Another special kind of constant that can be used in solving problems involving multiplication is called a conversion constant. A conversion constant is used to convert from one system of measurement to another.

For example, there are 1.61 kilometers in every mile. How would we write an equation that you could use to calculate d, the number of kilometers in m miles?

First, we need to take a closer look at the conversion factor, "There are 1.61 kilometers in every mile." How could you rewrite this as a ratio of kilometers to miles?

Interactive popup. Assistance may be required. Check Your Answer 1.61 kilometers over 1 mile 1.61 kilometers 1 mile

What units are in the denominator?

Interactive popup. Assistance may be required. Check Your Answer Miles

Do we want to multiply this conversion factor by d, kilometers or by m, miles?

Interactive popup. Assistance may be required. Check Your Answer Miles

How should we write the equation that calculates the number of kilometers in m miles?

Interactive popup. Assistance may be required. Check Your Answer Write the equation by multiplying the conversion factor by the number of miles.

Write the equation in your notes and then click on the "d" to check your answer.

How many kilometers are in 6 miles? Click on the "d" to check your answer.

Try another example.

You are making a cake to surprise your mom for her birthday. You look online and find a recipe for her favorite cake, but the units are all metric. The recipe calls for 0.30 liters of milk and all you have is a measuring cup. Luckily, you have your science textbook with you at home, and there is a table in the back of conversion factors. The table says that there are 4.23 cups in one liter.

Write this conversion factor as a ratio of cups to liters.

Interactive popup. Assistance may be required. Check Your Answer 4.23 cups over 1 liter 4.23 cups 1 liter

What units are in the denominator?

Interactive popup. Assistance may be required. Check Your Answer Liters

Do you want to multiply this conversion factor by cups or by liters to make the units cancel?

Interactive popup. Assistance may be required. Check Your Answer Liters

Record your equation in your notes. Click on the "c" to check your answer.

How many cups are there in 0.30 liters of milk? Click on the "c" to check your answer.