What is Dimensional Analysis?

A fancy term for converting from one unit to another

Examples …Going from dollars to centsGoing from miles to kilometersGoing from meters to cm to inchesGoing from seconds to yearsGoing from mph to m/s

What is Dimensional Analysis?

I will teach you a systematic way of doing these problems

The method uses conversion factors

Some Typical Conversion Factors

60 s = 1 min as 60 s or 1 min 1 min 60 s

1.6 km = 1 mile as 1.6 km or 1 mile 1 mile 1.6 km

13.38 US dollars = 0.075 Mexican pesos

as 13.38 USD or 0.075 pesos 0.075 pesos 13.38 USD

How Does Dimensional Analysis Work?

A conversion factor is used, along with what you’re given, to determine what the new unit will be.

Enough talk lets do one or two on the board!!!

Examples of Conversions

Again, just be careful how you write the fraction.

The fraction must be written so that like units cancel.

Steps

1. Start with the given value.2. Write the multiplication symbol.3. Choose the appropriate conversion factor.4. The problem is solved by multiplying the

given data & their units by the appropriate unit factors so that the desired units remain.

5. Remember, cancel like units.

Let’s try some examples together…

1. Suppose there are 12 slices of pizza in one pizza. How many slices are in 7 pizzas?

Given: 7 pizzasWant: # of slices

Conversion: 12 slices = one pizza

7 pizzas1

Solution

Check your work…

X 12 slices1 pizza = 84 slices

Let’s try some examples together…

2. How old are you in days?

Given: 17 yearsWant: # of days

Conversion: 365 days = one year

Solution

Check your work…

17 years1 X 365 days

1 year = 6052 days

Multiple-Step Problems

Most problems are not simple one-step solutions. Sometimes, you will have to perform multiple conversions.

Example: How old are you in hours?

Given: 17 yearsWant: # of days

Conversion #1: 365 days = one yearConversion #2: 24 hours = one day

Solution

Check your work…

17 years1 X

365 days1 year X

24 hours1 day =

148,920 hours