Problems Using Conversion Factors

Conversion Factor: A ratio of two different units

Equalities: The relationship between two units. Or Different expressions of the same thing.

For example, One dollar = 4 quarters = 10 dimes = 20 nickels = 100 pennies

In a conversion factor, the measurement in the numerator (on the top)

is equal to the measurement in the denominator (on the bottom)

Some common U.S. system equalities

1 foot = 12 inches

1 yard = 3 feet

1 mile = 5280 feet

There are also metric conversions that uses a prefix to describe how many

1 meter = 100 centimeter

1 kilogram = 1000 gram

1000 milliliter = 1 liter

Now our exercise will be to convert from Metric to U.S. system. Suppose that you need to convert from pounds (a U.S. unit) to kilograms (a metric or S.I. unit)

The equality for this conversion is, 1 kg = 2.2 pounds

The conversion factor would be and

Writing Conversion Factors from Equalities

Write conversion factors for the relationship for the following pairs of units:

a. Milligrams and grams

b. Minutes and hours

c. Quarts and milliliters

Solution:

Equality Conversion Factors

a. 1 g = 1000 mg

b.1 hr = 60 min

c. 1 qt = 946 ml

DA:Dimensional Analysis

The set up for this is using the following formula

Quantity (initial unit) x Conversion factor = Same Quantity (New Unit)

Problem: Convert 3 eggs to dozens

Step 1:

The quantity given and the initial unit is 3 (quantity) eggs (initial unit)

Step 2:

Devise a unit, course of action, or in other words a unit plan

Given UnitNew Desired Unit

Eggs  Dozen

Step 3:

Write the two possible conversion factors

and

Step 4:

Now write the setup to solve the problem using the unit plan (step 2) and the appropriate conversion factor (step 3). Which is the right conversion factor to use? Remember you can only USE 1 of them. The correct one is the one that has the unit you want to get rid of in the denominator because it will cancel out the given unit in the numerator (top number in a fraction)

Problem Setup

Given Conversion FactorAnswer

(initial unit)(cancels initial unit)(desired unit)

3 eggs x 1 dozen = 0.25 dozen

1 12 eggs

Step 5:

Ask yourself the question; DOES THE ANSWER MAKE SENSE?!

Yes, it does make sense…. 0.25 is less than 1 and 3 is less than 12. This is very important that you think about the answer that you arrive at.

Exercises

  1. How many yards in 24 ft?
  2. How many seconds in 15 min?
  3. You need 3.5 qt of oil for your car. How many gallons is that?
  4. A necklace contains 2.6 oz of gold. How many pounds is that?
  5. You ran 3.5 miles; How far is that in feet? ( 1 mile = 5280 ft)
  6. To play a video game at the mall you need three quarters. You have $3.75 in your pocket. How many games can you play?