# Metric System

This section covers:

Let’s talk about learning the metric system 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!

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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.

KING HENRY DIED DRINKING CHOCOLATE MILK

 Mnemonic: King Henry Died Base Unit Drinking Chocolate Milk Length: Abbreviation: Kilogram* km Hectometer hm Decameter dam Meter m Decimeter dm Centimeter cm Millimeter mm Weight: Abbreviation: Kilogram kg Hectogram hg Decagram dag Gram g Decigram dg Centigram cg Milligram mg Volume: Abbreviation: Kiloliter kL Hectoliter hL Decaliter daL Liter L Deciliter dL Centiliter cL Milliliter mL Example: How many are in 1 meter/gram/liter? .001 .01 .1 1 10 100 1000 Example: How many meters/grams/liters are in this unit? 1000 100 10 1 .1 .01 .001 $$\Leftarrow$$          BIGGER SMALLER         $$\Rightarrow$$

*In the “real world”, the kilogram is a base unit.

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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), the kilogram (kg) (not the gram), and second (s). 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.

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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.

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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:

 Problem/Solution Explanation 1 liter = ______milliliters   1000 Liters are bigger than milliliters so we need more than 1 milliliter. Since there is only 1 liter, we need 1000 milliliters (add three zeroes and move decimal three places to the right). 1000 milligrams = ______grams   1 Milligrams are smaller than grams, so we need fewer than 1000 grams. Since there are 1000 milligrams in a gram, we just need 1 gram (move decimal three places to the left). 166 centimeters = ______millimeters   1660 Centimeters are bigger than millimeters, so we need more than 166 millimeters. Since there are 10 millimeters in a centimeter, we need 10 times 166 = 1660 millimeters (add zero and move decimal one place to the right). 13 grams = ______kilograms   .013 Grams are smaller than kilograms, so we need fewer than 13 kilograms. Since there are 1000 grams in a kilogram, we need one-thousandth of 13, or .013 kilograms (move decimal three places to the left). 1000 meters = ______centimeters   100,000 Meters are larger than centimeters, so we need more than 1000 centimeters. Since there are 100 centimeters in a meter, we need 100 times 1000, or 100,000 centimeters (add zeros and move decimal two places to the right).

Understand how to do these conversions! We will also learn how to set these up as proportions, when we get to that section.

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!!

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