Artem has a doctor of veterinary medicine degree.
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:
- The basic ingredients; what you're starting with
- The smoothie; what you want to end up with
- 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.
- What are our fruity ingredients? We're starting with 2,000 meters (m).
- What is our smoothie? We want to end up with kilometers (km).
- 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.
Just in case you were wondering, our original equation has a 1 underneath 2,000 meters. It's there for show only and has no bearing on the math here, as you probably already know, since x / 1 is always x. This lesson uses the 1 so you can clearly see the relationship among the numerators, denominators, and the units cancelling out. Once you get good at this, you won't need the 1. Think of it as a pair of training wheels on an adult bicycle.
Let's cook up some more smoothies to get our skills down pat! Convert 1.5 kilograms (kg) into grams (g), using the conversion factor of 1,000 grams per kilogram. Set up your kitchen! It should look like this when cooking:
(1.5 kg / 1) * (1,000 g / 1 kg) = g
Your answer should be 1,500 grams. Note the placement of the units again. The kilograms are on the opposite sides of the fraction bar. This way, the units of kilograms cancel out and we're left solely with units of grams when multiplying - the same units required in our answer.
Okay, how about this one? Convert 13,000 milliliters (mL) into liters (L). The conversion factor you can use is 1,000 milliliters per liter. Set up your equation like this:
(13,000 mL / 1) * (1 L / 1,000 mL) = L
With simple division, you'll get an answer of 13 liters.
When converting units in the metric system, you must always remember three things:
- What you're starting with
- What you need to get to
- The conversion factor, which helps you get from #1 to #2
Always remember to place the units of what you're starting with on the opposite side of the fraction line from those same units in the conversion factor so they can cancel out.
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