7.3: Analyze Units

7.3: Analyze Units Objective: Learn to use one or more conversion factors to solve rate problems. Palg Review 1 foot = 12 inches 1 yd = 3 feet 1 mile = 5280 feet 1 meter = 100 centimeters 1 pound = 16 ounces 1 minute = 60 seconds 1 hour = 60 minutes

Conversion Factors Problem solving skills. Dimensional analysis or unit analysis, is used to convert from one unit to another unit. To convert units, multiply by one or more ratios of equal quantities called conversion factors. To convert inches to feet, you would use the ratio below as a conversion factor. 1 ft = 12 in. 1 ft This fraction reduces to 1. 12 in. Why? Finding Conversion Factors

Example 1: Find the appropriate factor for each conversion. A) Feet to yards What do we know??? 1 yd = 3 feet 1 yd Write a conversion factor that is equivalent to 1: 3 ft 1 yd 1 yd 3 ft 1 why? Because 1 3 ft 3 ft 3 ft

B) Pounds to ounces What do we know??? 1 lb = 16 oz 1lb Write a conversion factor that is equivalent to 1: 16oz 1lb 1lb 16oz 1 why? Because 1 16oz 16oz 16oz

Using Conversion Factors to Solve Problems Example 2: The average American uses 580 pounds of paper per year. Find the number of pounds of paper the average American uses per month, to the nearest tenth. 580lb Set up a ratio: and we want to convert to months. 1 yr What is the relationship between months and a year? 1 yr = 12 months 1 yr This can be used as a conversion factor: 12months 580lb

1yr 48.3lb 580lb 48.3 lb/mo 1yr 12months 12months 1month Using Conversion Factors to Solve Problems Example 3: A car traveled 60 miles on a road in 2 hours. How many feet per second was the car traveling? 60mi 30mi

Set up a ratio: and we want to convert to 1hr feet per second. 2hrs What is the relationship between hours and seconds, miles and feet? 1 hr = 60 secs 1 mi = 5280 ft 1hr 5280 ft Both can be used as a conversion factor: ; 60 sec s

1mile 30mi 30mi 1hr 5280 ft 2640 ft 1hr 1hr 60 sec 1mile 1sec Using Conversion to Solve Problems Example 4: A strobe lamp can be used to

measure the speed of an object. The lamp flashes every 1/100 of a second, or 0.01 secs. A camera records the object moving 52 cm between flashes. How fast is the object moving in m/s? Using Conversion to Solve Problems Example 5: The rate 1 knot equals 1 nautical mile per hour. One nautical mile is 1852 meters. What is the speed in kilometers per hour of a ship traveling at 5 knots? HOMEWORK 7.3 hw pg. 352: 2 22 (evens)

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