Warm Up – Dimensional Analysis Practice

1. Susanna is 5.50 ft tall. What is her height in centimeters?

(1 in = 2.54 cm)

2. If we are in class for 1.5 hours, how many seconds are we in class?

Warm Up – Dimensional Analysis Practice

We are going to plan a hypothetical pizza party. How much will it cost? (write it down with explanation)

If you’re stuck consider these questions:• How many students are in the class?• How many slices of pizza do you think each

student will eat?• How many slices of pizza are in a whole pizza• How much does a whole pizza cost?

Let’s Throw a Pizza Party

How much will it cost for our class?• How many students?• Slices per student?

Slices per pizza?Price per pizza?

class

price

pizza

price

slices

pizza

student

slices

class

students

How to convert units? (1)Step 1: When to

convert

Numbers with units, like 16.2 meters or 32 ft/sec², are treated exactly the same as coefficients with variables, like 16.2x or 32y/z².

So What?:

You can’t add euros to dollars

You can’t add feet to feet/sec

How to convert units? (2)Step 2: Multiply by 1 You can multiply anything by 1 and not

change its value.Convert 4.5 hours to minutes: (1) 60 minutes = 1 hour (2) 60 minutes = 1

1 hour (3) 4.5 hr × 60 min

1 hr

(4) 4.5 hr x 60 min = 4.5x 60 min = 1 hr

Is it really multiplying by 1?• In which case will you overcook the

Turkey? Which is longer, cooking a Turkey for 3.25 hours or 195 minutes?

Note: If you converted 3.5 hours and came out with .0583 minutes, you probably messed up. Always see if the answer makes sense

How to convert units? (3)Step 3: How to pick a “1” (1) Find a conversion factor between the

given units and the desired units, and write it as an equation.

EX: to convert km to miles1 km = 0.621 miles(2) Convert that equation to a fraction

with the desired units on top and the given units on the bottom

1 km there’s your “1” conversion 0.621 miles factor

How to convert units? (4)Step 4: Chaining Conversions (1)  combine conversions to avoid

looking up a specific conversion (2) Like in the pizza exampleEX: how many meters are in the 440-yard

dash?

440 yd = 402 m

ConvertingInches to centimeters

10.0 in

We start by writing down the number and the unit

ConvertingInches to centimeters

10.0 in

1 in

2.54 cm

Our conversion factor for this is 1 in = 2.54 cm.Since we want to convert to cm, it goes on the top.

ConvertingInches to centimeters

10.0 in

1 in

2.54 cm

Now we cancel and collect units. The inches cancel out, leaving us with cm –

the unit we are converting to.

ConvertingInches to centimeters

10.0 in

1 in

2.54 cm = 25.4 cm

Since the unit is correct, all that is left todo is the arithmetic...

The Answer

Recap of the Procedure

1. Find conversion factor as a fraction with the given units in the opposite position from the original measurement

2. Raise the conversion fraction to that same power

3. Multiply the original measurement by the conversion fraction, and simplify.