Problem-Solving Strategy for Unit Conversions Teaching a specific method and need to evaluate student understanding of method Dimensional analysis

How many kilograms are in 150 lbs? Dimensional analysis Problem-solving strategy to convert measurements in one unit to an equivalent quantity in another unit How many kilograms are in 150 lbs? How many calories are in 42 joules? How many inches are in 127 miles? How many seconds are in 22 days?

Conversion factors Identify the relationship between two values with different units that express the same quantity Provide the step-by-step directions to go from the starting point to the ending point 1 min = 60 s 1 hr = 60 min 12 in = 1 ft 1 cal = 4.184 J 1 kg = 2.2 lbs 1 g = 1000 mg

Conversion factors Such factors are ratios and can be expressed as fractions The fractions may be written in two ways and always equal a value of 1 If you have one dozen eggs, how many eggs do you have? Therefore, 1 dozen eggs = 12 eggs 12 eggs 1 dz eggs 12 eggs 12 eggs 1 dz eggs = 1 = 1

Dimensional analysis KNOW WHERE YOU ARE GOING KNOW WHERE YOU START Identify (underline) the unknown in the problem statement. KNOW WHERE YOU START Identify (circle) the given in the problem statement. DRAW THE BRIDGE Outlines the path to be taken from start to finish STEP-BY-STEP DIRECTIONS Determined by the applicable conversion factors. It’s all in the units!

How many kilograms are in 150 lbs? Dimensional analysis How many kilograms are in 150 lbs? What conversion factor applies to this problem? 1 kg = 2.2 lbs Expressed as fractions: Write the UNKNOWN, start with the GIVEN, and then draw the BRIDGE to connect the two quantities 1 kg 2.2 lbs 2.2 lbs 1 kg

bridges Bridges provide the structure for the problem-solving strategy of dimensional analysis STEP-BY-STEP DIRECTIONS DRAW THE BRIDGE GIVEN CONVERSION FACTOR UNKNOWN = KNOW WHERE YOU ARE GOING KNOW WHERE YOU START

How many kilograms are in 150 lbs? from LBS to KG How many kilograms are in 150 lbs? 1 kg = 2.2 lbs STEP-BY-STEP DIRECTIONS DRAW THE BRIDGE GIVEN CONVERSION FACTOR 1 kg 150 lbs kilograms = UNKNOWN = 2.2 lbs KNOW WHERE YOU ARE GOING KNOW WHERE YOU START

Now, it’s time for the math. from LBS to KG How many kilograms are in 150 lbs? When the only unit left standing matches the unknown, the bridge is complete. 1 kg 150 lbs kilograms = 2.2 lbs Now, it’s time for the math.

from LBS to KG 1 kg 150 lbs kilograms = 2.2 lbs kg MULTIPLY all numbers on the top of the bridge 150 x 1 = 150 DIVIDE by each number on the bottom 150 / 2.2 = 68.18181818 kg The unit left standing is the unit of the answer: CHECK number of significant figures in GIVENs and express answers to same number of SF ROUND to 2 SF  68 kg

Dimensional analysis How many calories are in 42 joules? 1 calorie = 4.184 joules How many inches are in 127 miles? 12 inches = 1 foot 5,280 feet = 1 mile How many seconds are in 22 days? 60 seconds = 1 minute 60 minutes = 1 hour 24 hours = 1 day