Presentation on theme: "Unit Conversions-Take II"— Presentation transcript:
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 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 = 11 km mWhich one to use?Depends on which direction you are trying to go.
3 Use 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
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 or2.54 cm = 1 inch
5 given 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
6 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 cm1 inchThree sig figs
7 Ex #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
8 You 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
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 = km; 1 gal = L7.2 km x 1mi x L =1L km 1 gal17.0 mpgAre the Sig Figs right?NO!! 17 mpg
10 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 sec89.0 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 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!)
12 Doing 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