Presentation on theme: "Unit Conversions-Take II"— Presentation transcript:
1Unit 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
2Any 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 = 11 km mWhich one to use?Depends on which direction you are trying to go.
3Use the conversion factor that allows units to cancel. Which one? For example:Convert 25 km to metersUse the conversion factor that allows units to cancel. Which one? m or 1 km1 km m25 km x 1000 m = m (or 2.5 x 104 m)1 kmgiven conversion factor
4Step-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 or2.54 cm = 1 inch
5given conversion factor Step 2:Turn the statement into a “conversion factor”1 inch = 1 or cm = 12.54 cm inchStep 3: Multiply the given by the conversion factor which will allow the unit to cancel out.5.54 inch X cm = 14.1 cm1 inchgiven conversion factor
65.54 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 cm1 inchThree sig figs
7Ex #2. How many kilometers is the 26.2 mile marathon? Definition: 1 mi = km or1 km = mi26.2 mi x km = 42.2km1 migiven conversion factor
8You can do more than one conversion at a time. Example: How many inches in 4.2 meters?Definitions: 1 meter = 100 cm1 inch = 2.54 cmSet up:4.2 meters X 100 cm X inch = ???1 meter cmgiven conversion conversionfactor factor
9Top 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 = L7.2 km x 1mi x L =1L km 1 gal17.0 mpgAre the Sig Figs right?NO!! 17 mpg
1089.0 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 sec89.0 mph Big League speed!
11Doing Area Conversions Use the conversion factors, but square them!!Example: How many square feet in 3.3 square yards?The linear conversion factor1 yard = 3 feetHas to be squared!3.3 yd2 X 3 ft X 3 ft = 3.3 yd2 x 3ft 2 =1 yd yd ydAnswer = 29.7 sq ft = 3.0x101 sq ft (sig figs!)
12Doing Volume Conversions Use the conversion factors, but cube them!!Example: How many cubic meters in 357 cm3?The linear conversion factor1 m = 100 cmHas to be cubed!3.57 cm3 X 1m X 1m X 1m = cm3 x 1m 3100 cm cm 100cm cmAnswer = 3.57x10-6 cubic meters
13Homework Paddy’s Pool Procedure (Your individual best!) Conversion WS #3
14Learning CheckA Nalgene water bottle holds 1000 cm3 of dihydrogen monoxide (H2O). How many cubic decimeters is that?
15Solution( )1000 cm dm 310 cm= 1 dm3So, a dm3 is the same as a Liter !A cm3 is the same as a milliliter.