Bellringer How many pounds do you weigh? How many ounces? How did you arrive at that figure?

Dimensional Analysis aka Factor Label Method aka Conversion Factors Ms. Hanlon’s Science Classes

Objectives Correctly set up word problems and cancel units to solve dimensional analysis problems.

Definition Dimensional Analysis: checking a derived equation by making sure dimensions are the same on both sides. Units, or “labels” are canceled, or “factored” out

Steps 1. Identify starting & ending units. 2. Line up conversion factors so units cancel. 3. Multiply all top numbers & divide by each bottom number. 4. Check units & answer.

Conversion Factors Fractions in which the numerator and denominator are EQUAL quantities expressed in different units but always equal to one. You can always multiply any equation by this equality and not change the quantity, just the units. Example: 1 in. = 2.54 cm Factors: 1in. and 2.54 cm 2.54 cm 1 in.

First write down the desired quantity Factor label Example How many kilometers are in 47.0 miles? (note: 1 km = 0.621 miles) # km First write down the desired quantity

Next, equate desired quantity to the given quantity Factor label Example How many kilometers are in 47.0 miles? (note: 1 km = 0.621 miles) # km = 47.0 mi Next, equate desired quantity to the given quantity

Now we have to choose a conversion factor Factor label Example How many kilometers are in 47.0 miles? (note: 1 km = 0.621 miles) # km = 47.0 mi Now we have to choose a conversion factor

What conversion factors are possible? Factor label Example How many kilometers are in 47.0 miles? (note: 1 km = 0.621 miles) # km = 47.0 mi 1 km 0.621 mi 0.621 mi 1 km What conversion factors are possible?

Pick the one that will allow you to cancel out miles Factor label Example How many kilometers are in 47.0 miles? (note: 1 km = 0.621 miles) # km = 47.0 mi 1 km 0.621 mi 0.621 mi 1 km Pick the one that will allow you to cancel out miles

Pick the one that will allow you to cancel out miles Factor label Example How many kilometers are in 47.0 miles? (note: 1 km = 0.621 miles) # km = 47.0 mi 1 km 0.621 mi 0.621 mi 1 km Pick the one that will allow you to cancel out miles

Multiply given quantity by chosen conversion factor Factor label Example How many kilometers are in 47.0 miles? (note: 1 km = 0.621 miles) # km = 47.0 mi 1 km 0.621 mi 0.621 mi 1 km Multiply given quantity by chosen conversion factor

Multiply given quantity by chosen conversion factor Factor label Example How many kilometers are in 47.0 miles? (note: 1 km = 0.621 miles) # km = 47.0 mi x 1 km 0.621 mi Multiply given quantity by chosen conversion factor

Cross out common factors Factor label Example How many kilometers are in 47.0 miles? (note: 1 km = 0.621 miles) # km = 47.0 mi x 1 km 0.621 mi Cross out common factors

Cross out common factors Factor label Example How many kilometers are in 47.0 miles? (note: 1 km = 0.621 miles) x 1 km 0.621 # km = 47.0 Cross out common factors

Are the units now correct? Factor label Example How many kilometers are in 47.0 miles? (note: 1 km = 0.621 miles) x 1 km 0.621 # km = 47.0 Are the units now correct? Yes – km on both sides!

Factor label Example Now finish the math. How many kilometers are in 47.0 miles? (note: 1 km = 0.621 miles) # km = 47.0 x 1 km 0.621 = 75.68438003 km Now finish the math.

Not Finished Yet Complete the math with no rounding Make certain the sig figs are correct by rounding to the correct number of sig figs at the very end Don’t forget the order of operations when you complete the math Conversion factors do not determine sig. figs.!

Factor label Example The final answer is 75.7 km How many kilometers are in 47.0 miles? (note: 1 km = 0.621 miles) x 1 km 0.621 = 75.7 km # km = 47.0 The final answer is 75.7 km

Classwork Get into groups as assigned. Rotate among stations and complete lab activities.

Homework Complete the worksheet provided.