The Purdue Global Science Center presents Unit Conversions using the Multiplication Method. Throughout history, humans have used standard

standards of measurement to compare mass, volume, length, time, and temperature. In the United States, you will primarily encounter

two of these standards. First is the English, also known as the imperial system. This system has been in use since the middle

ages. It is based on standards such as a foot, which was equal to the length of a man’s foot. It was not very accurate, but over time these

measurements have been further standardized to the units we are now familiar with such

as pounds, ounces, and feet. Another system you may have heard of is the

metric system. The system is used worldwide and in the United

States in common industries such as science, medicine, and in the military. The metric system originated in Paris in the

16th century and is known as the SI or System Internationale. It is based on the decimal system where the

standards are found in nature. For example, the meter was originally based

on the dimensions of the earth. Some of the units in the metric system include

kilograms, liters, and meters. In order to compare or convert measurements

between different systems, you need to know how these units are related. For example, how many inches are in a meter? How many pounds are in a kilogram? These quantities are known and have been calculated

and revised by scientists and mathematicians throughout history. We can use conversion tables to find these

relationships. Here are some conversion tables for converting

mass, volume, and length. We will refer back to them as we work through

some of our conversions. Take a moment to review. Let’s do an example. In this example, we are going to convert kilometers

to miles. Let’s pretend that we are traveling by car

in Germany where the metric system is used, and a road sign says we have 72 kilometers

to our destination. We want to know how many miles is that in

case we want to stop for lunch. How do we convert 72 kilometers to miles? First, find the correct conversion in the

table. We go back to the conversion tables. We see that to convert kilometers to miles

we multiply kilometers by the conversion factor of 1.609. The result of multiplying 72 km by 1.609 is

115.8 miles. Notice that in this example I begin with the

example of kilometers and end with the unit labeled as miles. Double check that your units are correctly

matching the question. For this example, we correctly labeled our

conversion from kilometers to miles. In our second example, we are going to convert

kilograms to pounds. Let’s just pretend that we are on vacation

in Mexico, and you want to know if your suitcase it too heavy since you bought so many souvenirs. You find a scale and measure the weight of

the suitcase. It reads 25 kilograms. You want to convert this to pounds. First, we are going to find the correct conversion

in the table. We see that to get pounds we multiply kilograms

by 2.205. In our example, we multiply 25 kilograms by

2.205, which equals 55.12 pounds. The other thing you will notice here is that

our result always contains the same number of units as our conversion factor. If the conversion factor is given with four

significant digits to 2.205, our results will also be four significant digits 55.12. Four here and four here. Next, what if we want to convert units within

a system of measurement either metric or standard. Within the metric system, converting units

is easy because it is based on multiples of ten. In the metric system, each prefix stands for

a multiple of ten. As you can see here from the chart that if

you want to convert centimeters to meters we simply divide centimeters by a hundred. On the other hand converting units in the

imperial system is not as easy as in the metric system because the units are not related in

the same way. For this we have to have a reference for how

the units are related, so another conversion table. Let us say that we want to convert inches

to miles. First, we don’t have inches and miles in

our conversion table, so we first have to convert feet to miles. In our example, we are going to convert 50

miles and see how many inches that is. In each mile, there are 5280 feet. To calculate how many feet in 50 miles,

we would multiply 50 by 5,280 to get 264,000 feet. Next, we can convert feet to inches by multiplying by 12 as seen in the chart. 264,000 multiplied by 12 three million one

hundred and sixty eight thousand inches is 50 miles. To wrap up what we have learned today, we

see that we can convert units between the English or imperial system and the metric

system, but we need to know how these units are related and we use conversion tables for this. We have demonstrated how you can use the multiplication

method to convert units between these systems. Finally use your common sense to analyze if

the answers makes sense. For example, we know that one pound is about

2.2 kilograms so your weight in kilograms would be less than your weight in pounds.