The Factor-Label Method: a unit conversion process

Factor-Label: a unit conversion process
The most important mathematical process in chemistry!

As you know, numbers in science almost always have some measurement units. The numbers and units are equally important and what is done to the number must be done to the units as well.

You also know that any number multiplied by one is still the same number.

Factor-label multiplies a given number and unit by fractions equal to one to convert units. These fractions are known as conversion factors.

The general form of a factor-label problem is shown below.
The horizontal line means to divide and each vertical line means to multiply.

Sample Problem	Explanation
Problem #1: Convert 1000 grams to pounds.	Write what is given. Draw the horizontal and vertical lines. It is known that 1 pound = 454 grams. This becomes my fraction. The fraction is turned to put grams on bottom so it will cancel the given units of grams. The problem is solved when all units except pounds are canceled. Use your calculator to do the math - 1000 times 1 divide by 454.
Problem #2: Convert 65 miles/hour to meters/second.	Put 65 miles / hour into the factor-label form. It does not matter if we convert miles or hours first - just don't try to do them at the same time. Do you know how many seconds are in an hour - or how many meters are in a mile? If not, do not try to calculate it. Use a fraction that you know. You know there are 60 minutes in an hour and there are 2.54 cm in an inch. This will take more steps, but that's ok. You know you have worked the problem when all units cancel except those you are asked to find.
Solution to problem #2: 29 feet / second There are several ways to solve for the answer on a calculator. The way with the least possible mistakes is as follows: Enter the numbers on top of the horizontal line, from left to right. Each time you cross a vertical line (above the horizontal line), press the "multiply" button. That would be: 65 times 5280 times 12 times 2.54 We can disregard the number 1, since it does not change the result. Notice that the "equals" button has not been pressed. After entering the last number on the right, drop below the horizontal line by pressing the "divide" button. Now enter the numbers below the horizontal line from right to left. Each time you cross a vertical line (below the horizontal line), press the "divide" button. That would be: divide by 100 divide by 60 divide by 60 When you get to the end of the line, press "equals". The number answer is now on your calculator.

Sample Problem

Explanation

Problem #1: Convert 1000 grams to pounds.

calculation

Write what is given.
Draw the horizontal and vertical lines.
It is known that 1 pound = 454 grams. This becomes my fraction.
The fraction is turned to put grams on bottom so it will cancel the given units of grams.
The problem is solved when all units except pounds are canceled.
Use your calculator to do the math - 1000 times 1 divide by 454.

Problem #2: Convert 65 miles/hour to meters/second.

calculation

Put 65 miles / hour into the factor-label form.
It does not matter if we convert miles or hours first - just don't try to do them at the same time.
Do you know how many seconds are in an hour - or how many meters are in a mile?
If not, do not try to calculate it. Use a fraction that you know. You know there are 60 minutes in an hour and there are 2.54 cm in an inch.
This will take more steps, but that's ok.
You know you have worked the problem when all units cancel except those you are asked to find.

Solution to problem #2:

29 feet / second

There are several ways to solve for the answer on a calculator. The way with the least possible mistakes is as follows:

Enter the numbers on top of the horizontal line, from left to right.
Each time you cross a vertical line (above the horizontal line), press the "multiply" button.
- That would be: 65 times 5280 times 12 times 2.54
- We can disregard the number 1, since it does not change the result.
- Notice that the "equals" button has not been pressed.
After entering the last number on the right, drop below the horizontal line by pressing the "divide" button.
Now enter the numbers below the horizontal line from right to left.
Each time you cross a vertical line (below the horizontal line), press the "divide" button.
- That would be: divide by 100 divide by 60 divide by 60
- When you get to the end of the line, press "equals".
The number answer is now on your calculator.

You understand factor label when you can work these two practice problems.

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