 inch given conversion factor

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Step 4 : Check your sig figs and dont forget units! 5.54 inch X 2.54 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 1 inch = ??? 1 meter2.54 cm givenconversionconversion factor

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Top and Bottom Conversions : Mr Clausons 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 x1mi x L = 1L km 1 gal Are the Sig Figs right? NO!! 17 mpg

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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

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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 yd 2 X 3 ft X 3 ft = 3.3 yd 2 x 3ft 2 = 1 yd 1 yd 1 yd Answer = 29.7 sq ft = 3.0x10 1 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 cm 3 ? The linear conversion factor 1 m = 100 cm Has to be cubed! 3.57 cm 3 X 1m X 1m X 1m = 3.57 cm 3 x 1m cm 100 cm 100cm 100 cm Answer = 3.57x10 -6 cubic meters

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Homework Paddys Pool Procedure (Your individual best!) Conversion WS #3

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Learning Check A Nalgene water bottle holds 1000 cm 3 of dihydrogen monoxide (H 2 O). How many cubic decimeters is that?

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

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