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Private: Learning Math: Measurement
The Metric System Part A: Metric System Basics (35 minutes)
Session 3, Part A
In This Part
- History
- Units and Prefixes
- Working With Metric Prefixes
History
The metric system was introduced in France in the 1790s as a single, universally accepted system of measurement. But it wasn’t until 1875 that the multinational Treaty of the Meter was signed (by the United States and other countries), creating two groups: the International Bureau of Weights and Measures and the international General Conference on Weights and Measures. The purpose of these groups was to supervise the use of the metric system in accordance with the latest pertinent scientific developments.
Since then, the Bureau and Conference have recommended improvements in terms of the accuracy and reproducibility of metric units. In fact, by 1960, improvements were so great that a “new” metric system, called the International System of Units (abbreviated SI), was created. The metric system we use today is actually SI. Although there are some discrepancies between the two systems, these differences are slight from a nonscientific perspective; therefore, we will refer to SI as “the metric system.”
Let’s begin by reviewing the metric system. Note 3
Problem A1
Make a list of some of the facts, relationships, and symbols you recall about the metric system.
Problem A2
Why do you think most countries use the metric system?
Units and Prefixes
One of the strengths of the metric system is that it has only one unit for each type of measurement. Other units are defined as simple products or quotients of these base units.
For example, the base unit for length (or distance) is the meter (m). Other units for length are described in terms of their relationship to a meter: A kilometer (km) is 1,000 m; a centimeter (cm) is 0.01 of a meter; and a millimeter (mm) is 0.001 of a meter.
Prefixes in the metric system are short names or letter symbols for numbers that are attached to the front of the base unit as a multiplying factor. A unit with a prefix attached is called a multiple of the unit — it is not a separate unit. For example, just as you would not consider 1,000 in. a different unit from inches, a kilometer, which means 1,000 m, is not a different unit from meters.
Use the chart below to explore some common units and prefixes in the metric system. Pay attention to the patterns that emerge as you look at the different prefixes.
Working With Metric Prefixes
Here is a detailed table of some metric prefixes: Note 4
| Prefixes and Their Equivalents | ||||||||||
|
Symbol |
Prefix |
Factor |
Ordinary Notation |
U.S. Name |
European Name |
|||||
| T | tera | 1012 | 1,000,000,000,000 | trillion | billion | |||||
| G | giga | 109 | 1,000,000,000 | billion | milliard | |||||
| M | mega | 106 | 1,000,000 | million | ||||||
| k | kilo | 103 | 1,000 | thousand | ||||||
| h | hecto | 102 | 100 | hundred | ||||||
| da | deka | 101 | 10 | ten | ||||||
| 100 | 1 | one | ||||||||
| d | deci | 10-1 | 0.1 | tenth | ||||||
| c | centi | 10-2 | 0.01 | hundredth | ||||||
| m | milli | 10-3 | 0.001 | thousandth | ||||||
| µ | micro | 10-6 | 0.000 001 | millionth | ||||||
| n | nano | 10-9 | 0.000 000 001 | billionth | thousand millionth | |||||
| p | pico | 10-12 | 0.000 000 000 001 | trillionth | billionth | |||||
Problem A3
- What patterns do you notice in this table?
- Some of these prefixes are more commonly used than others, particularly when the base unit is a meter. Which prefixes are you most familiar with?
- How can a centimeter, a millimeter, a kilometer, and a micrometer be expressed in terms of a meter?
- A kilometer is 1,000 m, but we can also state that it is 1,000,000 mm. Explain how these relationships work.
- Try expressing the following quantities in at least two different ways: centimeter, millimeter, and decimeter.
Problem A4
You have probably noticed that the metric system never uses fractions. Instead, fractional quantities are recorded using decimals. Why do you think this is the case?
Think about the nature of the base ten system and how you can easily divide by powers of 10. Since the relationship between prefixes is based on powers of 10, we can switch prefixes easily by simply moving a decimal point.
Problem A5
- If you want to change 3,600 m to kilometers, what do you do? Explain.
- If you want to change 0.028 m to millimeters, what do you do?
- If you want to change 4,600,000 mm to kilometers, what do you do?
Take It Further
Problem A6
The Sun is 150 gigameters (Gm) from the Earth. The Moon is 384 megameters (Mm) from the Earth. How many times farther from the Earth is the Sun than the Moon?
Notes
Note 3
This session focuses only on the metric system, but you may also want to use this session to review what you know about the customary system. The concept of a coherent system may be confusing. If the customary system were coherent (which it is not), then there would be a single base unit for length; area and volume would also be based on this unit. For example, if the inch were the base unit, then we would measure area in square inches (not in acres or square yards) and volume in cubic inches (not in pints or cubic feet). In a coherent system, units can be manipulated with simple algebra rather than by remembering complex conversion factors.
Note 4
If you are working in a group that isn’t very familiar with the metric system, you can take this opportunity to practice expressing quantities in more than one way. For example, working in pairs or as a class, participants can make up questions for one another to answer and/or quantities to express using different prefixes. Refer to Problems A3-A5 for guidance.
Solutions
Problem A1
Answers will vary. Some of the common measurements are the meter, the liter, and the gram. Most people associate the number 10 with the metric system, since relationships in this system are determined by powers of 10.
Problem A2
Most countries use the metric system because it is an international standard; it makes it easy for different countries to talk about the same units of length or mass. The metric system is also designed for easy calculation.
Problem A3
- There are many patterns in the table that you may want to discuss. First, the metric system uses prefixes in front of a unit name as a multiplying factor. Most prefixes multiply or divide units in steps of 1,000 as you go up and down the table.
- The more commonly used prefixes are those from 10-3 to 103. These units are commonly used when measuring areas, volumes, and lengths. Throughout this session, you should focus on gaining familiarity with those particular prefixes.
- A centimeter is a 100th of a meter (1 m = 100 cm). A millimeter is a 1,000th of a meter (1 m = 1,000 mm). A kilometer is 1,000 m (1,000 m = 1 km). A micrometer is a millionth of a meter (1 m = 1,000 000 μm).
- These measurements are related because they are all built on powers of 10, with the meter as the base unit. The prefix tells you how many meters (or how much of a meter) you’re talking about.
- A centimeter could be 10 mm or 0.01 m. A millimeter could be 0.1 cm or 0.001 m. A decimeter could be 10 cm, 100 mm, 0.1 m. Other answers are also possible!
Problem A4
One primary reason is that a number written in metric units can easily be converted by multiplying or dividing by powers of 10, since this type of multiplication is done by moving the decimal point. For example, 2.54 cm is equivalent to 25.4 mm and 0.0254 m. Each of these conversions is done by knowing the power of 10 associated with the conversion and moving the decimal point by that many places.
Problem A5
- As 1,000 m is 1 km, 3,600 m is 3.6 km. We simply moved the decimal point three places to the left.
- Since 0.001 m is 1 mm, 0.028 m is 28 mm. Again, we just moved the decimal point three places to the right.
- One way is to convert the millimeters to meters and then to kilometers: 1,000 mm equals 1 m, so 4,600,000 mm equals 4,600 m. Similarly, 1,000 m equals 1 km, so 4,600 m equals 4.6 km (i.e., we moved the decimal point six places to the left).
Problem A6
To make a fair comparison, we must first convert gigameters to megameters (or vice versa). Since 1 Gm = 1,000 Mm, the Sun’s distance from the Earth is 150 • 1,000, or 150,000 Mm. The ratio is now 150,000:384, or about 390 times farther away.
