# How to Convert Units in the Metric System

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• 0:00 The Metric System
• 0:34 How to Set Up the Conversion
• 1:45 How to Calculate
• 5:33 Lesson Summary

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Lesson Transcript
Instructor: Artem Cheprasov
If you can make dinner, you can convert units in the metric system. It's that easy! In this lesson, you'll learn about the three key things you'll need to perform conversions.

## The Metric System

When making a smoothie, your first step is to assemble some fruits. You then convert them into a smoothie using an appliance, like a blender. In addition to how great that smoothie will taste, you know what you're starting with (or the basic ingredients you need to make the smoothie), what you want to end up with (or the final smoothie product), and what you need to get there (or the methods for producing the smoothie). We're going to apply a very similar three-pronged approach to converting units in the metric system in this lesson.

## How to Set Up the Conversion

So, how do we convert units in the metric system? It's actually very easy. Here's what you need to know for every single metric system conversion you'll ever perform:

1. The basic ingredients; what you're starting with
2. The smoothie; what you want to end up with
3. The blender; what you need to get there

We'll call this blender a conversion factor in the problems to come, since it helps us convert the ingredients into the final product. This conversion factor is a key part of the process. We can't get a smoothie without a blender or some other appliance, right? So where are you going to get your conversion factor? In this lesson, we'll provide you with one. When working on other conversion problems, you may need find one online or in a textbook. Understanding the relationship between a metric unit's name and its value can also serve as your conversion factor. For instance, anything that begins with 'kilo-,' like kilometer, is 1,000 of that unit (1,000 meters). But this lesson isn't about what the metric units are or how they're signified. It's about converting from one metric unit to another, so we'll assume you know this already.

## How to Calculate

So, let's start making some smoothies! Here's a sample problem: convert 2,000 meters into kilometers.

1. What are our fruity ingredients? We're starting with 2,000 meters (m).
2. What is our smoothie? We want to end up with kilometers (km).
3. What is our blender? The conversion factor is 1,000 meters per 1 kilometer.

This is the same thing as saying 1 kilometer / 1,000 meters. In other words, there's 1 kilometer in 1,000 meters. Both statements mean exactly the same thing. This nuance is very important for you to remember; otherwise, you won't set up your problem correctly. In our kitchen, we're always going to cook from left to right, just like we read a book. When setting up our equation, we'll always put the fruity ingredients first, followed by the blender and then, after the equals sign, the finished product, the smoothie. Our equation should look like this:

(2,000 m / 1) * (1 km / 1,000 m) = km

Please make a note of something very important. When you multiply the ingredients by the conversion factor, the units of the ingredients must always be on the opposite side of the fraction bar in order to cancel out. That is to say, if our ingredients are the numerator, as they are in this case, the conversion factor's similar units, meters in this case, must be placed in the denominator. If the equation looks like this: (2,000 m / 1) * (1,000 m / 1 km) = km, also add the number 1 to the denominator so it will match the preceding equation. Then the units we're trying to cancel out (meters) are both on the numerator side of the fraction bar, which is incorrect.

So, let's get back to our first and, thus, correct equation. Because the units of meters are on opposite sides of the fraction bar, they cancel out. This leaves us solely with units of kilometers and, what a surprise, these are exactly the units of our smoothie and, thus, exactly what we need. We now have a simple division problem where we divide 2,000 by 1,000, which gives us an answer of 2. Thus, our smoothie is 2 kilometers.

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