Metric System |

More Practice |

Let’s talk about learning the **metric system** (as opposed to the Imperial System that is used here in the United States) and why it is used all over the world! Note that the correct name for the metric system is actually the **International System of Units**, or **SI** (from **Système Internationale** d’Unités in French).

I must admit that I really don’t like working with the metric system. It could be because I never studied it as a kid (I don’t really remember — maybe I did!), but I always have to look it up for my students. They teach it to you since the metric system is still used a lot for engineering disciplines here in the United States and is used in almost every other country in the world! But, honestly, you won’t see a lot of it used throughout your years in high school math.

The metric system is used for many types of measurements, but we’re just going to look at length, weight, and volume. Later, we’ll work with temperatures and convert back and forth from our system to the metric system using a math formula.

The metric system actually makes a lot more sense than what we use, since it is based on using multiples of ten (how many fingers we have!) Think of it — why do we need **12** inches in a foot — we don’t have **12** toes on our feet?! Or why are there **16** ounces in a pound — who can count by **16**‘s? I seem to remember that we in the states have tried to convert a couple of times when I was a kid (in fact, in the 70’s some laws were passed to convert), but I guess it was just too overwhelming. Actually, the United States is one of the (or maybe the only) industrialized country that doesn’t use the metric system as its system of measurement!

I always like to teach the major units of the metric system with a King Henry mnemonic (a mnemonic is a way to use familiar words to remember something). The following table will help you with the different units used with the metric system. The **middle** column is the standard unit (main measurement), or the base unit. Note that the units beginning with “dec” have to do with tens or tenths, the units that start with “cent” or “hect” have to do with hundreds or hundredths, and the units that start with “milli” or “kilo” have to do with thousands or thousandths. These are Latin and Greek stems of words.

**Note**: Even though this table depicts how the metric system is taught in the states, when the system is used in the “real world”, there are three main units: the **meter** (m) for length, the **kilogram** (kg) (not the gram) for weight/mass, and **second(s)** for time. Note also that the units in between the thousand units (such as centi, and deca) are normally not used with SI units, whereas millimeters would be. Also, technically, not all metric units are SI units, even though they are used with SI units. For example, the liter, which is used to measure volume, is technically a non-SI unit.

As an example, from the table, **1** meter is the same as **10** decimeters which is the same as **100** centimeters, and so on. As another example, there are **1000** meters in a kilometer (since a meter is $ \displaystyle \frac{1}{{1000}}$ of a kilometer). If you get confused between “deca” and “deci” remember that a decathlon is a series of **10** events in sports.

You may have noticed tinier marks on the other side of your ruler with letters “cm” next to them; the tiny marks are millimeters, which are $ \displaystyle \frac{1}{{1000}}$ of a meter, and **10** of these make up a centimeter. An inch is about **25.4** millimeters, or about **2.54** centimeters.

In comparison to “our” measurements, one meter is about the same as a yard; two meters might be your (tall) father’s height. A centimeter is about $ \displaystyle \frac{1}{2}$ inch, and a millimeter is about the thickness of a dime. A liter is about the same as a quart and there are about **5** milliliters in a teaspoon. A gram weighs very little — about the mass of a paper clip. A kilogram is about **2** pounds — about the weight of your purse full of a lot of stuff.

**Note**: We learned how to use **proportions** to go back and forth between the metric system and customary measurements **here** in the **Percentages, Ratios, and Proportions** section. We also work with **Unit Multipliers** in that section, which is sometimes called **Dimensional Analysis**.

Let’s do some problems that you might have with converting between two metric measurements**. You should understand these concepts**; if we are going from bigger to smaller units, we need more of the smaller units, and if we are going from smaller to bigger units, we need fewer of the bigger units:

**Understand how to do these conversions! ** A couple of more things about the metric system:

- There are free conversion programs on the web where you can type in the number of inches, for example, and get the number of centimeters, millimeters, and so on.
- If you sew, you may notice a lot of metric measurements, since patterns are usually universal.
- You may also notice that when you grocery shop, you see both the “American” and metric measurements on the labels.
- It’s fun to look at other countries’ signs or newspapers to see the metric system in use! You’ve probably heard about km/hour with regard to driving in Europe, for example.

**Learn these rules and practice, practice, practice!**

Click on Submit (the arrow to the right of the problem) to solve this problem. You can also type in more problems, or click on the 3 dots in the upper right hand corner to drill down for example problems. If you click on “Tap to view steps”, you will go to the **Mathway** site, where you can register for the **full version** (steps included) of the software. You can even get math worksheets. You can also go to the **Mathway** site here, where you can register, or just use the software for free without the detailed solutions. There is even a Mathway App for your mobile device. Enjoy!

On to **Pre-Algebra: Percentages, Ratios, and Proportions **– you are ready!!