Converting Units

Contributor: Marlene Vogel. Lesson ID: 10795

Quick! How many seconds old are you? You can probably answer for years, but seconds takes some conversion work! Take an online quiz and design a fort to learn about converting units!


Pre-Algebra, Ratios, Rates, Percentages, and Proportions

learning style
personality style
Lion, Otter
Grade Level
Middle School (6-8)
Lesson Type
Dig Deeper

Lesson Plan - Get It!

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How Old Are You?

  1. What is your age in years? In days? In hours?
  2. Find your age in seconds.
  3. How many years equal one million seconds? One billion seconds?
  4. Is your age closer to a million seconds or a billion seconds? Explain.

You can complete this activity after the lesson and then check your answers with the How Old Are You? Answer Key found in the Downloadable Resources in the right-hand sidebar.

Do you like to cook or bake?

Have you ever had a situation where you could not find the correct measuring cup or spoon? Did you use another one instead? Did you have a hard time trying to figure out how much of the ingredient you needed to add to the recipe when using the wrong measuring utensil?

This is just one situation in life where you would need to convert units in order to complete a task. Situations like this happen often in life, and you need to be able to quickly and comfortably convert from one unit to another in order to complete a task.

Before moving on, if you missed, or would like to review, the first Related Lesson in our Dimensional Analysis series, find it in the right-hand sidebar.

Usually when you are asked to convert units, you are asked to convert from one unit to a different unit. The example above portrays a situation where you are converting from one size to another in the same unit (cup to cup or teaspoon to teaspoon).

This lesson will show you how to convert from one unit to another unit (e.g., days to seconds).

What is a Conversion Factor?

When you are converting from one unit to another you need to use a conversion factor. A conversion factor is a ratio that will help you change the information you have from the current unit to another unit.

An important point to note is that the conversion factor is equal to 1.

To better understand this point, assume that you are going to convert from hours to minutes. The conversion factor that you would use would be the ratio 1 hour/60 minutes.

As you can see, the fraction is equal to 1 because 1 hour is the same as 60 minutes.

Conversion Factor Problem

Below is an example problem that will help you see this concept in action, as well as help you understand how to convert from one unit to another unit:

The reticulating python is the world's longest snake. Many of these pythons are more than 20 feet long. Convert 20 feet to inches.

  • This is a typical conversion problem. Notice how you are given the information in one unit (feet) and asked to convert it to another unit (inches).
  • The first step is to make sure you understand what the problem says — and is asking you to find — by making a list of the important information:

- Reticulating pythons can be 20 feet long
- Convert 20 feet to inches

  • Your next step is to figure out what conversion factor you are going to use. Hint: the problem gives it to you.


  • Now, set up your problem. To set up your problem you need to compare your conversion factor to the information found in the problem. For your conversion factor, your fraction will look like the one below.
  1 foot
  12 inches


  • Your information from the problem needs to be put in fraction form as well. Put the information the problem gives you in the numerator and the letter x in the denominator. The letter "x" represents the number that you do not know at the moment or the answer to the problem. See below:
  20 feet


  • Now, put the whole problem together. See below:
  1 foot = 20 feet
  12 inches x


  • Now, cross multiply. You will cross multiply the numerator from one fraction with the denominator from the other fraction. At this point, don’t worry about the units, just cross multiply the numbers.
  • Your problem will now look like the one below:
  1x = 12 x 20


  • Multiply 12 and 20 to get 240:
  1x = 240


You now have your answer! The unit for 240 is inches. You know this because that is what the problem is asking you to find. You can now say with certainty that 20 feet equals 240 inches.

  • Go back to the problem at the beginning of the lesson (How Old Are You) and complete it. Hint: You are being asked to convert to several different units in that problem. Focus on one unit at a time and you will be able to answer all of the questions correctly!

The next section offers activities that will help you practice your new skill of converting units.

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