How will you write the conversion factor?

The easiest way to do stoichiometric calculations involves using conversion factors. A conversion factor is a ratio (or fraction) which represents the relationship between two different units. A conversion factor is ALWAYS equal to 1. Here are some examples of conversion factors:

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How do you use Conversion Factors?
What is a conversion factor example?
How many conversion factors are written?

All these conversion factors are equal to 1. If it doesn't seem obvious at first, think about it for a second. Realize that 1 minute is equivalent to 60 seconds. Simply replace 1 minute in the fraction with its equivalent 60 seconds and it becomes clear that 60 seconds / 60 seconds = 1. Numerator and denominator are equivalent; they are just expressed differently.

As you can see it is extremely important to keep track of your units when using conversion factors. Without units, the first fraction would be 1 / 60. This is not equal to 1 and could very easily lead to wrong answers.

Furthermore, when you use units, you make it very easy to check your work. For example, perhaps you are trying to find out how many dozen eggs you have to buy to make three cakes. If you're getting an answer of 12 dozen eggs you might want to check your work. Could you even fit 12 of those cartons in your refrigerator? If you look back on your calculations you may immediately see the incorrect conversion factor: 1 egg / 12 dozen. It is easy to see that this is where the error occurred since this does NOT equal 1.

How do you use Conversion Factors?

We all know from elementary school math that if you multiply any quantity by 1 you get the same quantity back. You can do this as many times as you want. For example, 2×1 = 2, and 18×1×1×1 = 18.

Multiplication by 1 is what you do whenever you do a problem involving conversion factors. The best way to explain how to solve using conversion factors is to work through some simple examples.

Problem: How many days are there in 3 years? (Assume none of these years are leap years)

Solution: Here we basically want to convert years to days. Our conversion factor is:

Since this is equivalent to 1, multiplication of this ratio with our original value will only change its units and not its magnitude. Therefore:

3 years×

= 1, 095 days

Notice that years is on the bottom of the conversion factor. This is VERY important. You always want to have the units of what you currently have on the bottom of the conversion factor and the units you want on the top.

Conversion Factor =

In this case we are multiplying our conversion factor by years. We therefore put years on the bottom of the conversion factor. When multiplied together, the resulting fraction has years in both numerator AND denominator. These units can now "cancel each other out". How? You might want to think about it like this. When you see the fraction 2 / 2, you cancel the 2s in both numerator and denominator. You can do the same thing with units.

When doing any type of problem involving conversion factors, feel free to draw a line through any unit you see on the top and bottom of the fraction to make it visually obvious that the units cancel.

3 years×

= 1, 095 days

Canceling units in this way makes it much easier to check your work. The units you want in your answer should be the only unit not to cancel. If your calculations yield other units, which cannot be cancelled, you have made a mistake likely resulting from a missing conversion factor or an upside down conversion factor that needs to be flipped.

Here's another, slightly harder problem: How many seconds are there in 3 years?

Solution: It is easiest to use multiple conversion factors for this problem. Starting with the units you are given, find the conversion factor needed to express to current unit in terms of the next smaller unit.

Let's start with a simple example: convert 3 km to m (3 kilometers to meters). There are 1000 m in 1 km, so the conversion is easy, but let's follow a system.

The system is:

Write the conversion as a fraction that equals 1
Multiply it out (leaving all units in the answer)
Cancel any units that are both top and bottom

We can write the conversion as a fraction that equals 1:

1000 m1 km = 1

And it is safe to multiply by 1 (does not affect the answer):

3 km × 1 = 3 km

so we can do this:

3 km × 1000 m 1 km = 3000 km · m 1 km

The answer looks strange! But we aren't finished yet ... we can "cancel" any units that are both top and bottom:

3000 km · m 1 km = 3000 m

So, 3 km equals 3000 m. Well we knew that, but we want to follow a system, so that when things get harder we know what to do!

And when we do it correctly we get to cancel units that are both top and bottom, and get a neat answer.

Note: if we do it wrong (with the conversion upside down) we get this:

3 km × 1 km 1000 m = 3 km · km 1000 m

And that doesn't let us do any cancelling!

Example 2:

Let's use this method to solve the km/h to m/s conversion from the top of the page.

We will do it in two stages:

from km/h (kilometers per hour) to m/h (meters per hour), then
from m/h (meters per hour) to m/s (meters per second).

1. From km/h (kilometers per hour) to m/h (meters per hour)

1 km h × 1000 m1 km = 1000 km · m 1 h · km

Now "cancel out" any units that are both top and bottom:

1000 km · m 1 h · km = 1000 m 1 h

It is now in meters per hour.

2. From m/h (meters per hour) to m/s (meters per second)

To go from m/h (meters per hour) to m/s (meters per second) we put the "3600 seconds in an hour" conversion "upside down" because we want an "h" on top (so they will cancel later) :

What is a conversion factor example?

A conversion factor is a number used to change one set of units to another, by multiplying or dividing. When a conversion is necessary, the appropriate conversion factor to an equal value must be used. For example, to convert inches to feet, the appropriate conversion value is 12 inches equal 1 foot.

How many conversion factors are written?

Two conversion factors can be written for any relationship in the metric or U.S. system. A percentage is written as a conversion factor by expressing matching units as the parts in 100 parts of the whole. The mass and volume of any object can be measured.